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Dispersal, landscape and travelling waves in cyclic vole populations
Abstract
Travelling waves (TW) are among the most striking ecological phenomena emerging in oscillating populations. Despite much theory, understanding how real-world TW arise remains a challenge for ecology. Herein, we analyse 16-year time series of cyclic vole populations collected at 314 localities covering 2500 km² in France. We found evidence for a linear front TW spreading at a speed of 7.4 km year(-1) along a north-west/south-east direction and radiating away from a major landscape discontinuity as predicted by recent theory. The spatial signature of vole dispersal was assessed using genetic data collected at 14 localities. Both data sets were handled using similar autocorrelation approaches. Our results revealed a remarkable congruence of the spatial extent and direction of anisotropy of both demographic and genetic structures. Our results constitute the first empirical evidence that effective dispersal is limited in the direction of TW while most of the individual exchanges occur along the wave front.
... 2005; Somoano et al. 2017), las enfermedades (Vidal et al. 2009; Barraquand et al. 2014), los cambios en el paisaje (Berthier et al. 2013(Berthier et al. , 2014 y uso del suelo (Truchetet et al. 2014;Jareño et al. 2015) o la disponibilidad de alimento (Barraquand et al. 2014), que están muy interrelacionados entre sí, lo que dificulta notablemente la determinación del papel de cada uno de estos factores por separado (Saucy 1994; Barraquand et al. 2014;Truchetet et al. 2014;Giraudoux et al. 2019). ...
... Además de la variación estacional, han podido registrarse grandes cambios de abundancia entre años, siendo patente la existencia de temporadas de alta densidad o "picos de abundancia" y temporadas de baja densidad. El tiempo transcurrido entre dos picos ha sido de 4 años (primaveras de 2016 y de 2020), cifra comparable a la descrita en los ciclos del Jura y el macizo central en Francia (Saucy 1994;Giradoux et al. 1997;Berthier et al. 2013Berthier et al. , 2014. En nuestro caso, el número de años monitorizado no es lo suficientemente amplio como para poder hablar de ciclos, pero estos primeros datos inducen a pensar que la población de rata topera del Pirineo podría seguir, tal vez, un patrón similar al de las poblaciones más norteñas que presentan fluctuaciones interanuales más o menos regulares. ...
... La mayoría de los trabajos previos realizados en el Norte de Europa coinciden en la gran importancia de la estructura del paisaje y el manejo agrícola en las variaciones de abundancia de la rata topera (Giradoux et al. 1995(Giradoux et al. , 1997Duhamel et al. 2000;Fichet-Calvet et al. 2000;Morilhat et al. 2007Morilhat et al. , 2008Berthier et al. 2013Berthier et al. , 2014. Todos ellos concluyen que los ambientes simplificados con predominio de praderas intensivas sujetas a escaso laboreo y con alto grado de abonado junto con la escasa presencia de setos o bosque favorecen el incremento y expansión de este roedor. ...
La rata topera (Arvicola scherman) es una especie de gran interés, tanto por su papel como presa de multitud de depredadores, como por el impacto de sus daños sobre la agricultura. Las variaciones en su abundancia poblacional y el papel de los factores que la modulan han sido ampliamente estudiadas en el norte de Europa, pero hasta el momento, se carecía de esta información para las poblaciones del Pirineo. En el presente trabajo se exponen los resultados obtenidos en el plan de monitorización de la especie en Navarra desde 2016 hasta 2020, describiendo tanto los cambios de abundancia registrados, como la influencia de los factores ambientales y de gestión agroganadera analizados. Describimos una variación de la abundancia a lo largo del año, con valores significativamente mayores en primavera que en verano; y entre los 5 años de muestreo, con una abundancia significativamente mayor en 2016 y 2020. La pluviometría acumulada en los meses previos al censo y el pastoreo con ovejas han sido los factores retenidos en los modelos con influencia significativa. Ambos han ejercido un efecto positivo sobre la rata topera, aumentando su abundancia al incrementarse la pluviometría y con el aprovechamiento con ganado ovino. Se discute el papel de estos factores y otras variables de estructura del paisaje y de gestión agrícola en los cambios de abundancia poblacional de la rata topera.
... anisotropic, henceforth termed planar wave, e.g. Berthier et al., 2014;Bjørnstad et al., 2002;Lambin et al., 1998) or in all directions (i.e. isotropic; henceforth termed radial wave, e.g. ...
... Empirical research projects, which by their nature occur in heterogenous environments, have often used planar wave parameterisations to describe the observed travelling waves in cyclic populations (Berthier et al., 2014;Lambin et al., 1998). Such a mismatch between the predicted (i.e. ...
... Thus, true planar waves may arise due to approximately linear physical features in the landscape. Building on Sherratt and Smith's (2008) work, which suggested physical features may generate travelling waves, Berthier et al. (2014) invoked quasi-linear physical features in their landscape as potentially responsible for planar waves in cyclic water vole populations. However, because of the necessary theoretical assumptions for how physical features interact with organisms (resulting in boundary conditions that are hard to quantify empirically), Berthier et al. (2014) could not ascertain which plausible features were responsible. ...
The dynamics of cyclic populations distributed in space result from the relative strength of synchronising influences and the limited dispersal of destabilising factors (activators and inhibitors), known to cause multi‐annual population cycles. However, while each of these have been well studied in isolation, there is limited empirical evidence of how the processes of synchronisation and activation–inhibition act together, largely owing to the scarcity of datasets with sufficient spatial and temporal scale and resolution. We assessed a variety of models that could be underlying the spatio‐temporal pattern, designed to capture both theoretical and empirical understandings of travelling waves using large‐scale (>35,000 km²), multi‐year (2011–2017) field monitoring data on abundances of common vole (Microtus arvalis), a cyclic agricultural rodent pest. We found most support for a pattern formed from the summation of two radial travelling waves with contrasting speeds that together describe population growth rates across the region.
... Landscape characteristics are a key factor in the population dynamics of most animal species [1][2][3]. Their relative influence on population connectivity not only depends on patch configuration, but also on behavioural patterns related to the response of individuals to a given landscape [4,5]. Thus, the distribution of each species will be influenced by dispersal capability, resource availability, and the abiotic environment [2,6]. ...
... This subterranean species lives throughout mountainous areas, where landscapes are now mainly characterised by pasture predominance and forest scarcity or absence [37]. Spatial demographic and genetic structural analyses of fossorial water voles have shown that there is often unimpeded dispersal and hence merged and synchronised populations in these homogeneous landscapes [4,18,38]. Consequently, the multiannual fluctuations in the density and the outbreaks of this species may occur at the regional scale [4,32]. ...
... Spatial demographic and genetic structural analyses of fossorial water voles have shown that there is often unimpeded dispersal and hence merged and synchronised populations in these homogeneous landscapes [4,18,38]. Consequently, the multiannual fluctuations in the density and the outbreaks of this species may occur at the regional scale [4,32]. ...
The population dynamics of most animal species inhabiting agro-ecosystems may be determined by landscape characteristics, with agricultural intensification and the reduction of natural habitats influencing dispersal and hence limiting gene flow. Increasing landscape complexity would thus benefit many endangered species by providing different ecological niches, but it could also lead to undesired effects in species that can act as crop pests and disease reservoirs. We tested the hypothesis that a highly variegated landscape influences patterns of genetic structure in agricultural pest voles. Ten populations of fossorial water vole, Arvicola scherman, located in a bocage landscape in Atlantic NW Spain were studied using DNA microsatellite markers and a graph-based model. The results showed a strong isolation-by-distance pattern with a significant genetic correlation at smaller geographic scales, while genetic differentiation at larger geographic scales indicated a hierarchical pattern of up to eight genetic clusters. A metapopulation-type structure was observed, immersed in a landscape with a low proportion of suitable habitats. Matrix scale rather than matrix heterogeneity per se may have an important effect upon gene flow, acting as a demographic sink. The identification of sub-populations, considered to be independent management units, allows the establishment of feasible population control efforts in this area. These insights support the use of agro-ecological tools aimed at recreating enclosed field systems when planning integrated managements for controlling patch-dependent species such as grassland voles.
... 2005; Somoano et al. 2017), las enfermedades (Vidal et al. 2009; Barraquand et al. 2014), los cambios en el paisaje (Berthier et al. 2013(Berthier et al. , 2014 y uso del suelo (Truchetet et al. 2014;Jareño et al. 2015) o la disponibilidad de alimento (Barraquand et al. 2014), que están muy interrelacionados entre sí, lo que dificulta notablemente la determinación del papel de cada uno de estos factores por separado (Saucy 1994; Barraquand et al. 2014;Truchetet et al. 2014;Giraudoux et al. 2019). ...
... Además de la variación estacional, han podido registrarse grandes cambios de abundancia entre años, siendo patente la existencia de temporadas de alta densidad o "picos de abundancia" y temporadas de baja densidad. El tiempo transcurrido entre dos picos ha sido de 4 años (primaveras de 2016 y de 2020), cifra comparable a la descrita en los ciclos del Jura y el macizo central en Francia (Saucy 1994;Giradoux et al. 1997;Berthier et al. 2013Berthier et al. , 2014. En nuestro caso, el número de años monitorizado no es lo suficientemente amplio como para poder hablar de ciclos, pero estos primeros datos inducen a pensar que la población de rata topera del Pirineo podría seguir, tal vez, un patrón similar al de las poblaciones más norteñas que presentan fluctuaciones interanuales más o menos regulares. ...
... La mayoría de los trabajos previos realizados en el Norte de Europa coinciden en la gran importancia de la estructura del paisaje y el manejo agrícola en las variaciones de abundancia de la rata topera (Giradoux et al. 1995(Giradoux et al. , 1997Duhamel et al. 2000;Fichet-Calvet et al. 2000;Morilhat et al. 2007Morilhat et al. , 2008Berthier et al. 2013Berthier et al. , 2014. Todos ellos concluyen que los ambientes simplificados con predominio de praderas intensivas sujetas a escaso laboreo y con alto grado de abonado junto con la escasa presencia de setos o bosque favorecen el incremento y expansión de este roedor. ...
Resumen: La rata topera (Arvicola scherman) es una especie de gran interés, tanto por su papel como presa de multitud de depredadores, como
por el impacto de sus daños sobre la agricultura. Las variaciones en su abundancia poblacional y el papel de los factores que la modulan han sido
ampliamente estudiadas en el norte de Europa, pero hasta el momento, se carecía de esta información para las poblaciones del Pirineo. En el presente
trabajo se exponen los resultados obtenidos en el plan de monitorización de la especie en Navarra desde 2016 hasta 2020, describiendo
tanto los cambios de abundancia registrados, como la influencia de los factores ambientales y de gestión agroganadera analizados. Describimos
una variación de la abundancia a lo largo del año, con valores significativamente mayores en primavera que en verano; y entre los 5 años de muestreo,
con una abundancia significativamente mayor en 2016 y 2020. La pluviometría acumulada en los meses previos al censo y el pastoreo con
ovejas han sido los factores retenidos en los modelos con influencia significativa. Ambos han ejercido un efecto positivo sobre la rata topera, aumentando
su abundancia al incrementarse la pluviometría y con el aprovechamiento con ganado ovino. Se discute el papel de estos factores y otras
variables de estructura del paisaje y de gestión agrícola en los cambios de abundancia poblacional de la rata topera.
Abstract: The Fossorial Water Vole (Arvicola scherman) is a species of great interest, both because of its role as prey for a wide variety of predators,
and the damages on agriculture. The variation in its population abundance and the factors that modulate it have been widely studied in northern Europe,
but they are rather unknown for Pyrenean populations. Here we show the results obtained in the monitoring plan for the species in Navarra
from 2016 to 2020, describing both the inter- and intra-annual changes in population abundance, as well as the effect of environmental factors and
agricultural management. We found intra-annual variation in its abundance, with significantly higher values in spring than in summer. Interannually,
there was a significantly higher abundance both in 2016 and 2020. The accumulated rainfall in the three months prior to sampling and grazing with
sheep were the two most important factors that explain variation in population abundance. Both factors had a positive effect on the Fossorial Water
Vole, so that its abundance increased with wetter months before sampling and in areas where sheep were present. The role of these factors and
other variables of landscape and agricultural management in the changes of abundance of this rodent are also discussed.
... From 1989, Patrick Giraudoux and collaborators monitored these vole populations in the Alps (Massif des Ecrins) and in eastern France, in particular within the framework of the Zone Atelier Arc Jurassien and the Zone Atelier Alpes, see in [21,4,23]. Direct observations, realized in different countries and ecosystems, show that density variations of voles are due to multiple driving factors: climate, topography, the proportion between farmland and forest, different kinds of predators, and so on (see [17] and references therein). In more detail, as described in the papers [21,23,41,29], voles are herbivores rodents, who dig underground tunnels where they breed and stay most of the time. ...
... Land-use patterns were studied based on agriculture and forestry data from the French Ministry of Agriculture, collected over several years. In [4] they provide empirical evidence showing that the wave-like profile detected for the vole population, adds to the list of empirical examples supporting the theory that periodic Travelling Wave solutions do occur in natural populations undergoing multi-year cycles. ...
... This model is introduced and analyzed in the published paper [9], in collaboration with my supervisors Giuseppe M. Coclite and Carlotta Donadello. Recently, there have been two different approaches to consider the spatial population of voles, introduced by Berthier in [4], and Giraudoux et al in [29]. They are the first endeavors in understanding the spatial dimension of the vole population dynamics. ...
The main objective of the thesis is to propose and analyze mathematical models based on partial differential equations (PDE) to describe the spatial dynamics of two species of voles (Microtus arvalis and Arvicola terrestris), which are particularly monitored in Eastern France. The models that we have proposed are based on PDE which describe the evolution of the density of the population of voles as a function of time, age and position in space. We have two complementary approaches to represent the dynamics. In the first approach, we propose a first model that consists of a scalar PDE depending on time, age, and space supplemented with a non-local boundary condition. The flux is linear with constant coefficient in the direction of age but contains a non-local term in the directions of space. Moreover, the equation contains a second order term in the spatial variables only. We have demonstrated the existence and stability of weak entropy solutions for the model by using, respectively, the Panov's theorem of the multidimensional compensated and a doubling of the variables type argument. In the second approach we were inspired by a Multi Agent model proposed by Marilleau-Lang-Giraudoux, where the spatial dynamics of juveniles is decoupled from local evolution in each plot. To apply this model, we have introduced a directed graph whose nodes are the plots. In each node, the evolution of the colony is described by a transport equation with two variables, time and age, and the movements of dispersion, in space, are represented by the passages from one node to the other. We have proposed a discretization of the model, by finite volume methods, and noticed that this approach manages to reproduce the qualitative characteristics of the spatial dynamics observed in nature. We also proposed to consider a predator-prey system consisting of a hyperbolic equation for predators and a parabolic-hyperbolic equation for preys, where the prey's equation is analogous to the first model of the vole populations. The drift term in the predators' equation depends nonlocally on the density of prey and the two equations are also coupled via classical source terms of Lotka-Volterra type. We establish existence of solutions by applying the vanishing viscosity method, and we prove stability by a doubling of variables type argument. Moreover, concerning the numerical simulation of the first model in one-dimensional space, we obtain a finite volume discretization by using the upwind scheme and then validate the numerical scheme.The last part of my thesis work is a project in which I participated during a Summer school CEMRACS. The project was on a subject of biomathematics different from that of the thesis (an epidemiological model for salmonellosis). A new generic multi-scale modeling framework for heterogeneous transmission of pathogens in an animal population is suggested. At the intra-host level, the model describes the interaction between the commensal microbiota, the pathogen and the inflammatory response. Random fluctuations in the ecological dynamics of the individual microbiota and transmission at the inter-host scale are added to obtain a PDE model of drift-diffusion of pathogen distribution at the population level. The model is also extended to represent transmission between several populations. Asymptotic behavior as well as the impact of control strategies, including cleaning and administration of antimicrobials, are studied by numerical simulation.
... However, elsewhere in Europe water voles are also found in dry grassland habitats and are regarded as fossorial. Water voles found in dry grassland favour upland meadows and can be found at high population densities in mountain regions (Berthier et al., 2014). Distribution is not limited by water features and burrow systems can exceed 100 m in length in a complex array of runs, nest chambers, food stores and bolt holes and will usually house a single breeding unit, a male and female, with their offspring (Meylan, 1977). ...
... Various techniques have been used previously in order to estimate the abundance of water vole populations, including surveying for field signs (Telfer et al., 2001;Berthier et al., 2014), and by capture-mark-recapture (CMR) studies (Telfer et al., 2003), although most population estimations have been undertaken in riparian habitats. Previous work in Glasgow included field sign surveys, but no significant relationship was found between the abundance of field signs and water vole density (Stewart et al., 2017; see the Appendix for a guide to identifying field signs). ...
... Water vole abundance varies seasonally and across years and from previous studies in the UK densities of 40 to 50 animals ha -1 have been recorded in reed beds (Strachan & Moorhouse, 2006), while the fossorial populations of Scottish Islands had an average density of 26 ha -1 , increasing to 70 ha -1 in Spring (Telfer et al., 2003) which indicates that the water vole density found at Cranhill Park appears to be one of the highest recorded in the UK. In continental Europe fossorial populations oscillate with a four to eight year cycle and in peak years water vole numbers can reach "outbreak" densities of 1,000 ha -1 (Meylan, 1977;Giraudoux et al., 1995;Weber et al., 2002;Berthier et al., 2014). A mean population density of 476 ha -1 (range 80-900 ha -1 ) has been reported for fossorial water voles in Jura Mountains of Switzerland (Weber & Aubrey, 1993). ...
Water vole (Arvicola amphibius) populations have undergone a serious decline throughout the UK, and yet a stronghold of these small mammals is found in the greater Easterhouse area of Glasgow. The water voles in this location are mostly fossorial, living a largely subterranean existence in grasslands, rather than the more typical semi-aquatic lifestyle in riparian habitats. In this study, we carried out capture-mark-recapture surveys on water voles at two sites: Cranhill Park and Tillycairn Drive. We made a total of 62 captures including retraps, and the resulting population estimates were 78 individuals (95% confidence interval 41-197) for Cranhill Park and 42 individuals (20-141) for Tillycairn Drive. From these figures we estimated a population density of water voles, which appeared to be higher than other reports from the UK. Despite the difficulties of sampling in urban environments that resulted in relatively low capture rates, our data suggest that the greater Easterhouse area of Glasgow holds water voles at relatively high population densities. These results will inform future conservation in the City of Glasgow and surrounding areas, as well as raise awareness of important water vole populations in urban environments.
... Il est aujourd'hui établi que ces vagues sont plus qu'une curiosité mathématique issue des modèles théoriques. Elles ont ainsi été décrites pour des populations cycliques de rongeurs, d'oiseaux, d'insectes ainsi que pour les pathogènes responsables, chez l'homme, de la dengue et de la rougeole (GIRAUDOUX et al., 1997 ;LAM-BIN et al., 1998 ;MOSS et al., 2000 ;MCKINNON et al., 2001 ;GRENFELL et al., 2001 ;BJØRNSTAD et al., 2002 ;JOHNSON et al., 2004 ;CUMMINGS et al., 2004 ;TENOW et al., 2013 ;BERTHIER et al., 2014). La particularité de ces vagues d'abondance est d'émerger en l'absence de propagation nette des individus impliqués dans la dynamique cyclique. ...
... Dans le massif du Jura, en France et en Suisse, la dynamique cyclique des populations de campagnols terrestres est caractérisée par une période de 5 à 8 ans (SAUCY, 1994 ;GIRAUDOUX et al., 1997 ;BERTHIER et al., 2014). Au cours d'un cycle, les densités des populations peuvent varier de moins d'un individu à l'hectare, en phase de faible densité, à plus de 500 individus à l'hectare lors des pics de pullulations. ...
... Ces estimations semi-quantitatives distinguent trois classes d'abondance : 0 : pas de colonies de campagnols dans les prairies, 1 : quelques colonies isolées, 2 : des colonies présentes dans la plupart des prairies sur le domaine communal et 3 : de nombreuses colonies présentes et des dégâts importants sur les prairies. Ces données, qui couvrent quasiment 3 cycles de pullulation, ont permis d'analyser finement la synchronie spatiale des fluctuations d'abondance du campagnol terrestre sur une surface de plus de 2 500 km 2 (BERTHIER et al., 2014). ...
Certaines populations de campagnol terrestre connaissent des variations cycliques de leurs effectifs. La désynchronisation dans l'espace de ces fluctuations peut conduire à l'émergence de "vagues voyageuses" d'abondance. L'hétérogénéité paysagère (qualité d'habitat et obstacles à la dispersion) est l'hypothèse la plus probable pour expliquer ce phénomène. Dans le massif du Jura, l'analyse de données d'abondance du campagnol terrestre, collectées depuis 1989 dans les communes du Doubs, a révélé l'existence d'une vague d'abondance se propageant à la vitesse de 7 km/an le long d'un axe orienté nord-ouest / sud-est, perpendiculairement à l'un des obstacles majeurs à la dispersion. A une échelle plus locale, la vague est freinée par la présence de haies et de massifs boisés, milieux défavorables aux campagnols.
... Colour indicates voles abundance: red is high abundance, orange is moderate abundance, yellow is low abundance, pale yellow is absence and grey is no data. From Berthier et al. (2014) The study area. a) An elevation map of the Doubs and Jura departments in eastern France. ...
... Rodent species that reach sexual maturity quickly and can produce large litters early in life are more likely to be significant reservoirs for zoonoses (Han et al., 2015) making A. terrestris, with its capacity for explosive population growth, of particular interest as a potential reservoir for emerging infectious diseases. Population densities of A. terrestris in Franche-Comté fluctuate dramatically, with outbreaks characterized by densities of over 200 individuals/ha and forage production losses of over 1000 kg/ha/year occurring every 5-8 years (mean period, 6 years, Berthier et al., 2014). Fluctuations in A. terrestris density have been documented in neighbouring Switzerland as early as the 16th century (Korner, 1993;Saucy, 1994b), but current outbreaks of such magnitude emerged in the late 1960s in Franche-Comté in conjunction with significant land-use changes; agricultural policy at the time encouraged specialization in milk production which led farmers to convert ploughed fields to permanent grassland (Giraudoux et al., 1997) and remove hedges to create larger homogeneous patches. ...
... A. terrestris and T. europaea will use the same Colour indicates voles abundance: red is high abundance, orange is moderate abundance, yellow is low abundance, pale yellow is absence and grey is no data. From Berthier et al. (2014) tunnel networks when A. terrestris density is low Fritschy and Meylan, 1980). At the regional scale (~2500 km 2 ), risk of outbreak is highest when the ratio of permanent grassland to agricultural land is >90 % but outbreaks still occur at ratios as low as 40% (Giraudoux et al., 1997). ...
Context In France, during cyclic population surges, water voles, Arvicola terrestri, cause extensive damage to mountain grassland. A working group consisting of researchers from the University of Franche-Comté (UFC), INRA (Centre de Biologie et de Gestion des Populations) agricultural organizations (Fédération Régionale de Défense contre les Organismes Nuisibles de Franche-Comté, FREDON) are working on systems approach in which interactions between voles, their habitat (landscape, predators) and agricultural practices are analysed hierarchically (in space and time). One of the objectives is to highlight the largest possible number of control factors on which it is possible to act, and the scale at which these actions are relevant. These studies have helped initiate a strategy, successfully tested in Franche-Comté and in Auvergne, which promotes the integrated control of water vole populations. Nevertheless, there are still grey areas in the understanding of the cycle, particularly on the determinants of the decline phase. The role of pathogen communities (some species may even be transmitted to humans) so far remains the subject of debate in the scientific literature. The understanding of the key factors determining this phase should allow farmers to better anticipate economic impacts and to adopt optimal strategies for vole population control Objectives: (1) To test the pathogens and senescence hypotheses in order to explain the population decline. (2) To look for biological indicators (diversity of pathogens and / or immune indicators) that may predict the decline phase in order to anticipate appropriate measures to restore grasslands. (3) To assess the role of the transition between high population density phase and the decline phase for the emergence of pathogens in vole populations that may cause human diseases.General Methodology Population monitoring with regular (monthly) sampling will be made on several populations (replicates) in the period that brackets the vole population declines. Methods based on Next Generation Sequencing (NGS) makes it possible to establish extensive catalogues of pathogens (viruses, bacteria, other parasites) hosted by vole populations and to measure the prevalence.
... Understanding the spatial dimensions of population dynamics is an endeavour in which the dialogue between theoretical and empirical studies has been particularly intense (Berthier et al., 2014). One particular aspect of the spatial dimensions of population dynamics is dispersal, the process by which organisms move, settle and reproduce away from their birthplace. ...
... Here, we propose coupling ABM and EBM in a multiscale model to overcome these limits, and as an example, we seek to build a model to simulate the spread of a montane water vole, Arvicola scherman, population in the Haute-Romanche valley (France). The population surges of montane water voles have been studied in a number of mountain ranges in France (Giraudoux et al., 1997;Fichet-Calvet et al., 2000;Delattre and Giraudoux, 2009;Berthier et al., 2014;Michelin et al., 2014;Halliez et al., 2015). This work provides basic knowledge on the ecology of this species and its population dynamics. ...
... Given the proximity of the Parc National des Écrins and considering the potential risk to wildlife posed by the side effects of vole control, the staff of the park carefully mapped the annual progress of the colonization from 1998 to 2010 until it reached the Col du Lautaret and stopped in the 13th year. Mapping was based on the observation of surface activity indices after the snowmelt, which is a reliable indicator of variations in vole abundance (Giraudoux et al., 1995(Giraudoux et al., , 1997Berthier et al., 2014). This unique situation of primary colonization made it possible to know the characteristics of an invasion pattern of a valley from a known starting point (the end of the Buffe valley) over a surface area of approximately 2500 ha constrained by the relief of valleys. ...
The incorporation of the spatial heterogeneity of real landscapes into population dynamics remains extremely difficult. We propose combining equation-based modelling (EBM) and agent-based modelling (ABM) to overcome the difficulties classically encountered. ABM facilitates the description of entities that act according to specific rules evolving on various scales. However, a large number of entities may lead to computational difficulties (e.g., for populations of small mammals, such as voles, that can exceed millions of individuals). Here, EBM handles age-structured population growth, and ABM represents the spreading of voles on large scales. Simulations applied to the spreading of a montane water vole population demonstrated that our model is quite efficient in representing the pattern observed and might help to highlight some key parameters during population expansion. This method paves the way for further developments, including the introduction of density-dependent parameters (predation, diseases, etc.) capable of triggering population declines in an explicitly spatial context.
... On the other hand, heterogeneous landscapes can prevent colonisation of fossorial water voles directly by slowing their dispersion and indirectly by favouring predation (Giraudoux et al. 1997;Fichet-Calvet et al. 2000;Foltête et al. 2016). Connected favourable habitats lead to merged populations of A. scherman and a synchronization of their population densities (Giraudoux et al. 1997;Morilhat et al. 2008;Berthier et al. 2013). For example, fossorial water voles from France and Switzerland show well-marked multiannual fluctuations of density, commonly named cycles, every 5 to 9 years (Saucy 1988; Giraudoux et al. 1997;Fichet-Calvet et al. 2000). ...
... For example, fossorial water voles from France and Switzerland show well-marked multiannual fluctuations of density, commonly named cycles, every 5 to 9 years (Saucy 1988; Giraudoux et al. 1997;Fichet-Calvet et al. 2000). Consequently, A. scherman outbreaks spread as a wave at a regional scale with an estimated propagation speed of 7.4 km per year in France (Berthier et al. 2013). Individual dispersal of fossorial water voles is unlikely to reach more than a hundred of meters (Saucy 1988;Saucy & Schneiter 1994), which suggests that outbreak spreads would involve consecutive effective movements of these synchronous populations (Fichet-Calvet et al. 2000;Berthier et al. 2013). ...
... Consequently, A. scherman outbreaks spread as a wave at a regional scale with an estimated propagation speed of 7.4 km per year in France (Berthier et al. 2013). Individual dispersal of fossorial water voles is unlikely to reach more than a hundred of meters (Saucy 1988;Saucy & Schneiter 1994), which suggests that outbreak spreads would involve consecutive effective movements of these synchronous populations (Fichet-Calvet et al. 2000;Berthier et al. 2013). ...
The montane water vole Arvicola scherman occurs in mountainous areas of Europe, living in underground burrow systems located in grasslands and fruit orchards. This species feeds on the root system of plants, including fruit trees. Specifically, the subspecies A. scherman cantabriae is nowadays one of the main causes of economical loss in apple orchards of Asturias (northwestern Spain). An official control program in Spain considers all sustainable phytosanitary measures that can reduce population growth of this species. Since the pest condition of A. scherman depends on its biology and ecology, a deep knowledge of these aspects is needed to set up specific and suitable control strategies. Thus, the aim of this research is to obtain essential information on the reproductive biology and population genetics of this species in the agricultural landscape of Asturias.
More than 800 individuals of A. scherman cantabriae were gathered in apple orchards located at low altitude in Villaviciosa and Nava municipalities during two annual cycles (from February 2011 to January 2013). Sexual characteristics, body measurements and relative age class of each specimen were recorded. Body condition of females, which indicates energy provision, and the number of embryos of each one were also wrote down. Skeletal muscle samples of 137 specimens from ten demes were used to conduct a microsatellite-based analysis (12 microsatellite loci). These orchards are placed in a landscape conformed by a mosaic of small and different land-use plots, which was assessed in a vector based geographic information system and it was focused on soil-occupancy categories.
Pregnant females and young specimens were detected over the whole year, which mean that A. scherman cantabriae showed a continuous breeding pattern during the study period. Intra-annual changes in body mass and size of sexual organs of males did not affect significantly reproduction at a population scale. Thus, primary demands of these voles seem to be properly fulfilled during the whole year and hence energy budgets can be destined to cop continuous reproduction. To our knowledge, no other A. scherman population shows regularly this reproductive pattern. Females were able to produce a high number of litters per year (7.30) although litter size was relatively moderate (embryos/female: first year: 3.87; second year: 3.63). Each female was able to produce 28.25 pups per year. The reproductive potential showed by Cantabrian voles is, to our knowledge, the highest one reported to date for this species; probably because the breeding season does not entail a critical factor in this area. A positive correlation between litter size and the body condition of the mother was observed. Therefore, the body condition of females seems to be one of the main factors involved in the variation of the reproductive potential in A. scherman cantabriae.
These studied demes showed relatively low level of genetic diversity (HE = 0.621; HO = 0.601; AR = 4.42) probably due to both the inbreeding and genetic drift effects. Significant genetic differentiation appeared among demes, which revealed a strong pattern of significant isolation-by-distance both for Euclidean distances (r = 0.790) and effective distances (r = 0.780). The spatial autocorrelation analysis detected four genetic clusters or populations in this study area (120 km2). Thus, this mosaic of different land-use plots decreases connectivity among suitable habitats even at local scale, in which A. scherman populations mainly depend on birth and death rates. An estuary and a four-lane road did not suppose a barrier for gene flow of this species. Less seasonal environment and highly patched landscape would suggest that this species does not show well marked multiannual fluctuations of density at large scale in this area.
Control strategies for A. scherman cantabriae at a regional scale can be discarded. The monitoring of each population, or management unit, will be essential to know the population dynamic and to establish coordinated control strategies. Preserving and promoting this patchy landscape would favour the presence of predators and hamper dispersion of this species. A continuous population control throughout the year would be advisable, using sustainable methods, such as traps, the installation of barriers and/or coordinated manipulation of habitat.
... In brief, variation in rodent abundance depends on the prevalence of their optimal habitat within a landscape. In addition, water vole outbreaks in Franche-Comté (also in the Massif Central) have been characterized by a spatial spreading over several years (Giraudoux et al., 1997;Berthier et al., 2013) called a traveling wave. Such pattern has also been documented for other species, such as the bank vole (M. ...
... The water vole population outbreak from 1998 to 2010 in the Haute-Romanche valley is similar in terms of temporal patterns to other areas where cyclic outbreaks occur (e.g., the Jura and the Massif Central Mountains). Considering the temporal aspect of the outbreak locally, we demonstrated a quick population increase (one year) in abundance followed by a non-linear slow decrease over the subsequent years In western Europe, water vole populations are usually cyclic, with a period of 5-7 years (Saucy, 1994;Giraudoux et al., 1997;Berthier et al., 2013). Here, we monitored the water vole population of the Haute-Romanche valley over thirteen years. ...
... The second time, receding took place between two villages (from 2003 to 2004) and the third time in an area with deep gullies (from 2005 to 2006). Here, the inhabited areas and gullies appeared to be obstacles to the water vole spread, corroborating the findings of Berthier et al. (2013) in the Jura Mountains. ...
... Il est aujourd'hui établi que ces vagues sont plus qu'une curiosité mathématique issue des modèles théoriques. Elles ont ainsi été décrites pour des populations cycliques de rongeurs, d'oiseaux, d'insectes ainsi que pour les pathogènes responsables, chez l'homme, de la dengue et de la rougeole (GIRAUDOUX et al., 1997 ;LAM-BIN et al., 1998 ;MOSS et al., 2000 ;MCKINNON et al., 2001 ;GRENFELL et al., 2001 ;BJØRNSTAD et al., 2002 ;JOHNSON et al., 2004 ;CUMMINGS et al., 2004 ;TENOW et al., 2013 ;BERTHIER et al., 2014). La particularité de ces vagues d'abondance est d'émerger en l'absence de propagation nette des individus impliqués dans la dynamique cyclique. ...
... Dans le massif du Jura, en France et en Suisse, la dynamique cyclique des populations de campagnols terrestres est caractérisée par une période de 5 à 8 ans (SAUCY, 1994 ;GIRAUDOUX et al., 1997 ;BERTHIER et al., 2014). Au cours d'un cycle, les densités des populations peuvent varier de moins d'un individu à l'hectare, en phase de faible densité, à plus de 500 individus à l'hectare lors des pics de pullulations. ...
... Ces estimations semi-quantitatives distinguent trois classes d'abondance : 0 : pas de colonies de campagnols dans les prairies, 1 : quelques colonies isolées, 2 : des colonies présentes dans la plupart des prairies sur le domaine communal et 3 : de nombreuses colonies présentes et des dégâts importants sur les prairies. Ces données, qui couvrent quasiment 3 cycles de pullulation, ont permis d'analyser finement la synchronie spatiale des fluctuations d'abondance du campagnol terrestre sur une surface de plus de 2 500 km 2 (BERTHIER et al., 2014). ...
In cyclic populations, fluctuations in abundance may be spatially asynchronous. This asynchrony can lead to the emergence of complex patterns, such as travelling waves. At present, landscape heterogeneity (driven by factors such as habitat quality and physical dispersal limitations) is often considered to be instrumental in generating travelling waves. In this study, 15 years of town-level abundance data obtained from cyclic water vole populations in the Jura mountain range in France (Doubs Department) were analysed. The results of this analysis suggest the presence of a wave that is moving at a speed of 7.4 km/year and at a perpendicular angle to one of the major physical obstacles to vole dispersal. At the local scale, the wave's propagation is slowed by the presence of habitat that is unfavourable to water voles, such hedgerow networks and forested areas.
... This debating is the case in the Jura mountains where massive outbreaks of a grassland vole species, the montane water vole, Arvicola amphibius (formerly A. terrestris (Chevret et al., 2020)), occur with 5-to 6-year cycles and population densities exceeding 500-1,000 ind.ha −1 . High-density peaks propagate over grasslands under the form of a traveling wave (Berthier et al., 2014;Giraudoux, 1997). ...
... In our study area, the population of the main prey species varied between 0 and approximately 1,000 ind.ha −1 on a scale of tens of km 2 (Berthier et al., 2014;Giraudoux et al., 1997) and an amplitude 5-100 times larger than those observed on a similar scale in different areas worldwide (Dupuy et al., 2009;Erlinge, 1983;Gilg et al., 2006;Lambin et al., 2000). A similar amplitude has been reported locally for M. arvalis in alfalfa semi-permanent plots of some ha in an intensive agriculture matrix of plowed fields of western France (50-1,500 ind.ha −1 ) (Pinot et al., 2016). ...
Voles can reach high densities with multiannual population fluctuations of large amplitude, and they are at the base of predator communities in Northern Eurasia and Northern America. This status places them at the heart of management conflicts wherein crop protection and health concerns are often raised against conservation issues. Here, a 20‐year survey describes the effects of large variations in grassland vole populations on the densities and the daily theoretical food intakes (TFI) of vole predators based on roadside counts. Our results show how the predator community responded to prey variations of large amplitude and how it reorganized with the increase in a dominant predator, here the red fox, which likely negatively impacted hare, European wildcat, and domestic cat populations. This population increase did not lead to an increase in the average number of predators present in the study area, suggesting compensations among resident species due to intraguild predation or competition. Large variations in vole predator number could be clearly attributed to the temporary increase in the populations of mobile birds of prey in response to grassland vole outbreaks. Our study provides empirical support for more timely and better focused actions in wildlife management and vole population control, and it supports an evidence‐based and constructive dialogue about management targets and options between all stakeholders of such socio‐ecosystems.
... The possibility that geometrid outbreaks travel as waves across distances of thousands of kilometers has been advocated based on qualitative time series of outbreak records (Tenow et al. 2013), but the validity of this claim has been questioned on both conceptual and analytical grounds (Jepsen et al. 2016;Tenow 2016). Meanwhile, there is a conspicuous absence of studies that employ quantitative population data to evaluate the presence of geometrid waves on more modest scales, where the existence of waves would be easier to reconcile both with general theory (Sherratt & Smith 2008) and empirical experience from other systems (Moss, Elston & Watson 2000;Bjørnstad et al. 2002;Berthier et al. 2014). ...
... For this species, we detected strong 1-year lagged correlations at distances of 50-80 km when moving roughly southwards, suggesting the presence of a travelling wave moving in this direction. This is in good accordance with the east-west directionality of within-year synchrony, as within-year synchrony (and dispersal) is expected to be more extensive parallel to the front of a travelling wave than in the direction of wave propagation (Berthier et al. 2014). Although the concept of travelling waves has been much discussed for geometrid moths (Tenow et al. 2007;Tenow et al. 2013;Jepsen et al. 2016;Tenow 2016), this is the first formal statistical analysis to provide evidence of waves based on quantitative time series for these species. ...
Spatial synchrony in population dynamics can be caused by dispersal or spatially correlated variation in environmental factors like weather (Moran effect). Distinguishing between these mechanisms is challenging for natural populations, and the study of dispersal‐induced synchrony in particular has been dominated by theoretical modelling and laboratory experiments.
The goal of the present study was to evaluate the evidence for dispersal as a cause of meso‐scale (distances of tens of kilometres) spatial synchrony in natural populations of the two cyclic geometrid moths Epirrita autumnata and Operophtera brumata in sub‐arctic mountain birch forest in northern Norway.
To infer the role of dispersal in geometrid synchrony, we applied three complementary approaches, namely estimating the effect of design‐based dispersal barriers (open sea) on synchrony, comparing the strength of synchrony between E. autumnata (winged adults) and the less dispersive O. brumata (wingless adult females), and relating the directionality (anisotropy) of synchrony to the predominant wind directions during spring, when geometrid larvae engage in windborne dispersal (ballooning).
The estimated effect of dispersal barriers on synchrony was almost three times stronger for the less dispersive O. brumata than E. autumnata . Inter‐site synchrony was also weakest for O. brumata at all spatial lags. Both observations argue for adult dispersal as an important synchronizing mechanism at the spatial scales considered. Further, synchrony in both moth species showed distinct anisotropy and was most spatially extensive parallel to the east–west axis, coinciding closely to the overall dominant wind direction. This argues for a synchronizing effect of windborne larval dispersal. Congruent with most extensive dispersal along the east–west axis, E. autumnata also showed evidence for a travelling wave moving southwards at a speed of 50–80 km/year.
Our results suggest that dispersal processes can leave clear signatures in both the strength and directionality of synchrony in field populations, and highlight wind‐driven dispersal as promising avenue for further research on spatial synchrony in natural insect populations.
... This ecotype has only been recorded in a small number of isolated islands, mainly in Scotland (Telfer et al. 2003). However, in continental Europe the fossorial ecotype is common, particularly in upland meadows (Meylan 1977;Berthier et al. 2014). Fossorial populations can become a serious pest in some areas due to the economic impact they can have on agricultural crops and orchards by damaging root systems, consuming plants and digging extensive burrow systems which can destabilize soil structure (Meylan 1977). ...
... Fossorial populations can become a serious pest in some areas due to the economic impact they can have on agricultural crops and orchards by damaging root systems, consuming plants and digging extensive burrow systems which can destabilize soil structure (Meylan 1977). These populations oscillate with a 4-8 years cyclicity and in peak years water vole numbers can reach 'outbreak' densities of a 1000 individuals per hectare (Giraudoux et al. 1995;Weber et al. 2002;Berthier et al. 2014). ...
Urbanisation is often linked with habitat loss and a reduction in species richness but some species may be able to adapt to urban environments. Water voles Arvicola amphibius, a rapidly declining species in the UK, have recently been recorded in isolated grassland habitats in Glasgow, Scotland’s largest city (human population 1.2 million). The aim of this study was to determine the distribution and habitat characteristics of water vole populations occupying these dry grasslands. Field work was undertaken from March to October 2014 in a 34 km² study area located 3 km east of the city centre. Field sign transects recorded water vole presence in 21/65 (32%) and 19/62 (31%) surveyed sites in spring and autumn, respectively. Vole occupancy increased with distance from water and was greatest in parkland, followed by sites with rank vegetation and roadside habitats. Occupancy was lower where signs of predators were recorded but surprisingly occupancy was found to be greater in the most disturbed sites, perhaps linked to the fact that many of these sites were public parks containing suitable grassland. Sites occupied by water voles were classed as neutral grasslands with species composition dominated by two main species. The number of grassland sites occupied by water voles, especially within public areas suggests that careful management of these urban grassland habitats will benefit the conservation of this highly threatened species in the UK.
... The intensity of attack rates imposed by parasitoids on their hosts may also affect their own distribution due to variation in host availability (bottom-up effect). A third process is the inherent dispersion ability of individuals among nearby populations (Bjørnstad et al., 1999;Reichenbach et al., 2007;Berthier et al., 2014). ...
... In some cases, however, after a certain distance, the synchrony stops decreasing and a new increase begins, producing travelling waves, a poorly understood ecological phenomenon (Bjørnstad et al., 1999;Moss et al., 2000;Johnson et al., 2004). Recent findings have suggested that landscape obstacles can create limits to dispersion, separating a large population into groups where individuals move more locally (i.e. at short distances), shaping travelling waves into space (Berthier et al., 2014). Although numerous ecological patterns detected at the level of populations may be hierarchically transferred into communities, as far as we know, travelling waves have not yet been explicitly described considering a pool of species. ...
Bruchine beetles are highly host specific seed feeders during the larval stage. Although some specific parasitoid families have been recorded attacking bruchine beetles, most studies have been done at small spatial scales. Therefore, the current knowledge about the diversity and the geographic distribution of parasitoid species parasitizing bruchines is scarce, especially at a wide geographic area that extends over large distances through a latitudinal cline (i.e., large-scale spatial structure). The present study determined the species richness and evenness of parasitoids attacking the bruchine beetle Acanthoscelides macrophthalmus feeding on Leucaena leucocephala seeds, examined their geographic distribution, and characterized the large-scale spatial structure in parasitoid species composition. A total of 1,420 parasitoids (all Hymenoptera) belonging to four families, five subfamilies and eight species were collected (genera: Horismenus, Paracrias, Urosigalphus, Stenocorse, Chryseida, Eupelmus). Most parasitoid species showed wide spatial distribution, high evenness in species abundance, and the species richness estimators were close to stabilization (approximately eight species). Overall, greater similarity was observed in the species composition of plant populations near to each other than those farther apart, revealing a large-scale spatial structure in parasitoid species composition.
... We used a Bayesian framework developed in Smout et al. (2010) to fit field data of those two generalist predators collected in the Jura mountains of eastern France. In this region, landscape composition and structure are favorable to population outbreaks of the water vole (Arvicola scherman) and the common vole (Microtus arvalis), two grassland rodents whose population biomasses are dominant in the landscape (Raoul et al. 2001, Berthier et al. 2014. Population declines of other small mammals species living in grassland and other habitats (e.g., the wood mouse Apodemus sylvaticus or the bank vole Myodes glareolus) are synchronous with the declines of grassland species (Raoul et al. 2001, Bernard et al. 2010, strengthening the interest for the predator's diet response to variation of total density of prey. ...
... However, in both systems, we observed clear evidence for negative switching, which is likely to have a destabilizing effect (Chesson 1984). This destabilizing effect is susceptible to accentuate population cycles in small-mammals, a demographic pattern occurring in the areas under study (Berthier et al. 2014). Several empirical studies showed that negative switching may be observed in marine (Kean-Howie et al. 1988, Rindorf et al. 2006) and terrestrial ecosystems (Weale et al. 2000, Palma et al. 2006, Hellström et al. 2014).There are numerous explanations for negative switching coming from those empirical studies. ...
The ability for a generalist consumer to adapt its foraging strategy (the
multi-species functional response, MSFR) is a milestone in ecology as it contributes to
the structure of food webs. The trophic interaction between a generalist predator, as the
red fox or the barn owl, and its prey community, mainly composed of small mammals,
has been empirically and theoretically widely studied. However, the extent to which these
predators adapt their diet according to both multi-annual changes in multiple prey species
availability (frequency dependence) and the variation of the total prey density (density
dependence) is unexplored.We provide a new general model of MSFR disentangling changes
in prey preference according to variation of prey frequency (switching) and of total prey
density (we propose the new concept of “rank switching”). We apply these models to two
large data sets of red fox and barn owl foraging. We show that both frequency-dependent
and density-dependent switching are critical properties of these two systems, suggesting
that barn owl and red fox have an accurate image of the prey community in terms of
frequency and absolute density. Moreover, we show that negative switching, which can
lead to prey instability, is a strong property of the two systems.
... Thus, their foraging activities have engineering effects on soils. Cyclic outbreaks of montane water vole populations (200 to 1000 individuals per hectare) occur every 5 to 8 years (Berthier et al. 2014) and do considerable damage on vegetation (Delattre & Giraudoux 2009), resulting in an important loss of forage production (Quéré et al. 1999;Schouwey et al. 2014). Many studies have been conducted to understand the determinism of these outbreaks (Giraudoux et al. 1997;Morilhat et al. 2007;Morilhat et al. 2008) and to limit their intensity (Couval & Truchetet 2014;Foltête et al. 2016). ...
En Europe, les prairies semi-naturelles de moyenne montagne sont principalement des écosystèmes ayant évolués au cours de plusieurs décennies d’activité humaine. Ces écosystèmes présentent une biodiversité remarquable et dépendent de régimes traditionnels de perturbations par la fauche ou le pâturage. Cependant, dans l’objectif d’augmenter leur production de fourrage, les prairies semi-naturelles sont soumises à des régimes de perturbations de plus en plus importants ainsi qu’à de nouveaux types de perturbations. Ce travail de thèse propose d’apporter de nouveaux éléments pour suivre et comprendre l’impact des perturbations sur la diversité des communautés végétales des prairies semi-naturelles.Dans un premier temps, la comparaison de relevés de végétation anciens (2005 à 2009) avec des relevés récents (2019) a été réalisée dans des prairies de fauche de moyenne montagne. Cette comparaison a permis de mettre en évidence des évolutions contrastées de la diversité végétale et des régimes de perturbations entre deux massifs. Dans le massif des Vosges, la diversité végétale ainsi que les régimes de perturbations ne semblent pas avoir évolué. A l’inverse, dans le massif du Jura, la diversité végétale a fortement diminué, probablement en association avec une augmentation de la fréquence des régimes de perturbations et de la fertilisation.Dans un second temps, l’impact de perturbations de forte intensité sur la diversité végétale a été évalué. Dans les prairies de fauche, les perturbations par les pullulations de campagnols terrestres semblent permettre une augmentation de la richesse spécifique par la réduction de la compétition pour la lumière. A l’inverse, ces perturbations semblent favoriser des espèces proches phylogénétiquement et entraîner une diminution de l’équitabilité phylogénétique. Dans les pelouses sèches, les perturbations par l’utilisation de broyeurs de pierres ne semblent pas impacter la diversité végétale. En revanche, la composition en espèces des milieux perturbés évolue vers des végétations de prairies productives suite à la perte des espèces typiques des pelouses.Dans un troisième temps, l’utilisation d’espèces diagnostiques comme indicateurs des régimes de perturbations et de la diversité végétale dans les prairies pâturées du massif du Jura a été testée. Le nombre d’espèces diagnostiques dans un relevé de végétation s’est révélé être un bon indicateur de la diversité végétale et des régimes de fertilisation. Cependant, les espèces diagnostiques ne semblent pas être de meilleurs indicateurs que des espèces généralistes des prairies pour évaluer l’intensité des régimes de perturbations.Nos résultats confirment que les changements de pratiques agricoles sont une menace majeure pour la diversité végétale des prairies semi-naturelles de moyenne montagne, en particulier dans le massif du Jura. Nos travaux mettent également en avant que l’augmentation de la fréquence des régimes de perturbations est susceptible d’avoir davantage d’effets négatifs sur la diversité végétale que des perturbations de forte intensité mais peu fréquentes. Néanmoins, certaines perturbations de forte intensité, comme l’utilisation de broyeurs de pierres, peuvent entraîner des modifications très importantes et irréversibles de la composition en espèces des milieux perturbés. Dans l’objectif de concilier enjeux sociétaux et environnementaux, il convient de maintenir des parcelles productives ou les régimes de perturbations par la fauche ou le pâturage sont fréquents, ce qui permet d’assurer une production fourragère importante. Cependant, Il est également nécessaire de limiter la fréquence et l’intensité des perturbations dans des parcelles encore peu intensifiées afin de protéger leur composition en espèces ainsi que leur diversité végétale.
... The dispersal process is then more akin to a diffusion process than to a discrete state-switching process (Ovaskainen et al. 2008;Jongejans et al. 2011;Foltête and Giraudoux 2012;Williams et al. 2017). Nevertheless, dispersal may still be spatially structured by landscape features (McRae et al. 2008;Spear et al. 2010;Berthier et al. 2013;Hanks and Hooten 2013) or by the social cues that the individuals use to decide where to move, such as conspecific population density and conspecific breeding success (Doligez et al. 2002;Péron et al. 2010b). ...
... The terrestrial vole, also known as Arvicola terrestris Scherman (ATS), is a fossorial rodent living in underground tunnels in mid-mountain regions generally located between 400 and 1500 m above sea level [1]. The proliferation of this rodent shows cyclical variations over a period of about 5 to 6 years, with densities ranging from 50-100 animals/hectare to more than 1000 during outbreaks [2,3]. The excessive cyclical proliferation and expansion of ATS colonization areas, since the 1970s, mainly in mid-mountain agronomic and tourist ecosystems, is an increasingly important problem with strong environmental and economic impacts [4][5][6]. ...
The cyclical proliferation of the wild fossorial rodent Arvicola terrestris scherman (ATS) is critical in mid-mountain ecosystems of several European countries. Our goal is to develop an immunocontraceptive vaccine to control their fertility, as a sustainable alternative to chemical poisons currently used. Indeed, these chemicals cause the death of ATS predators and animals sharing their ecosystem, and current laws progressively limit their use, making the development of a targeted vaccination strategy an interesting and efficient alternative. In order to identify species-specific sperm antigens, male and female ATS received subcutaneous injections of whole ATS spermatozoa to elicit an immune response. The analysis of the immune sera led to the identification of 120 immunogenic proteins of sperm cells. Of these, 15 were strictly sperm-specific and located in different regions of the male gamete. Some of these antigens are proteins involved in molecular events essential to the reproductive process, such as sperm–egg interaction, acrosomal reaction, or sperm motility. This approach not only identified a panel of immunogenic proteins from ATS sperm cells, but also demonstrated that some of these proteins trigger an immune response in both male and female ATS. These spermatic antigens are good candidates for the development of a contraceptive vaccine.
... To lay groundwork for understanding how parasite communities change in fluctuating host populations, we considered the bacterial parasite community of the fossorial form of the water vole Arvicola terrestris in the Doubs and Jura departments of Franche-Comté, eastern France. In this region, A. terrestris are found primarily in grasslands ≥400 m above sea level 23 , and population densities fluctuate dramatically, peaking at over 200 individuals/ ha every 5-8 years (mean period, 6 years) with concomitant forage production losses of over 1000 kg/ha/year 24 . Such peaks are followed by a decline phase which can be quite rapid, with a catastrophic decline in abundance during the winter months after the peak and a lack of recovery in population abundance the following spring. ...
Understanding the driving forces that control vole population dynamics requires identifying bacterial parasites hosted by the voles and describing their dynamics at the community level. To this end, we used high-throughput DNA sequencing to identify bacterial parasites in cyclic populations of montane water voles that exhibited a population outbreak and decline in 2014–2018. An unexpectedly large number of 155 Operational Taxonomic Units (OTUs) representing at least 13 genera in 11 families was detected. Individual bacterial richness was higher during declines, and vole body condition was lower. Richness as estimated by Chao2 at the local population scale did not exhibit clear seasonal or cycle phase-related patterns, but at the vole meta-population scale, exhibited seasonal and phase-related patterns. Moreover, bacterial OTUs that were detected in the low density phase were geographically widespread and detected earlier in the outbreak; some were associated with each other. Our results demonstrate the complexity of bacterial community patterns with regard to host density variations, and indicate that investigations about how parasites interact with host populations must be conducted at several temporal and spatial scales: multiple times per year over multiple years, and at both local and long-distance dispersal scales for the host(s) under consideration.
... The spatial scaling of synchrony of kestrel productivity reported in this study suggests that vole populations fluctuate synchronously over large distances in Switzerland (until 300 km). Previous studies reported population synchrony of voles at only medium distances, i.e., from 10 to 50 km (Steen et al., 1996; Bjørnstad et al., 1999;MacKinnon et al., 2001;Berthier et al., 2014), whereas others suggested synchrony at larger spatial scales. However, studies conducted at larger spatial scales were generally unable to identify at which distance the positive correlation vanished because of the limited size of the study area, i.e., up to 60 km (Lambin et al., 2006), 80 km (Huitu et al., 2003b), 120 km (Huitu et al., 2008), or 250 km (Gouveia et al., 2016). ...
Rodents are classical model species to investigate spatial synchrony in population fluctuation. Yet, previous studies have been strongly biased geographically toward high latitude (boreal ecosystem) and limited in their spatial scale, i.e., few sampling sites separated by a few tens of kilometers. Both aspects currently limit our understanding of rodent population dynamics across space. In this study we investigate vole population synchrony at a large spatial scale in central Europe. We used long-term breeding success of a vole-eating raptor specialist, the European kestrel, as an indicator of vole abundance. We first demonstrate that the productivity of kestrels is highly dependent on the availability of voles and as such is a good proxy of vole abundance. Secondly, we assessed the spatial synchrony of kestrel productivity and its scaling. We found that kestrel productivity fluctuated synchronously at a large spatial scale, up to a distance of 300 km. This result suggests that vole populations in central Europe varied in synchrony at large spatial scales, similarly as in northern latitudes. The most likely mechanism resulting in such large scale synchrony of vole populations is synchronized density-independent environmental conditions.
... In the context of gene traits evolution, u also stands for a proportion of individuals and can be seen as a solution of a bistable reaction-diffusion equation (for instance [3,20,21,22]). ...
Dynamic phenomena in social and biological sciences can often be modeled by employing reaction-diffusion equations. When addressing the control of these modes, from a mathematical viewpoint one of the main challenges is that, because of the intrinsic nature of the models under consideration, the solution, typically a proportion or a density function, needs to preserve given lower and upper bounds. Controlling the system to the desired final configuration then becomes complex, and sometimes even impossible. In the present work, we analyze the controllability to constant steady-states of spatially homogeneous semilinear heat equations, with constraints in the state, and using boundary controls, which is indeed a natural way of acting on the system in the present context. The nonlinearities considered are among the most frequent: monostable and bistable ones. We prove that controlling the system to a constant steady-state may become impossible when the diffusivity is too small (or when the domain is large), due to the existence of barrier functions. When such an obstruction does not arise, we build sophisticated control strategies combining the dissipativity of the system, the existence of traveling waves and some connectivity of the set of steady-states. This connectivity allows building paths that the controlled trajectories can follow, in a long time, with small oscillations, preserving the natural constraints of the system. This kind of strategy was successfully implemented in one-space dimension, where phase plane analysis techniques allowed to decode the nature of the set of steady-states. These techniques fail in the present multi-dimensional setting. We employ a fictitious domain technique, extending the system to a larger ball, and building paths of radially symmetric solution that can then be restricted to the original domain.
... The sites were located on the second Jura Plateau in a mid-mountain zone (range = 688-1028 m altitude), where WV populations show 6-year cycles moving in traveling waves. 11,28 WVs can reach 800 individuals ha −1 in the Jura Mountains, and WVs normally disperse short distances, with a mean of less than 100 m (WV home range = 100-200 m 2 ). 7,29 For each site, all surveys (i.e. the field work in Sections 2.2, 2.3 and 2.4) were conducted within a circular area of approximately 450 ha (i.e. a radius of 1.2 km). ...
BACKGROUND
The use of pesticides can affect non‐target species by causing population declines through indirect intoxication. Small mustelids (SMs; weasels, Mustela nivalis L.; stoats, Mustela erminea L.) consume water voles (WVs, Arvicola scherman S.) and can be exposed to bromadiolone, an anticoagulant rodenticide used in some countries to reduce WV damage to grasslands. Here, we investigated whether bromadiolone affected SM abundance.
RESULTS
We monitored SM abundance using footprint tracking tunnels in spring and autumn at 10 sites. Among these sites, 4 were treated with bromadiolone, while 6 were not treated. We found reduced SM abundance at these 4 sites from spring to autumn (treated sites, mean±SE SM abundance change=‐1.68±0.42; untreated sites, 0.29±0.25). Using a linear model, we observed that SM abundance decreased as a function of the quantity of bromadiolone applied during the 3 months before the autumn estimate. We found that WV abundance increased at treated sites (linear model, treated sites, mean±SE WV abundance change=1.4±0.4; untreated sites, 0.33±0.25). Thus, at treated sites, SM abundance declined despite increased food availability. By analyzing residues in vole livers and SM scats we showed that SMs may be exposed to bromadiolone at the sites where this compound was used.
CONCLUSION
This study is the first to document the relationship between SM abundance and bromadiolone usage for small mammal control. Declines in SM abundance were observed at treated sites, where bromadiolone residue was found in SM scats. This correlative approach suggests that bromadiolone treatment may lead to seasonal SM declines and associated WV increases.
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... scat counts, snow tracking, counts on dens, camera trapping, etc.) to verify their relative value is recommended (Beltran et al. 1991, Gompper et al. 2006. In some cases, observations of indices along transects have provided efficient ways for monitoring seasonal and inter-annual fine changes in population densities on multiple scales from local up to regional as shown for grassland voles (Delattre et al. 1992, 1999, Giraudoux et al. 1997, Berthier et al. 2014. ...
Studying elusive species of conservation concern might be difficult for technical and ethical reasons. However, censuses can be based on the observation of activity indices. When coupled to non-invasive genetic methods this approach can provide extremely precise information about population size, individual movements and diseases. However, the design of optimal sampling is dependent on a knowledge on group distribution and possible variations of detectability of index targets. The aim of this study was to document the distribution of Yunnan snub-nosed monkey indices in space and time in that perspective. Based on transects carried out across the range of a fed population and on counts along the trail across the range of a wild group, we show that 2–3 day stays of a group in a place of some hectares were sufficient to get an homogeneous distribution of indices. Furthermore, the number of indices found were dependent on both pig presence and season. On the other hand, on a large scale of 100 km ² indices were spatially distributed as nested clusters. Indices distribution indicated a strong preference towards southern slopes and altitudes ranging between 2900 and 3400 m. Those observations pinpoint the importance of considering spatial scale to organise sampling designed to estimate population distribution.
... Spatially-lagged synchrony (or periodic travelling waves, see Glossary in Box 1), can theoretically arise in both homogeneous and heterogeneous environments (Sherratt & Smith 2008), and will, according to empirical work, be shaped by landscape structure and dispersal dynamics (Bjørnstad et al. 2002;Berthier et al. 2014). Traveling waves can also arise during recurrent epidemic outbreaks, whereby large core cities provide the spark for the initiation of outbreaks in smaller satellite towns ). ...
Population cycling is a widespread phenomenon, observed across a multitude of taxa in both laboratory and natural conditions. Historically, the theory associated with population cycles was tightly linked to pairwise consumer-resource interactions and studied via deterministic models, but current empirical and theoretical research reveals a much richer basis for ecological cycles. Stochasticity and seasonality can modulate or create cyclic behaviour in non-intuitive ways, the high-dimensionality in ecological systems can profoundly influence cycling, and so can demographic structure and eco-evolutionary dynamics. An inclusive theory for population cycles, ranging from ecosystem-level to demographic modelling, grounded in observational or experimental data, is therefore necessary to better understand observed cyclical patterns. In turn, by gaining better insight into the drivers of population cycles, we can begin to understand the causes of cycle gain and loss, how biodiversity interacts with population cycling, and how to effectively manage wildly fluctuating populations, all of which are growing domains of ecological research.
... Indeed, less seasonal environments, like that of our study area, lead to more stable population dynamics due to less variations at first reproduction and the length of the breeding season (Tkadlec and Zejda, 1998). Likewise, multiannual fluctuations in vole abundance in heterogeneous landscapes with hedgerows, woodlots, as those in the study area, might be landscape-modulated directly by slowing dispersion and indirectly by favouring predation (Delattre et al., 1996;Fichet-Calvet et al., 2000;Berthier et al., 2013). Anyway, in our study area abundance fluctuations in M. lusitanicus have been observed at a local scale, with populations increasing when A. scherman is in low numbers . ...
The Lusitanian pine vole (Microtus lusitanicus) is a key pest of apple in Asturias (NW Spain). The sustainable management of populations of this vole requires a deep knowledge of relevant aspects of its biology and ecology. To improve our knowledge on the breeding characteristics of M. lusitanicus, we analysed a sample of 700 individuals collected monthly in apple orchards during two years. The continuous occurrence of immature specimens and pregnant females during the whole study period indicates that M. lusitanicus can breed continuously throughout the year in apple orchards in Asturias. The relatively mild weather conditions in winter and the presence of a permanent grass cover throughout the year seem to be favourable conditions for continuous breeding of the vole. Nevertheless, some data (decrease in the size of testes and seminal vesicle of mature males in winter, lower percentage of pregnant females in December and of non-mature specimens in March) suggest that reproduction activity decreases slightly in winter. Mean litter size was relatively low in comparison with that reported for other Microtus species. The balanced adult sex-ratio and the relatively small testis size are congruent with a monogamous mating system. Nevertheless, the frequent coexistence of matures with two or more other adult voles of the opposite sex, and even the cohabitation of one male with two pregnant females, suggest that monogamy was facultative in our population. This study adds significantly to the current knowledge on the biology of this vole pest and can help in the design and implementation of sustainable and efficient management plans. As a first step, control practices should be deseasonalized and applied throughout the year.
... However, in both systems, we observed clear evidence for negative switching, which is likely to have a destabilizing effect (Chesson, 1984). This destabilizing effect is susceptible to accentuate population cycles in small-mammals, a demographic pattern occurring in the areas under study (Berthier et al., 2014). Several empirical studies showed that negative switching may be observed in marine (Kean-Howie et al., 1988;Rindorf et al., 2006) and terrestrial ecosystems ( Weale et al., 2000;Palma et al., 2006;Hellström et al., 2014). ...
La structure et l’intensité des interactions ressources-consommateurs qui forment les réseaux trophiques régulent une très grande partie des transferts de biomasse mais aussi de contaminants biologiques et chimiques dans les écosystèmes. L’objectif de la thèse est de développer des modèles permettant d’étudier les mécanismes de transport des contaminants et d’évaluer ainsi d’une part la dynamique des maladies infectieuses et des pollutions chimiques, et d’autre part les réponses des réseaux trophiques soumis à ces contaminations.[...] À l’issue de ces travaux, une quatrième étape de la thèse a été d’intégrer les interactions trophiques, les dynamiques des parasites et les impacts des pollutions dans des méta-écosystèmes (i.e. avec dispersions d’individus entre écosystèmes). En utilisant la théorie des matrices aléatoires nous avons établi des mesures des risques d’émergence de parasites que nous avons évalués en fonction des perturbations extérieures.L’étude a ainsi montré que ces perturbations augmentent les risques épidémiques, mais que ces risques pouvaient être réduits par la dispersion des individus (sains et infectés) sous certaines conditions qui sont,par exemple pour les TTP, un nombre d’espèces plus grand que le nombre d’écosystèmes connectés, et un taux de virulence plus faible que le taux de contagion.Ainsi, dans un contexte planétaire d’augmentation des pressions anthropiques sur les écosystèmes,cette thèse de modélisation apporte un ensemble d’outils et de développements conceptuels permettant d’analyser quantitativement et qualitativement les transferts et les impacts des contaminants sur les écosystèmes.
... Many studies have been carried out to identify the determinants of this phenomenon, showing the effect of landscape composition, landscape configuration, and agricultural practices on the diffusion of water vole populations. These studies have shown that water voles ''swarm'' more intensively and more rapidly in homogeneous grassland openfields than in heterogeneous mosaics of grasslands, hedgerows, and wooded patches (Duhamel et al. 2000;Morilhat et al. 2008;Berthier et al. 2009;Berthier et al. 2014). In this context, the purpose is to use a landscape graph to delineate areas subjected to the same demographic dynamics, to provide a support for defining a long-term plan for monitoring water vole populations. ...
Context
Landscape graphs are widely used to model connectivity and to support decision-making in conservation planning. Compartmentalization methods applied to such graphs aim to define clusters of highly interconnected patches. Recent studies show that compartmentalization based on modularity is suitable, but it applies to non-weighted graphs whereas most landscape graphs involve weighted nodes and links.
Objectives
We propose to adapt modularity computation to weighted landscape graphs and to validate the relevance of the resulting compartments using demographic or genetic data about the patches.
Methods
A weighted adjacency matrix was designed to express potential fluxes, associating patch capacities and inter-patch distances. Eight weighting scenarios were compared. The statistical evaluation of each compartmentalization was based on Wilks’ Lambda. These methods were performed on a grassland network where patches are documented by annual densities of water voles in the Jura massif (France).
Results
The scenarios in which patch capacity is assigned a small weight led to the more relevant results, giving high modularity values and low Wilks’ Lambda values. When considering a fixed number of compartments, we found a significant negative correlation between these two criteria. Comparison showed that compartments are ecologically more valid than graph components.
Conclusions
The method proposed is suitable for designing ecologically functional areas from weighted landscape graphs. Maximum modularity values can serve as a guide for setting the parameters of the adjacency matrix.
... Finally, whatever the choice of place where actions can preferentially be implemented, as objectivized by the graph-based method proposed here, measuring the effects remains a challenge. The duration of a vole cycle (the time between two population peaks) is 5-6 years with large variations in amplitude from one cycle to the next (Giraudoux et al., 1997;Berthier et al., 2014). Practically this means that any actions taken should be maintained over the long term and that their effects on the dynamics of target and non-target species would not be immediately measurable. ...
The cyclic spread of montane water vole populations in the grasslands of the Jura plateaus causes severe economic, ecological, and public-health problems. Since this phenomenon cannot be managed by massive use of the anticoagulant rodenticide bromadiolone, the challenge is to limit it by reducing regional-level connectivity through landscaping and agro-environmental interventions such as planting hedgerows, ploughing, and cultivating cereals. We used landscape graphs – a spatial modelling approach based on graph theory – to represent the grassland network and identify key areas for intervention. Several strategies were compared in terms of their capacity to fulfil operational requirements by interchanging patches and meta-patches as nodes of the graph, and least-cost distances and resistance distances to weight links. The combination of meta-patches and resistance distances provides a relevant basis on which to design concrete action to decrease regional-level connectivity of grasslands. The results also indicate that the usual removal method applied to the links of the graph would benefit from data on the statistical distribution of cost values along the shortest paths. More broadly, this suggests the modelling approach should be better matched the actual field interventions if the connectivity analysis is to be operational.
... Traveling waves are known to occur in population dynamics. For example, the abundance of voles shows traveling wave dynamics over large spatial scales (Ranta and Kaitala 1997;Berthier et al. 2014). Although the available red squirrel sex ratio data lack the temporal resolution to explore this phenomenon more fully, the existence of a U-shaped autocorrelation pattern suggests that processes generating complicated spatiotemporal patterns may be operational. ...
Large-scale studies on population-level sex ratios are few, even though sex ratio is an important determinant of population viability and dynamics. Mechanisms driving large-scale sex ratio variation include spatially autocorrelated resources and scale differences in local versus global Fisherian feedback of the operational sex ratio. In this study, we reanalyze historic data on sex ratios based on 187,404 hunted subadult and adult red squirrels (Sciurus vulgaris) capturing spatial sex ratio variation in 50×50 km squares throughout Finland over a period of 8 years. Overall, sex ratio was slightly male biased (50.9%) and relatively more 50×50 km squares showed a bias toward males (19% of squares) compared to females (8% of squares). Sex ratio was spatially autocorrelated at distances up to 200 km and in some years showed a U-shaped pattern: regions that were in close proximity and those that were far apart had similar sex ratios, but regions in-between had opposite sex ratios. We found no evidence that food supply (spruce cone crop) drives regional red squirrel sex ratio. Our findings add to the scarce evidence that vertebrate sex ratios show spatial patterns over large scales.
... Indeed, in mountainous areas of France, land use poli cy led to an agricultural specialization towards grass production and towards lar ger parcel sizes (López-i-Gelats et al. 2011). This promoted the emergence of multiannual vole (Arvicola terrestris and Microtus arvalis) population fluctuations at large spatial and temporal scales (Delattre et al. 1992, Giraudoux et al. 1997, Delattre et al. 2006, Foltête et al. 2008, Berthier et al. 2013. Delattre et al. (1992) showed that damages due to multiannual fluctuation patterns of the Common Vole increases with the Ratio of Permanent Grassland to Farmland (RPGF). ...
Because of the worldwide distribution of the Barn Owl (Tyto alba) and the easily way to find its pellets, it is often used to diet studies. To investigate the eco-geographical impact of mountainous areas on its diet, we conducted studies in the Jura, Alpes, Central and Pyrénées mountains and we also did pellet analysis from 8 sites in the Jura mountains. Analysis of the tooth and skull content of pellets allowed us to draw up two types of change in the diet of Tyto alba in correlation with mountain elevation. The first one concerns the Jura, Alpes and Central mountains, where the diversity of the diet declines with the increase in elevation. The second one concerns the Pyrénées mountains, where there is no change in the diversity of the diet, perhaps because of the higher diversity of small mammals caused by mediterranean influence. Thus, it seems that elevation cau ses a decrease in diet diversity of Tyto alba in continental mountains (Jura, Alpes and Central mountains) probably because of more homogeneous landscapes dedicated to grass production. However, in Mediterranean mountains (Pyrénées), a more diversified small mammal guild provides a constant level of diet diversity.
... Quantifying temporal changes in neutral genetic patterns in relation to density fluctua-tions has emerged as an important topic to better understand demographic and microevolutionary processes in natural populations (Schwartz et al. 2007). In this field, genetic comparative studies, between populations being in different demographic states or temporal demo-genetic monitoring, have proved to be very useful approaches to better understand the role of dispersal in the maintenance of genetic diversity in populations regularly affected by low numbers (Østergaard et al. 2003;Berthier et al. 2006;Ehrich et al. 2009;Rikalainen et al. 2012) and in spatial synchrony and spread of outbreaks (Berthier et al. 2005(Berthier et al. , 2013Chapuis et al. 2008Chapuis et al. , 2009). Comparing patterns for both neutral and adaptive genetic variation may also provide insight on density-dependent changes in selection pressures such as parasitism (Bryja et al. 2007). ...
In highly fluctuating populations with complex social systems genetic patterns are likely to vary in space and time due to demographic and behavioural processes. Cyclic rodents are extreme examples of demographically instable populations that often exhibit strong social organisation. In such populations, kin structure and spacing behaviour may vary with density fluctuations and impact both the composition and spatial structure of genetic diversity. In this study, we analysed the multiannual genetic structure of a cyclic rodent, Microtus arvalis, using a sample of 875 individuals trapped over three complete cycles (from 1999 to 2007) and genotyped at 10 microsatellite loci. We tested the predictions that genetic diversity and gene flow intensity vary with density fluctuations. We found evidences for both spatial scale-dependant variations in genetic diversity and higher gene flow during high density. Moreover, investigation of sex-specific relatedness patterns revealed that, although dispersal is biased toward males in this species, distances moved by both sexes were lengthened during high density. Altogether, these results suggest that an increase of migration with density allows to restore the local loss of genetic diversity occurring during low density. We then postulate that this change in migration results from local competition, which enhances female colonisation of empty spaces and male dispersal among colonies.This article is protected by copyright. All rights reserved.
Cyclic predator-prey systems are often observed in nature. In a spatial setting, these can manifest as periodic traveling waves (PTW). Environmental change and direct human activity are known to, among other effects, increase the heterogeneity of the physical environment, which prey and predator inhabit. Aiming to understand the effects of heterogeneity on predator-prey PTWs, we consider a one-dimensional infinite landscape Rosenzweig-MacArthur reaction-diffusion model, with alternating patch types, and study the PTWs in this system. Applying the method of homogenisation, we show how heterogeneity can affect the stability of PTW solutions. We illustrate how the effects of heterogeneity can be understood and interpreted using Turchin's concept of residence index (encapsuling diffusion rate and patch preference). In particular, our results show that prey heterogeneity acts to modulate the effects of predator heterogeneity, by this we mean that as prey increasingly spend more time in one patch type over another the stability of the PTWs becomes more sensitive to heterogeneity in predator movement and behaviour.
These lecture notes address the controllability under state constraints of reaction-diffusion equations arising in socio-biological contexts. We restrict our study to scalar equations with monostable and bistable nonlinearities.
The uncontrolled models describing, for instance, population dynamics, concentrations of chemicals, temperatures, etc., intrinsically preserve pointwise bounds of the states that represent a proportion, volume-fraction, or density. This is guaranteed, in the absence of control, by the maximum or comparison principle.
We focus on the classical controllability problem, in which one aims to drive the system to a final target, for instance, a steady-state. In this context the state is required to preserve, in the presence of controls, the pointwise bounds of the uncontrolled dynamics.
The presence of constraints introduces significant added complexity for the control process. They may force the needed control-time to be large enough or even make some natural targets to be unreachable, due to the presence of barriers that the controlled trajectories might not be able to overcome.
We develop and present a general strategy to analyze these problems. We show how the combination of the various intrinsic qualitative properties of the systems' dynamics and, in particular, the use of traveling waves and steady-states' paths, can be employed to build controls driving the system to the desired target.
We also show how, depending on the value of the Allee parameter and on the size of the domain in which the process evolves, some natural targets might become unreachable. This is consistent with empirical observations in the context of endangered minoritized languages and species at risk of extinction.
Further recent extensions are presented, and open problems are settled. All the discussions are complemented with numerical simulations to illustrate the main methods and results.
Rodent outbreaks have, in historical memory and at more or less regular intervals, massively affected crops and stored goods locally and sometimes even regionally. The Jura Massif is known, among other things, for its cheese specialties with several emblematic protected designations of origin (PDO), such as Comté, Morbier, Mont‐d'or and Bleu de Gex. In the 1950s, in this region of medium‐altitude mountains, grassland covered between 20% and almost 75% of farmland, regardless of altitude. From the early 1980s to the mid‐1990s, population demographic monitoring of small mammals was carried out in the Septfontaines and Le Souillot area, covering nearly 20,000 hectares. It has been suggested that predation is a major driver of fluctuations in rodent populations. It has taken about 30 years to describe and understand the factors that determine vole outbreaks in the Jura Massif in PDO grassland areas and to establish the basis for controlling them.
We prove existence and stability of entropy solutions for a predator-prey system consisting of an hyperbolic equation for predators and a parabolic-hyperbolic equation for preys. The preys' equation, which represents the evolution of a population of voles as in [2], depends on time, t, age, a, and on a 2-dimensional space variable x, and it is supplemented by a nonlocal boundary condition at a=0. The drift term in the predators' equation depends nonlocally on the density of preys and the two equations are also coupled via classical source terms of Lotka-Volterra type, as in [4]. We establish existence of solutions by applying the vanishing viscosity method, and we prove stability by a doubling of variables type argument.
La surveillance biologique des micromammifères est un pilier de la lutte raisonnée qui permet de conserver l’autonomie fourragère des exploitations agricoles en minimisant les impacts environnementaux. Actuellement, les méthodes existantes à l’échelle du territoire («scoring communal») et à l’échelle de la parcelle (diagonale indiciaire) permettent d’établir un diagnostic des populations et de définir la stratégie de lutte à adopter en fonction des niveaux de populations. Ces méthodes sont très consommatrices de temps et exigent des observateurs confirmés pour bien différencier les indices de taupes de ceux de campagnols. L’utilisation d’un drone, couplée à l’expertise d’un technicien de terrain, peut aider à la détection précoce des indices de micromammifères. Il reste à définir les modalités de son intégration dans les stratégies de lutte collective et dans les dispositifs d’accompagnement des agriculteurs.
We prove existence and stability of entropy weak solutions for a macroscopic PDE model for the spatial dynamics of a population of voles structured in age. The model consists of a scalar PDE depending on time, t, age, a, and space x=(x1,x2), supplemented with a non-local boundary condition at a=0. The flux is linear with constant coefficient in the age direction but contains a non-local term in the space directions. Also, the equation contains a term of second order in the space variables only. Existence of solutions is established by compensated compactness, see Panov (2009), and we prove stability by a doubling of variables type argument.
It is recognized that disturbances by fossorial small mammals are important factors determining plant community diversity, especially in grasslands. However, although information about the effects of disturbances by fossorial small mammals on species richness are starting to accumulate, we know little about the impact of these disturbances on the functional and phylogenetic facets of plant community diversity in grasslands.
In a study site located in the French Jura Mountains, we compared taxonomic, functional and phylogenetic diversity of plant communities in areas highly disturbed by montane water vole (Arvicola terrestris) with areas lowly disturbed by this small mammal. In accordance with previous studies, we found that species richness was higher in highly disturbed communities. Indeed, competitive species unable to withstand disturbances were less abundant in disturbed communities, allowing species less adapted to competition for light to survive. Because these species have different trait values in comparison to strong competitors, functional richness was also higher in highly disturbed communities. Results were similar for phylogenetic richness, maybe due to the fact that the used metric was not independent from species richness. Although species composition differed between highly and lowly disturbed communities, functional composition was very similar. Thereby, the studied disturbances were probably not strong enough to affect plant community functioning. Rao functional diversity and functional evenness were not different between both community types. Interestingly, phylogenetic evenness was lower in highly disturbed areas, supporting the idea that disturbances might select for disturbance tolerance traits that are phylogenetically conserved.
Though correlational, our results suggest that water vole disturbances may modify multiple facets of plant community diversity, while ecosystem functioning is maintained across disturbance levels. Further research is needed to understand causal mechanisms in this system and the ecological repercussions of small mammal disturbances more broadly.
Diverse patterns of species persistence, abundance, and distribution are seen in nature. Ecological interactions, environmental and habitat heterogeneity, demographic and genetic inhomogeneity—are some of the factors that shape population persistence, spatial distribution, and diversity of the species, as well as their life history traits. In this paper we model the effect of various forms of environmental (landscape and demographic) heterogeneities on the spatial dynamics of host-parasitoid metapopulations. These different forms of heterogeneity, coupled to different connectivity patterns of the habitat patches, lead to evolution of different spatial patterns in population distributions. The results explore the roles of different types of dispersal barriers and coexistence of different genotypes of host and parasitoid populations in migration and disease spread.
Patch-based graphs are widely used to display and quantify landscape connectivity. They are specially relevant for decision support in land planning and biological conservation. Matching connectivity analyses with practical actions in agricultural landscapes involves considering management units rather than habitat patches. However, at a local scale, the classical method for prioritizing graph elements (node removal) using connectivity indexes such as delta IIC could be viewed as a highly contrived approach with respect to the actual changes in land use. Here we address the relevance of this method compared to simulations likely to display these land-use changes in a more realistic way. Prioritization as determined by the removal method is tested here against simulated land-use changes in four scenarios (e.g. replacing grasslands by croplands) for an agricultural area in the Jura massif (eastern France) where field actions are undertaken to combat the spread of grassland rodents. The results obtained by ranking all the parcels ("enumerative" approach) show that the removal method provides rankings similar to those obtained with the land-use change scenarios, except for the planting of hedgerows. However, defining a limited number of key parcels ("cumulative" approach) results in different rankings whatever the scenarios. This shows that when applying parcel-based graphs to practical actions, the reliability of the removal method depends on the way the connectivity analysis is conducted. Simulating land-use changes, which is more realistic but more time-consuming, proves relevant if only a few key parcels need to be identified for actions to be conducted in the field.
The montane water vole, Arvicola scherman, can be found at low altitude in northwestern Spain, where it has become a key pest in apple orchards. Its sustainable control entails the knowledge of its reproduction pattern, which is unknown for this region. Thus, we conducted a study on more than 800 voles caught monthly over two years in apple orchards located in Asturias. Sexual characteristics, body measurements and relative age class were recorded. Intra-annual changes in body mass, testicular volume and seminal vesicle length of males did not affect significantly reproduction at a population scale, since pregnant females were detected over
the whole year and their occurrence did not show significant intra-annual differences. Consequently, the recruitment of young specimens was also continuous during the study period. Mild temperatures, even in winter, and ample food all the year around presumably meets the demands of physiological cost of continuous reproduction of A. scherman in this area. The implications of our results for facing this vole control in this agroecosystem are discussed. Furthermore, the information here reported might be useful to accurately assess theeffect of sustainable control strategies on the reproductive biology of fossorial water voles in this and in similar environments.
Periodic traveling waves (wavetrains) have been extensively studied for reaction-diffusion equations. One important motivation for this work has been the identification of periodic traveling wave patterns in spatiotemporal data sets in ecology. However, for many ecological populations, diffusion is no more than a rough phenomenological representation of dispersal, and spatial convolution with a dispersal kernel is more realistic. This paper concerns periodic traveling wave solutions of differential equations with nonlocal dispersal terms, and with local dynamics of lambda-omega form. These kinetics include the normal form near a standard supercritical Hopf bifurcation and are therefore significant for a wide range of applications. For general dispersal kernels, an explicit family of periodic traveling wave solutions is derived, as well as the condition for waves to be stable to perturbations of arbitrarily small wavenumber. Three specific kernels are then considered in detail: Laplace, Gaussian, and top hat. For Laplace and Gaussian kernels, it is shown that stability to perturbations of arbitrarily small wavenumber implies stability, a result that also applies for reaction-diffusion equations with lambda-omega kinetics. However, for the top hat kernel it is shown that periodic traveling waves may be stable to perturbations with small wavenumber but not to those with larger wavenumber. The wave family for the top hat kernel also shows significant qualitative differences from those for the Laplace and Gaussian kernels, and for reaction-diffusion equations with the same kinetics.
A method to estimate the abundance of the fossorial form of the water vole Arvicola terrestris scherman (Shaw, 1801) has been developed, by using surface indices. Results are compared to the standard method of estimation using trap lines. These results show quantitatively that it is possible to differentiate reliably mole indices from water vole indices. Moreover, the two species are inclined to exclude each other. Even though water voles share the same galleries as moles, specific surface indices of the water vole occur for any density exceeding 2 ind/trap line (over 20 ind/ha). Several models of abundance estimation are put forward, all of them using linear multiple regressions. Correlations between the estimations from indices and the estimations from trap lines exceed 0.8 and the limits of using abundance classes are tested. Other limits are developed in the discussion. One of them is that the sampling intervals are saturated for densities exceeding 400 ind/ha. The index method, which is easy to carry out, offers the definite advantage of being suitable to space and time scales otherwise incompatible with estimations from trap lines. For instance, it allows distribution maps from wide transects about areas of more than 25 km(2) to be drawn, in less than two days.
This article reviews various procedures used in the analysis of circadian rhythms at the populational, organismal, cellular and molecular levels. The procedures range from visual inspection of time plots and actograms to several mathematical methods of time series analysis. Computational steps are described in some detail, and additional bibliographic resources and computer programs are listed.
Long term population fluctuations of the fossorial form of the water vole, Arvicola terrestris, can be reconstructed on the basis of the rewards given to vole trappers ("tail-return statistics"). Nine time series of at least 20 yr of continuous data recorded during the 20th century in Switzerland have been analysed using time series analysis and tested for direct and delayed density dependence. Seven of these data sets showed cyclic changes in abundance with statistically significant maxima of the periodogram for periods ranging between 5 and 7 yr. Their partial autocorrelation functions suggested the presence of both direct or delayed density dependence in the data. This was confirmed by regression analysis using the nonlinear approach advocated by Turchin. In contrast, no simple periodicity could be found in the two remaining time series, nor indication for direct or delayed density dependence in their partial autocorrelation functions. However, direct density dependence was also statistically demonstrated in these two data sets. In most cases, the analyses were complicated by the presence of trends in the data. The detection of density-dependent regulatory effects was obscured by linear and nonlinear trends in one and two cases, respectively. The data support the hypothesis that time-delayed and nonlinear mechanisms of population regulation operate in fossorial populations of A. terrestris. Furthermore, the data are consistent with regulatory mechanisms involving predator-prey interactions, while the causation of the unusually long cycle is still an open question. Finally, the presence of trends in these time series suggests that water vole populations track some long-term climatic changes in the environment.
We show that the population ecology of the 9‐ to 10‐year cyclic, broadleaf‐defoliating winter moth ( Operophtera brumata ) and other early‐season geometrids cannot be fully understood on a local scale unless population behaviour is known on a European scale.
Qualitative and quantitative data on O. brumata outbreaks were obtained from published sources and previously unpublished material provided by authors of this article. Data cover six decades from the 1950s to the first decade of twenty‐first century and most European countries, giving new information fundamental for the understanding of the population ecology of O. brumata .
Analyses on epicentral, regional and continental scales show that in each decade, a wave of O. brumata outbreaks travelled across Europe.
On average, the waves moved unidirectionally ESE–WNW, that is, toward the Scandes and the Atlantic. When one wave reached the Atlantic coast after 9–10 years, the next one started in East Europe to travel the same c . 3000 km distance.
The average wave speed and wavelength was 330 km year ⁻¹ and 3135 km, respectively, the high speed being incongruous with sedentary geometrid populations.
A mapping of the wave of the 1990s revealed that this wave travelled in a straight E–W direction. It therefore passed the Scandes diagonally first in the north on its way westward. Within the frame of the Scandes, this caused the illusion that the wave moved N–S. In analogy, outbreaks described previously as moving S–N or occurring contemporaneously along the Scandes were probably the result of continental‐scale waves meeting the Scandes obliquely from the south or in parallel.
In the steppe zone of eastern‐most and south‐east Europe, outbreaks of the winter moth did not participate in the waves. Here, broadleaved stands are small and widely separated. This makes the zone hostile to short‐distance dispersal between O. brumata subpopulations and prevents synchronization within meta‐populations.
We hypothesize that hostile boundary models, involving reciprocal host–herbivore–enemy reactions at the transition between the steppe and the broadleaved forest zones, offer the best explanation to the origin of outbreak waves. These results have theoretical and practical implications and indicate that multidisciplinary, continentally coordinated studies are essential for an understanding of the spatio‐temporal behaviour of cyclic animal populations.
Spatial synchrony refers to coincident changes in the abundance or other time-varying characteristics of geographically disjunct populations. This phenomenon has been documented in the dynamics of species representing a variety of taxa and ecological roles. Synchrony may arise from three primary mechanisms: (a) dispersal among populations, reducing the size of relatively large populations and increasing relatively small ones; (b) congruent dependence of population dynamics on a synchronous exogenous random factor such as temperature or rainfall, a phenomenon known as the "Moran effect"; and (c) trophic interactions with populations of other species that are themselves spatially synchronous or mobile. Identification of the causes of synchrony is often difficult. In addition to intraspecific synchrony, there are many examples of synchrony among populations of different species, the causes of which are similarly complex and difficult to identify. Furthermore, some populations may exhibit complex spatial dynamics such as spiral waves and chaos. Statistical tests based on phase coherence and/or time-lagged spatial correlation are required to characterize these more complex patterns of spatial dynamics fully.
Formulae are given for estimators for the parameters F, θ, f (FIT, FST, FIS) of population structure. As with all such estimators, ratios are used so that their properties are not known exactly, but they have been found to perform satisfactorily in simulations. Unlike the estimators in general use, the formulae do not make assumptions concerning numbers of populations, sample sizes, or heterozygote frequencies. As such, they are suited to small data sets and will aid the comparisons of results of different investigators. A simple weighting procedure is suggested for combining information over alleles and loci, and sample variances may be estimated by a jackknife procedure.
Climate change has been identified as a causal factor for diverse ecological changes worldwide. Warming trends over the last couple of decades have coincided with the collapse of long-term population cycles in a broad range of taxa, although causal mechanisms are not well-understood. Larch budmoth (LBM) population dynamics across the European Alps, a classic example of regular outbreaks, inexplicably changed sometime during the 1980s after 1,200 y of nearly uninterrupted periodic outbreak cycles. Herein, analysis of perhaps the most extensive spatiotemporal dataset of population dynamics and reconstructed Alpine-wide LBM defoliation records reveals elevational shifts in LBM outbreak epicenters that coincide with temperature fluctuations over two centuries. A population model supports the hypothesis that temperature-mediated shifting of the optimal elevation for LBM population growth is the mechanism for elevational epicenter changes. Increases in the optimal elevation for population growth over the warming period of the last century to near the distributional limit of host larch likely dampened population cycles, thereby causing the collapse of a millennium-long outbreak cycle. The threshold-like change in LBM outbreak pattern highlights how interacting species with differential response rates to climate change can result in dramatic ecological changes.
Spatially synchronized fluctuations in system state are common in physical and biological systems ranging from individual atoms to species as diverse as viruses, insects and mammals. Although the causal factors are well known for many synchronized phenomena, several processes concurrently have an impact on spatial synchrony of species, making their separate effects and interactions difficult to quantify. Here we develop a general stochastic model of predator-prey spatial dynamics to predict the outcome of a laboratory microcosm experiment testing for interactions among all known synchronizing factors: (1) dispersal of individuals between populations; (2) spatially synchronous fluctuations in exogenous environmental factors (the Moran effect); and (3) interactions with other species (for example, predators) that are themselves spatially synchronized. The Moran effect synchronized populations of the ciliate protist Tetrahymena pyriformis; however, dispersal only synchronized prey populations in the presence of the predator Euplotes patella. Both model and data indicate that synchrony depends on cyclic dynamics generated by the predator. Dispersal, but not the Moran effect, 'phase-locks' cycles, which otherwise become 'decoherent' and drift out of phase. In the absence of cycles, phase-locking is not possible and the synchronizing effect of dispersal is negligible. Interspecific interactions determine population synchrony, not by providing an additional source of synchronized fluctuations, but by altering population dynamics and thereby enhancing the action of dispersal. Our results are robust to wide variation in model parameters representative of many natural predator-prey or host-pathogen systems. This explains why cyclic systems provide many of the most dramatic examples of spatial synchrony in nature.
We demonstrate evidence for the presence of travelling waves in a cyclic population of field voles in northern Britain by fitting simple, empirical models to spatially referenced time series data. Population cycles were broadly synchronous at all sites, but use of Mantel correlations suggested a strong spatial pattern along one axis at a projection line 72 degrees from North. We then fitted a generalized additive model to log population density assuming a fixed-form travelling wave in one spatial dimension for which the density at each site was offset in time by a constant amount from a standard density-time curve. We assumed that the magnitude of this offset would be proportional to the spatial separation between any given site and the centroid of the sampling sites, where separation is the distance between sites in a fixed direction. After fitting this model, we estimated that the wave moved at an average speed of 19 km yr-1, heading from West to East at an angle of 78 degrees from North. Nomadic avian predators which could synchronize populations over large areas are scarce and the travelling wave may be caused by density-dependent dispersal by field voles and/or predation by weasels, both of which act at a suitably small spatial scale.
Northern vole populations exhibit large-scale, spatially synchronous population dynamics. Such cases of population synchrony provide excellent opportunities for distinguishing between local intrinsic and regional extrinsic mechanisms of population regulation. Analyses of large-scale survey data and theoretical modelling have indicated several plausible synchronizing mechanisms. It is difficult, however, to determine the most important one without detailed data on local demographic processes. Here we combine results from two field studies in southeastern Norway--one identifies local demographic mechanisms and landscape-level annual synchrony among 28 enclosed experimental populations and the other examines region-level multi-annual synchrony in open natural populations. Despite fences eliminating predatory mammals and vole dispersal, the growth rates of the experimental populations were synchronized and moreover, perfectly linked with vole abundance in the region. The fates of 481 radio-marked voles showed that bird predation was the synchronizing mechanism. A higher frequency of risky dispersal movements in slowly growing populations appeared to accelerate predation rate. Thus, dispersal may induce a feedback-loop between predation and population growth that enhances synchrony.
Spatio-temporal travelling waves are striking manifestations of predator-prey and host-parasite dynamics. However, few systems are well enough documented both to detect repeated waves and to explain their interaction with spatio-temporal variations in population structure and demography. Here, we demonstrate recurrent epidemic travelling waves in an exhaustive spatio-temporal data set for measles in England and Wales. We use wavelet phase analysis, which allows for dynamical non-stationarity--a complication in interpreting spatio-temporal patterns in these and many other ecological time series. In the pre-vaccination era, conspicuous hierarchical waves of infection moved regionally from large cities to small towns; the introduction of measles vaccination restricted but did not eliminate this hierarchical contagion. A mechanistic stochastic model suggests a dynamical explanation for the waves-spread via infective 'sparks' from large 'core' cities to smaller 'satellite' towns. Thus, the spatial hierarchy of host population structure is a prerequisite for these infection waves.
The vast majority of models for spatial dynamics of natural populations assume a homogeneous physical environment. However, in practice, dispersing organisms may encounter landscape features that significantly inhibit their movement. We use mathematical modelling to investigate the effect of such landscape features on cyclic predator-prey populations. We show that when appropriate boundary conditions are applied at the edge of the obstacle, a pattern of periodic travelling waves develops, moving out and away from the obstacle. Depending on the assumptions of the model, these waves can take the form of roughly circular 'target patterns' or spirals. This is, to our knowledge, a new mechanism for periodic-wave generation in ecological systems and our results suggest that it may apply quite generally not only to cyclic predator-prey interactions, but also to populations that oscillate for other reasons. In particular, we suggest that it may provide an explanation for the observed pattern of travelling waves in the densities of field voles (Microtus agrestis) in Kielder Forest (Scotland-England border) and of red grouse (Lagopus lagopus scoticus) on Kerloch Moor (northeast Scotland), which in both cases move orthogonally to any large-scale obstacles to movement. Moreover, given that such obstacles to movement are the rule rather than the exception in real-world environments, our results suggest that complex spatio-temporal patterns such as periodic travelling waves are likely to be much more common in the natural world than has previously been assumed.
Spatially extended population models predict complex spatiotemporal patterns, such as spiral waves and spatial chaos, as a result of the reaction-diffusion dynamics that arise from trophic interactions. However, examples of such patterns in ecological systems are scarce. We develop a quantitative technique to demonstrate the existence of waves in Central European larch budmoth (Zeiraphera diniana Gn.) outbreaks. We show that these waves travel toward the northeast-east at 210 kilometers per year. A theoretical model involving a moth-enemy interaction predicts directional waves, but only if dispersal is directionally biased or habitat productivity varies across the landscape. Our study confirms that nonlinear ecological interactions can lead to complex spatial dynamics at a regional scale.
Periodic patterns in time series resulting from biological experiments are of great interest. The commonly used Fast Fourier Transform (FFT) algorithm is applicable only when data are evenly spaced and when no values are missing, which is not always the case in high-throughput measurements. The choice of statistic to evaluate the significance of the periodic patterns for unevenly spaced gene expression time series has not been well substantiated.
The Lomb-Scargle periodogram approach is used to search time series of gene expression to quantify the periodic behavior of every gene represented on the DNA array. The Lomb-Scargle periodogram analysis provides a direct method to treat missing values and unevenly spaced time points. We propose the combination of a Lomb-Scargle test statistic for periodicity and a multiple hypothesis testing procedure with controlled false discovery rate to detect significant periodic gene expression patterns.
We analyzed the Plasmodium falciparum gene expression dataset. In the Quality Control Dataset of 5080 expression patterns, we found 4112 periodic probes. In addition, we identified 243 probes with periodic expression in the Complete Dataset, which could not be examined in the original study by the FFT analysis due to an excessive number of missing values. While most periodic genes had a period of 48 h, some had a period close to 24 h. Our approach should be applicable for detection and quantification of periodic patterns in any unevenly spaced gene expression time-series data.
The effect of landscape mosaic on recurrent traveling waves in spatial population dynamics was studied via simulation modeling across a theoretical landscape with varying levels of connectivity. Phase angle analysis was used to identify locations of wave epicenters on patchy landscapes. Simulations of a tri-trophic model of the larch budmoth (Zeiraphera diniana) with cyclic population dynamics on landscapes with a single focus of high-density habitat produced traveling waves generally radiating outwardly from single and multiple foci and spreading to isolated habitats. We have proposed two hypotheses for this result: (1) immigration subsidies inflate population growth rates in the high connectivity habitat and, thus, reduce the time from valleys to peaks in population cycles; (2) populations in the high connectivity habitat crash from peaks to valleys faster than in an isolated habitat due to over-compensatory density dependence. While population growth rates in the high connectivity habitat benefitted from immigration subsidies, times from population valleys to peaks were greater in high connectivity habitat due to a greater magnitude of fluctuations. Conversely, the mean time of the crash from population peaks to valleys was shorter in high connectivity habitat, supporting the second hypothesis. Results of this study suggest over-compensatory density dependence as an underlying mechanism for recurrent traveling waves originating in high connectivity habitats aggregated around a single focus.
We demonstrate changes over time in the spatial and temporal dynamics of an herbivorous small rodent by analyzing time series of population densities obtained at 21 locations on clear cuts within a coniferous forest in Britain from 1984 to 2004. Changes had taken place in the amplitude, periodicity, and synchrony of cycles and density-dependent feedback on population growth rates. Evidence for the presence of a unidirectional traveling wave in rodent abundance was strong near the beginning of the study but had disappeared near the end. This study provides empirical support for the hypothesis that the temporal (such as delayed density dependence structure) and spatial (such as traveling waves) dynamics of cyclic populations are closely linked. The changes in dynamics were markedly season specific, and changes in overwintering dynamics were most pronounced. Climatic changes, resulting in a less seasonal environment with shorter winters near the end of the study, are likely to have caused the changes in vole dynamics. Similar changes in rodent dynamics and the climate as reported from Fennoscandia indicate the involvement of large-scale climatic variables.
Periodic travelling waves have been reported in a number of recent spatio-temporal field studies of populations undergoing multi-year cycles. Mathematical modelling has a major role to play in understanding these results and informing future empirical studies. We review the relevant field data and summarize the statistical methods used to detect periodic waves. We then discuss the mathematical theory of periodic travelling waves in oscillatory reaction-diffusion equations. We describe the notion of a wave family, and various ecologically relevant scenarios in which periodic travelling waves occur. We also discuss wave stability, including recent computational developments. Although we focus on oscillatory reaction-diffusion equations, a brief discussion of other types of model in which periodic travelling waves have been demonstrated is also included. We end by proposing 10 research challenges in this area, five mathematical and five empirical.
Recent field data indicate that in a number of cyclic populations, the cycles are organized spatially with the form of a periodic traveling wave. One way in which this type of wave is generated is when dispersing individuals encounter landscape features that impede movement in certain directions. In this article, we investigate the dependence of such periodic waves on ecological parameters and on the form of the landscape feature. Using a standard predator-prey model as a prototype for a cyclic population, we calculate the speed and amplitude of waves generated by a large landscape feature. This enables us to determine parameters for which the waves are stable; in other cases, they evolve into irregular oscillations. We then undertake for the first time a detailed study of the effects of the size and shape of a landscape feature on the waves that it generates. We show that size rather than shape is the key wave-forming property, with smaller obstacles generating waves with longer wavelength and waves from larger landscape features dominating those from smaller ones. Our results suggest that periodic traveling waves may be much more common than has previously been assumed in real ecological systems, and they enable quantitative predictions on the properties of these waves for particular cases.
Ecological variables often fluctuate synchronously over wide geographical areas, a phenomenon known as spatial autocorrelation or spatial synchrony. Development of statistical approaches designed to test for spatial autocorrelation combined with the increasing accessibility of long-term, large-scale ecological datasets are now making it possible to document the patterns and understand the causes of spatial synchrony at scales that were previously intractable. These developments promise to foster significant future advances in understanding population regulation, metapopulation dynamics and other areas of population ecology.
Many empirical studies have assessed fine-scale spatial genetic structure (SGS), i.e. the nonrandom spatial distribution of genotypes, within plant populations using genetic markers and spatial autocorrelation techniques. These studies mostly provided qualitative descriptions of SGS, rendering quantitative comparisons among studies difficult. The theory of isolation by distance can predict the pattern of SGS under limited gene dispersal, suggesting new approaches, based on the relationship between pairwise relatedness coefficients and the spatial distance between individuals, to quantify SGS and infer gene dispersal parameters. Here we review the theory underlying such methods and discuss issues about their application to plant populations, such as the choice of the relatedness statistics, the sampling scheme to adopt, the procedure to test SGS, and the interpretation of spatial autocorrelograms. We propose to quantify SGS by an ' Sp ' statistic primarily dependent upon the rate of decrease of pairwise kinship coefficients between individuals with the logarithm of the distance in two dimensions. Under certain conditions, this statistic estimates the reciprocal of the neighbourhood size. Reanalysing data from, mostly, published studies, the Sp statistic was assessed for 47 plant species. It was found to be significantly related to the mating system (higher in selfing species) and to the life form (higher in herbs than trees), as well as to the population density (higher under low density). We discuss the necessity for comparing SGS with direct estimates of gene dispersal distances, and show how the approach presented can be extended to assess (i) the level of biparental inbreeding, and (ii) the kurtosis of the gene dispersal distribution.
Red Grouse (Lagopus lagopus scoticus) showed two population density cycles during an 18-yr study on 14 km2 of heather moorland that formed part of a larger moorland tract in northeast Scotland. Fluctuations on 22 different parts of the study area were somewhat asynchronous. Synchrony between parts decreased with distance. The dependence of densities in adjacent parts upon one another was analyzed in two stages. First, population trajectories were modeled with no time component. Second, the fit of these models was significantly improved by adding a time component. This provided evidence for a demographic wave traveling at 2-3 km/yr. It traveled from the center of the moorland tract toward its margin, which adjoined farms and woodland unoccupied by grouse.
It is shown that trapping figures for the lynx are definitely related to
weather conditions. The significance of this for the various theories of the
origin and synchronization of the cycle is discussed.
This study investigates the effect of land use, and landscape composition and structure on the population dynamics of fossorial water vole (Arvicola terrestris scherman Shaw). Water vole populations were monitored from 1989 to 1994 in the Doubs department, France, by using index methods. Land use patterns were studied based on agriculture and forestry data from the French Ministry of Agriculture collected in 1956, 1970, 1979 and 1988. Grassland quality and landscape structure were studied based on field transects, combined with the assessment of landscape structure from maps at 1:25,000 scale. Outbreaks of water vole populations occurred as a wave, spreading from epicentres over more than 2500 km2. The propagation speed was in excess of 10 km/yr. On a regional level (n × 10 km) and over 5 years and more, density variation patterns of water vole were linked to the ratio of ploughed land and of permanent grassland to farmland. At a sectional scale (n × 1 km), forests and uncultivated lands had a dampening effect both on the outbreaks and on their duration. The evolution of farmlands from 1956 to 1988 was apparently the major cause of increase in density variations of water vole. Therefore, land use and landscape management could be a way to control water vole outbreaks, and their effects are discussed.
Pour tenter de prévenir les pullulations d'Arvicola terrestris scherman, certaines communes de Suisse offrent une prime de piégeage pour tout micromammifère capturé sur leur territoire. L'analyse des carnets de comptes permet ensuite de reconstituer les cycles d'abondance d'A. t. scherman. Les données récoltées en Suisse occidentale auprés de 11 communes du Jura et des Préalpes ont permis de reconstituer 37 cycles complets entre 1935 et 1984. La durée de ces cycles est plus longue que chez la plupart des autres espéces de rongeurs, soil 6 ans en moyenne, avec des extrêmes compris entre 4 et 8 ans. Ce matériel a étéétudie par les techniques de l'analyse des séries temporelles. Les résultats prouvent qu'une périodicité, statistiquement démontrée, existe dans ces données et que les fluctuations d'abondance d'A. terrestris ne se déroulent pas selon un rythme aléatoire. L'indice de cyclicité de Lewontin est généralement supérieur à 0,50 et le périodogramme présente un maximum compris entre 5 et 7,5 ans, suivant les cas. Mis à part dans deux localités des Préalpes adjacentes, les pullulations ne sont pas synchrones entre stations éloignées au plus de quelques dizaines de km les unes des autres. Une analyse de corrélation a mis en évidence des décalages entre les séries compris entre 1 et 7 ans. Ces résultats suggèrent que des causes de nature intrinséque sont à l'origine des cycles d'abondance chez A. terrestris. L'impact de la prédation par Mustela erminea en période de déclin et de faible densité explique probablement la durée inhabituelle du cycle.
1 . Earlier studies have reported that field vole Microtus agrestis populations in Kielder Forest, UK, exhibit typical 3–4‐year cyclical dynamics, and that the observed spatiotemporal patterns are consistent with a travelling wave in vole abundance moving along an axis south‐west–north‐east at approximately 19 km year –1 . One property of this wave is that nearby populations fluctuate more synchronously than distant ones, with correlations falling lower than the average for the sampling area beyond approximately 13 km.
2 . In this paper we present a series of models that investigate the possibility that both the observed degree of synchrony and the travelling wave can be explained as a simple consequence of linking a series of otherwise independently oscillating populations. Our ‘coupled oscillator’ models consider a series of populations, distributed either in a linear array or in a two‐dimensional regular matrix. Local population fluctuations, each with a 3–4‐year period, were generated using either a Ricker equation or a set of discrete‐time Lotka–Volterra equations. Movement among populations was simulated either by a fixed proportion of each population moving locally to their nearest neighbour populations, or the same proportion being distributed via a continuous geometric function (more distant populations receiving less).
3 . For a variety of different ways of generating cycles and a number of different movement rules, local exchange between oscillating populations tended to generate synchrony domains that extended over a large number of populations. When the rates of exchange between local populations were relatively low, then permanent travelling waves emerged, especially after an initial invasion phase. There was a non‐linear relationship between the amount of dispersal and the domain of synchrony that this movement generated. Furthermore, the observed spatiotemporal patterns that emerged following an initial invasion phase were found to be highly dependent on the extreme distances reached by rare dispersers.
4 . As populations of voles are predominantly distributed in grassland patches created by clear‐cutting of forest stands, we estimated the mean patch diameter and mean interpatch distance using a geographical information system (GIS) of the forest. Our simplified models suggest that if as much as 5–10% of each vole population dispersed a mean of 178 m between clear‐cuts per generation, then this would generate a synchrony domain and speed of wave in the region of 6–24 km (per year), which is reasonably consistent with the observed synchrony domain and speed. Much less dispersal would be capable of generating this scale of domain if some individuals occasionally moved beyond the nearest‐neighbour patch.
5 . While we still do not know what causes the local oscillations, our models question the need to invoke additional factors to explain large‐scale synchrony and travelling waves beyond small‐scale dispersal and local density‐dependent feedback. Our work also suggests that the higher degrees of synchrony observed in Fennoscandian habitats compared with Kielder may be due in part to the relative ease of movement of voles in these former habitats. As our work confirms that the rates of exchange among local populations will have a strong influence on synchrony, then we anticipate that the spatiotemporal distribution of clear‐cuts will also have an important influence on the dynamics of predators of voles.
Recent characterizations of the spatial scale of population dynamics have typically considered patterns at a single scale and ignored the possibility that different patterns may arise at different scales. In this study we assessed population densities of field voles with cyclic dynamics in northern England at 147 sites from three spatial scales on five occasions over a 2·5‐year period.
The scale over which densities were similar was estimated by comparing the variance of density at the three scales (< 1 km ² , 10 km ² , and 70 km ² ) and by using autocorrelation techniques. Closer sites were more similar in density than more distant sites and the autocorrelations suggested that sites up to within 8–20 km had more similar densities and higher population synchrony than the average similarity for all the sampling sites.
A generalized additive model fitted to all the data showed that the data supported the hypothesis of a travelling wave of vole densities moving through the study area. The model assumed that the wave moved at a constant speed and in a uniform direction. Estimates of the wave’s speed (14 km year ⁻¹ ) and direction (travelling in a direction of 66° from north) were consistent with the estimates which had previously been calculated from a time series of vole densities covering a much smaller spatial area but a longer temporal scale.
The spatio‐temporal pattern of vole densities detected over a small spatial scale therefore appears to extend over much larger scales and occurs despite the fragmentation of suitable vole habitat at local (a few square kilometres) and regional (hundreds of square kilometres) scales.
Travelling waves in cyclic populations refer to temporal shifts in peak densities moving across space in a wave-like fashion. The epicentre hypothesis states that peak densities begin in specific geographic foci and then spread into adjoining areas. Travelling waves have been confirmed in a number of population systems, begging questions about their causes. Herein we apply a newly developed statistical technique, wavelet phase analysis, to historical data to document that the travelling waves in larch budmoth (LBM) outbreaks arise from two epicentres, both located in areas with high concentrations of favourable habitat. We propose that the spatial arrangement of the landscape mosaic is responsible for initiating the travelling waves. We use a tri-trophic model of LBM dynamics to demonstrate that landscape heterogeneity (specifically gradients in density of favourable habitat) alone, is capable of inducing waves from epicentres. Our study provides unique evidence of how landscape features can mould travelling waves.
Population changes in long-eared owls Asio otus, polecats Mustela putorius, red foxes Vulpes vulpes, stone martens Martes foina and badgers Meles meles were monitored during a water vole Arvicola terrestris scherman cycle in western Switzerland. Long-eared owls confirmed their status of highly mobile specialist predators in responding strongly and without time lag to water vole population changes. Even though polecats are considered generalists, they exhibited also a strong response to water vole fluctuations. Their numbers tracked water vole densities with a 1-yr time lag. Marked population changes were also recorded in red foxes and stone martens, but these changes were not related to water vole densities. Lastly, badgers did not show any significant population changes during the water vole cycle. We discuss the possible reasons for these differences and conclude that multi-factorial approach is clearly required to understand population processes in predator-prey systems.
The statistical properties of least-squares frequency analysis of unequally spaced data are examined. It is shown that, in the least-squares spectrum of gaussian noise, the reduction in the sum of squares at a particular frequency is aX
2
2
variable. The reductions at different frequencies are not independent, as there is a correlation between the height of the spectrum at any two frequencies,f
1 andf
2, which is equal to the mean height of the spectrum due to a sinusoidal signal of frequencyf
1, at the frequencyf
2. These correlations reduce the distortion in the spectrum of a signal affected by noise. Some numerical illustrations of the properties of least-squares frequency spectra are also given.
Extensions of nondirectional spatial autocorrelation techniques to two dimensions have existed for many years, but the results are difficult to compare to the traditional nondirectional techniques and often lack ease of interpretability. This paper reviews the traditional one- and two-dimensional spatial autocorrelation methods and proposes a new directional method which is both easier to compare to nondirectional methods and easier to interpret than previous directional methods.
Ecology Letters (2011) 14: 163–168
Spatially separated populations of many species fluctuate synchronously. Synchrony typically decays with increasing interpopulation distance. Spatial synchrony, and its distance decay, might reflect distance decay of environmental synchrony (the Moran effect), and/or short-distance dispersal. However, short-distance dispersal can synchronize entire metapopulations if within-patch dynamics are cyclic, a phenomenon known as phase locking. We manipulated the presence/absence of short-distance dispersal and spatially decaying environmental synchrony and examined their separate and interactive effects on the synchrony of the protist prey species Tetrahymena pyriformis growing in spatial arrays of patches (laboratory microcosms). The protist predator Euplotes patella consumed Tetrahymena and generated predator–prey cycles. Dispersal increased prey synchrony uniformly over both short and long distances, and did so by entraining the phases of the predator–prey cycles. The Moran effect also increased prey synchrony, but only over short distances where environmental synchrony was strongest, and did so by increasing the synchrony of stochastic fluctuations superimposed on the predator–prey cycle. Our results provide the first experimental demonstration of distance decay of synchrony due to distance decay of the Moran effect. Distance decay of the Moran effect likely explains distance decay of synchrony in many natural systems. Our results also provide an experimental demonstration of long-distance phase locking, and explain why cyclic populations provide many of the most dramatic examples of long-distance spatial synchrony in nature.
The search for mechanisms behind spatial population synchrony is currently a major issue in population ecology. Theoretical studies highlight how synchronizing mechanisms such as dispersal, regionally correlated climatic variables and mobile enemies might interact with local dynamics to produce different patterns of spatial covariance. Specialized statistical methods, applied to large-scale survey data, aid in testing the theoretical predictions with empirical estimates. Observational studies and experiments on the demography of local populations are paramount to identify the true ecological mechanisms. The recent achievements illustrate the power of combining theory, observation and/or experimentation and statistical modeling in the ecological research protocol.
Dengue fever is a mosquito-borne virus that infects 50-100 million people each year. Of these infections, 200,000-500,000 occur as the severe, life-threatening form of the disease, dengue haemorrhagic fever (DHF). Large, unanticipated epidemics of DHF often overwhelm health systems. An understanding of the spatial-temporal pattern of DHF incidence would aid the allocation of resources to combat these epidemics. Here we examine the spatial-temporal dynamics of DHF incidence in a data set describing 850,000 infections occurring in 72 provinces of Thailand during the period 1983 to 1997. We use the method of empirical mode decomposition to show the existence of a spatial-temporal travelling wave in the incidence of DHF. We observe this wave in a three-year periodic component of variance, which is thought to reflect host-pathogen population dynamics. The wave emanates from Bangkok, the largest city in Thailand, moving radially at a speed of 148 km per month. This finding provides an important starting point for detecting and characterizing the key processes that contribute to the spatial-temporal dynamics of DHF in Thailand.
Many empirical studies have assessed fine-scale spatial genetic structure (SGS), i.e. the nonrandom spatial distribution of genotypes, within plant populations using genetic markers and spatial autocorrelation techniques. These studies mostly provided qualitative descriptions of SGS, rendering quantitative comparisons among studies difficult. The theory of isolation by distance can predict the pattern of SGS under limited gene dispersal, suggesting new approaches, based on the relationship between pairwise relatedness coefficients and the spatial distance between individuals, to quantify SGS and infer gene dispersal parameters. Here we review the theory underlying such methods and discuss issues about their application to plant populations, such as the choice of the relatedness statistics, the sampling scheme to adopt, the procedure to test SGS, and the interpretation of spatial autocorrelograms. We propose to quantify SGS by an 'Sp' statistic primarily dependent upon the rate of decrease of pairwise kinship coefficients between individuals with the logarithm of the distance in two dimensions. Under certain conditions, this statistic estimates the reciprocal of the neighbourhood size. Reanalysing data from, mostly, published studies, the Sp statistic was assessed for 47 plant species. It was found to be significantly related to the mating system (higher in selfing species) and to the life form (higher in herbs than trees), as well as to the population density (higher under low density). We discuss the necessity for comparing SGS with direct estimates of gene dispersal distances, and show how the approach presented can be extended to assess (i) the level of biparental inbreeding, and (ii) the kurtosis of the gene dispersal distribution.
Genetic structure can be strongly affected by landscape features and variation through time and space of demographic parameters such as population size and migration rate. The fossorial water vole (Arvicola terrestris) is a cyclic species characterized by large demographic fluctuations over short periods of time. The outbreaks do not occur everywhere at the same time but spread as a wave at a regional scale. This leads to a pattern of large areas (i.e. some hundreds of km2), each with different vole abundances, at any given time. Here, we describe the abundance and genetic structures in populations of the fossorial water vole. We use the data to try to understand how landscape and demographic features act to shape the genetic structure. The spatial variability of vole abundance was assessed from surface indices, collected in spring 2002 (April) in eastern central France. Genetic variability was analysed using eight microsatellite loci at 23 localities sampled between October 2001 and April 2002. We found some congruence between abundance and genetic structures. At a regional scale, the genetic disruptions were associated with both sharp relief and transition between an area of low abundance and another of high abundance. At a local scale, we observed a variation of the isolation-by-distance pattern according to the abundance level of vole populations. From these results we suggest that the dispersal pattern in cyclic rodent populations varies throughout the demographic cycle.
Theory predicts that the impact of gene flow on the genetic structure of populations in patchy habitats depends on its scale and the demographic attributes of demes (e.g. local colony sizes and timing of reproduction), but empirical evidence is scarce. We inferred the impact of gene flow on genetic structure among populations of water voles Arvicola terrestris that differed in average colony sizes, population turnover and degree of patchiness. Colonies typically consisted of few reproducing adults and several juveniles. Twelve polymorphic microsatellite DNA loci were examined. Levels of individual genetic variability in all areas were high (H(O) = 0.69-0.78). Assignments of juveniles to parents revealed frequent dispersal over long distances. The populations showed negative F(IS) values among juveniles, F(IS) values around zero among adults, high F(ST) values among colonies for juveniles, and moderate, often insignificant, F(ST) values for parents. We inferred that excess heterozygosity within colonies reflected the few individuals dispersing from a large area to form discrete breeding colonies. Thus pre-breeding dispersal followed by rapid reproduction results in a seasonal increase in differentiation due to local family groups. Genetic variation was as high in low-density populations in patchy habitats as in populations in continuous habitats used for comparison. In contrast to most theoretical predictions, we found that populations living in patchy habitats can maintain high levels of genetic variability when only a few adults contribute to breeding in each colony, when the variance of reproductive success among colonies is likely to be low, and when dispersal between colonies exceeds nearest-neighbour distances.
In cyclic populations, high genetic diversity is currently reported despite the periodic low numbers experienced by the populations during the low phases. Here, we report spatio-temporal monitoring at a very fine scale of cyclic populations of the fossorial water vole (Arvicola terrestris) during the increasing density phase. This phase marks the transition from a patchy structure (demes) during low density to a continuous population in high density. We found that the genetic diversity was effectively high but also that it displayed a local increase within demes over the increasing phase. The genetic diversity remained relatively constant when considering all demes together. The increase in vole abundance was also correlated with a decrease of genetic differentiation among demes. Such results suggest that at the end of the low phase, demes are affected by genetic drift as the result of being small and geographically isolated. This leads to a loss of local genetic diversity and a spatial differentiation among demes. This situation is counterbalanced during the increasing phase by the spatial expansion of demes and the increase of the effective migration among differentiated demes. We provide evidences that in cyclic populations of the fossorial water voles, the relative influence of drift operating during low density populations and migration occurring principally while population size increases interacts closely to maintain high genetic diversity.