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A Matrix Model to Study the Colonization by Brown Trout of a Virgin Ecosystem in the Kerguelen Islands
Abstract
We present a matrix model for the study of the population dynamics of brown trout Salmo trutta L., introduced in the '60s in the virgin aquatic ecosystems of the Kerguelen Islands. This species clearly acclimatized very well: a portion of the population became migratory and spent a part of its life cycle in the sea, which allowed the rapid colonization of two rivers close to the stream of origin in the same bay (Baie Norvégienne).
These migratory trout can become a smolt at 2, 3, or 4 years of age. The model takes into account age and smolt age structures and in a first step considers the fish from the Baie Norvégienne as belonging to a single population. The transition matrix looks like a 32 × 32 Leslie matrix in which some survival rates are not on the subdiagonal. They represent survival after the first sea migration and are particularly important for the dynamics of the whole population.
The estimate of demographic parameters was obtained from a data base containing information collected in the field since 1970. The model was calibrated on the population size estimate and the stock structure of the migratory trout in 1979. Population size was estimated by tagging-recapture and monitoring of the migratory trout in freshwater when they returned to overwinter or reproduce. Under the hypothesis of a constant survival rate for all ages and categories of fish, it was possible to determine relationships between the annual population growth rate and survival rates at first downstream migration, for which no direct estimate was available.
These constraints on the model induced paradoxical results. For instance, an increase in survival rate reduced migratory trout numbers in the first years of colonization. These data suggested that the average survival rate should be around 0.3 and not 0.5 as surmised in previous studies. However, the model systematically underestimated numbers of migratory trout during the first years of development. Thus, to improve the model it will be necessary to introduce survival rates varying with time. Another possible approach would be to consider the population as three subunits corresponding to the three colonized rivers of the Baie Norvégienne.
... Modelling is then a convenient tool to describe and understand fish population dynamics. Some recent models have been developed to describe these phenomena, especially with salmonids (Elliott, 1985; Beall, 1992, 1997; Ratner et al., 1997; Sabaton et al., 1997; Jarry et al., 1998; Shuter et al., 1998; Gouraud et al., 1999), but always at a small spatial scale involving a single stream (one patch) and without considering a time scale faster for migration than for demography . Nevertheless, fishes, and S. trutta is a good example, generally migrate to achieve their life cycle: especially for reproduction once a year (Ovidio et al., 1998), or frequently for habitat or food searching. ...
... Nevertheless, fishes, and S. trutta is a good example, generally migrate to achieve their life cycle: especially for reproduction once a year (Ovidio et al., 1998), or frequently for habitat or food searching. Even if homing behaviour is described for brown trout population, few studies have been performed to quantify either the proportion of returning adults into their natal stream, or the in-stream mortality during this spawning migration (Jarry et al., 1998; Ovidio et al., 1998). Other authors described individual movements of a brown trout population at fast time scales in food searching (Gowan et al., 1994). ...
In the present paper, the annual spawning migration of adults is introduced into a model, describing the Salmo trutta population dynamics in a hierarchically organized river network (four levels and 15 interconnected patches) model based on previous work. The model describes simultaneously demographic and migration processes taking place at different time scales: migrations of individuals between patches at a fast time scale (e.g. the week or the month), the annual spawning migration of adults and the demography at the slow time scale of the year. The S. trutta population is sub-divided into three age-classes (young of the year, juveniles, and adults). We used a Leslie-type model, coupled with a migration matrix associated with the annual spawning process, and a second migration matrix associated with fast movements of individuals between patches throughout the year. All demographic and migratory parameters are constant, leading to a linear model governing 45 state variables (15 patches x three age-classes). By taking advantage of the two time scales and using aggregation techniques for the case of discrete time models, the complete model was approximated by a reduced one, with only three global variables (one per age-class) evolving at the slow time scale. Demographic indices were calculated for the population, and a sensibility analysis was performed to detect which parameters influence the most model predictions. We also quantified how modifications of the river network structure, by channels (change in connections between patches) or dams (patch deletion), influence the global population dynamics. We checked that the strategy of annual spawning migrations is actually beneficial for the population (the asymptotic population growth rate is increased), and that dams may have a more detrimental effect on the whole population dynamics than channelling.
... For each river, 30 one-year fish (juveniles) from a single station were randomly chosen for genotyping. This age was chosen to make sure the individuals studied were born in the river because Kerguelen trout do not migrate before they reach 2 years of age (Jarry et al. 1998). Thirty adult sea trout from the 3 source rivers (i.e., individuals returning in the river after a growth period in the sea) were genotyped. ...
... Adult sea trout are the most efficient colonizing individuals because of a very high fecundity and capacity to migrate (Davaine and Beall 1997). However, they are the least abundant class of fish in a population (Thomas et al. 1981;Jarry et al. 1998) and, in addition, the proportion of strayers in brown trout is known to be low within a population (Le Cren 1985). Therefore the colonization of a nearby new river will probably not become effective until the number of sea trout and, consequently, the whole population size have become quite large. ...
Human-mediated biological invasions constitute interesting case studies to understand evolutionary processes, including the role of founder effects. Population expansion of newly introduced species can be highly dependant on barriers caused by landscape features, but identifying these barriers and their impact on genetic structure is a relatively recent concern in population genetics and ecology. Salmonid populations of the Kerguelen Islands archipelago are a favorable model system to address these questions as these populations are characterized by a simple history of introduction, little or no anthropogenic influence, and demographic monitoring since the first introductions. We analyzed genetic variation at 10 microsatellite loci in 19 populations of brown trout (Salmo trutta L.) in the Courbet Peninsula (Kerguelen Islands), where the species, introduced in 3 rivers only, has colonized the whole water system in 40 years. Despite a limited numbers of introductions, trout populations have maintained a genetic diversity comparable with what is found in hatchery or wild populations in Europe, but they are genetically structured. The main factor explaining the observed patterns of genetic diversity is the history of introductions, with each introduced population acting as a source for colonization of nearby rivers. Correlations between environmental and genetic parameters show that within each "source population" group, landscape characteristics (type of coast, accessibility of river mouth, distances between rivers, river length ...) play a role in shaping directions and rates of migration, and thus the genetic structure of the colonizing populations.
... While several studies have focused specifically on the post-introduction fate of S. trutta in the islands (e.g. Jarry et al., 1998;Morat et al., 2008;Hórreo et al., 2011;Labonne et al., 2013;Jaffal et al., 2015;Aymes et al., 2016;Jarry et al., 2018;Marandel et al., 2018), none have focussed in detail on the fate of S. alpinus despite its relative colonization success, i.e. one success in two trials . ...
Subsequent to their introduction in the 1950s, Arctic charr Salvelinus alpinus have been able to establish a self-sustaining population that has adapted to the unique conditions of the Kerguelen Islands in the sub-Antarctic. Here, 48 individuals (198-415 mm) were caught with gillnets and their basic biology and feeding ecology were examined using stable isotope analysis. The Lac des Fougères population split use of littoral and pelagic resources evenly, although larger fish relied more heavily on littoral production and appear to follow the size-dependent life-history habitat template seen in many Scandinavian lakes where smaller sized individuals occupy the pelagic zone and larger individuals dominate the littoral habitat. In Kerguelen Arctic charr mature at the same ages (5.6 years) as Arctic charr in both sub-Arctic and Arctic lakes. Whereas mortality was average in comparison to comparator sub-Arctic lakes, it was high in comparison to Arctic lakes. Maximal age (>7+) was at the lower end of the range typically seen in sub-Arctic lakes. Although they inhabit a resource poor environment, Kerguelen Arctic charr showed no evidence of cannibalism. Thus, while Arctic charr can survive and reproduce in the relatively unproductive Kerguelen lake environments, survival and growth nevertheless appear to be traded off against survival and longevity.
... Cependant, plusieurs travaux de modélisation se sont déjà intéressés à ce cas d'étude. Ainsi, Jarry et al. (1998) ont construit un modèle matriciel de dynamique de population. Plus récemment, Labonne et al. (2013) ont utilisé une approche de modélisation mécaniste avec un cadre métapopulationnel, basé sur une dispersion de propagules et une fonction de colonisation, pour analyser l'importance de la configuration spatiale et de facteurs temporels et écologiques dans le succès de la colonisation des îles Kerguelen par la truite de mer. ...
Le changement climatique en cours modifie les conditions environnementales et les espèces doivent s'adapter à ces nouvelles conditions, en restant sur place ou en se déplaçant conduisant alors à de nouvelles distributions. Ce repositionnement revêt deux dimensions principales : (i) l'adaptabilité des espèces aux nouvelles conditions (changement de traits d'histoire de vie) liée à la résilience des populations et (ii) leur capacité à explorer de nouveaux habitats favorables. Cette étude avait pour objectif l’élaboration d’un modèle dynamique mécaniste intégrant ces deux dimensions de manière à pouvoir évaluer, comprendre et prédire les possibilités de repositionnement des poissons migrateurs amphihalins européens face au changement climatique. Pour accomplir leurs cycles de vie, les espèces migratrices amphihalines utilisent nécessairement des écosystèmes dulçaquicoles, estuariens et marins. Ces cycles de vie particuliers leur confèrent un plus grand potentiel de repositionnement que les espèces dulçaquicoles. Une base de données sur les traits de vie de ces espèces intégrant notamment ceux pouvant potentiellement être influencés par le changement climatique et ceux pouvant jouer un rôle dans le potentiel de dispersion des espèces a été construite pour l’ensemble des espèces amphihalines européens. Une méthode d’analyse multicritère hiérarchique a été proposée pour définir un indice basé sur les traits de vies visant à caractériser le potentiel de repositionnement des espèces migratrices amphihalines. Le modèle GR3D (Global Repositioning Dynamics for Diadromous fish Distribution) a ensuite été développé pour étudier de façon dynamique le repositionnement potentiel de ces espèces, à large échelle, dans un contexte scénarisé de changement climatique. Il s’agit d’un modèle de simulation stochastique, individus centré, intégrant les principaux processus de dynamique de population d’un poisson migrateur amphihalin (reproduction, mortalité, croissance, migration de montaison avec dispersion, migration de dévalaison). Un premier cas d’étude exploratoire simulant le repositionnement d’une population virtuelle de grande alose (Alosa alosa) de son bassin versant d’origine à un bassin versant voisin inhabité dans un contexte d’augmentation de la température a permis de réaliser une analyse de sensibilité globale du modèle GR3D à la fois aux paramètres incertains de dynamique de population et aux paramètres reliés à la structure de l’environnement. Il a été mis en évidence une sensibilité particulière du modèle aux paramètres liés à la durée de vie et à la mortalité en mer ainsi qu’à la distance entre les deux bassins versants de l’environnement pour déterminer le succès de colonisation. Enfin, l’utilisation du modèle GR3D sur un cas d’application réel a permis de commencer à évaluer l’évolution de la persistance de la grande alose à l’échelle de son aire de répartition (i.e. la façade atlantique) dans un contexte de changement climatique. Les simulations du modèle GR3D devraient ainsi trouver à terme des applications pour la gestion et la conservation des espèces migratrices amphihalines.
... The invasive migratory phenotype of brown trout indeed reaches sizes and weights among the highest recorded to date, as well as a substantial reproductive investment. Additionally, the migratory tactic has probably been dominant since the first natural reproductions in Kerguelen (Jarry et al. 1998), supporting the idea that the product of survival and fecundity were higher than in the resident tactic. In a context of colonization, with no interspecific and weak intraspecific competition, data from our study indicate that any potential advantages arising from increased growth and therefore potential dispersal ability may not be balanced by reduced reproductive cost. ...
Brown trout (Salmo trutta L.) was voluntarily introduced in some rivers of the Kerguelen Islands in the 1950s–1960s. Fish originating from hatcheries rapidly colonized other streams, thanks to the early occurrence of anadromous (i.e., migratory) form. Getting insight into the success of colonization requires investigating fitness-related traits such as growth and reproductive investment. In particular, increased growth and body size—traits that are broadly related to dispersal ability—are predicted on colonization front, to the possible detriment of reproductive ability. We here report such investigation on early data following the first natural reproductions in the founder populations of Kerguelen, from 1971 to 1994, assessing the main characteristic on growth at sea and reproductive investment for both sexes. Our results reveal that growth of sea trout is excellent with individuals fully benefiting from their relatively short period of growth at sea, sizes and weights ranking among the highest recorded to date. During the reproduction period, males lose on average 15–21% of their weight, whereas females lose 18–19% of their weight. Although a trade-off between growth and reproduction may arise at marginal distribution of invasive species, our study indicates that any potential advantages arising from increased growth and therefore potential dispersal ability may not be directly balanced by reduced reproductive investment, with respect to other published studies. Results overall shed light on intrinsic invasiveness of the brown trout in a post-glacial landscape with barely any interaction with human activities.
... Cependant, plusieurs travaux de modélisation se sont déjà intéressés à ce cas d'étude. Ainsi, Jarry et al. (1998) ont construit un modèle matriciel de dynamique de population. Plus récemment, Labonne et al. (2013) ont utilisé une approche de modélisation mécaniste avec un cadre métapopulationnel, basé sur une dispersion de propagules et une fonction de colonisation, pour analyser l'importance de la configuration spatiale et de facteurs temporels et écologiques dans le succès de la colonisation des îles Kerguelen par la truite de mer. ...
The ongoing climate change is modifying the environmental conditions and species have to adapt to these new constraints, either on the same site or migrating in new suitable sites leading to a modification of distribution area. This repositioning has two main dimensions: (i) the species capacity to adapt to the new conditions (modification of life history traits) which is linked to the species resilience and (ii) the species capacity to explore new suitable habitats. The objective of this study was to build a mechanistic model incorporating these two dimensions in order to evaluate, understand and predict the repositioning possibilities of European diadromous fish facing climate change.In their life cycles, diadromous fish species have to use freshwater, estuarine and marine ecosystems. These specific life history strategies represent a great repositioning potential in comparison to freshwater fish species. A database of diadromous fish life history traits, incorporating those that could be influenced by climate change and those that could have an importance in the species repositioning potential, has been built. An Analytic Hierarchy Process has been suggested to develop a composite score based on life traits aiming at assessing the diadromous species repositioning potential.Then, the GR3D model (Global Repositioning Dynamics for Diadromous fish Distribution) has been developed in order to study with a dynamic approach the repositioning potential of diadromous fish, at a large scale, in a context of climate change. This model is a simulation, stochastic and individual-based model incorporating the main population dynamics processes of a diadromous fish (reproduction, mortality, growth, upstream migration with dispersal and downstream migration).A first exploratory application case simulating the repositioning of a virtual allis shad (Alosa alosa) population between two river catchments under a scenario of temperature increase has been carried out and the associated global sensitivity analysis has been performed in order to determine the influence of uncertain population dynamics parameters and of parameters defining the landscape stucture. The results showed that dispersal distance and parameters related to sea lifespan and to survival at sea were crucial to determine the success of colonization.Finally, the use of GR3D in a real application case allowed improving the understanding of allis shad persistence at the scale of its distribution area (i.e. the Atlantic coast) in a context of climate change.Over time, simulation results of GR3D should be relevant and useful in management and conservation of diadromous fish species.
... The demographic lag not included in our model may generate an artifactual effect: indeed, large patches may not be saturated as quickly as small patches, and if propagule release depends on demographic saturation (i.e., anadromy dependent on density), then we should expect such patterns at least temporarily. We could not include a demographic lag in the model, because it would require considering a full demographic model, not only a binary state approach, which is difficult-f not intractable-at such a large scale, although it has been attempted locally [53]. Alternatively, if patch size is correlated to patch quality, small patches may release more propagules than larger ones. ...
Metapopulation dynamics over the course of an invasion are usually difficult to grasp because they require large and reliable data collection, often unavailable. The invasion of the fish-free freshwater ecosystems of the remote sub-Antarctic Kerguelen Islands following man-made introductions of brown trout (Salmo trutta) in the 1950's is an exception to this rule. Benefiting from a full long term environmental research monitoring of the invasion, we built a Bayesian dynamic metapopulation model to analyze the invasion dynamics of 85 river systems over 51 years. The model accounted for patch size (river length and connections to lakes), alternative dispersal pathways between rivers, temporal trends in dynamics, and uncertainty in colonization date. The results show that the model correctly represents the observed pattern of invasion, especially if we assume a coastal dispersal pathway between patches. Landscape attributes such as patch size influenced the colonization function, but had no effect on propagule pressure. Independently from patch size and distance between patches, propagule pressure and colonization function were not constant through time. Propagule pressure increased over the course of colonization, whereas the colonization function decreased, conditional on propagule pressure. The resulting pattern of this antagonistic interplay is an initial rapid invasion phase followed by a strong decrease in the invasion rate. These temporal trends may be due to either adaptive processes or environmental gradients encountered along the colonization front. It was not possible to distinguish these two hypotheses. Because invasibility of Kerguelen Is. freshwater ecosystems is very high due to the lack of a pre-existing fish fauna and minimal human interference, our estimates of invasion dynamics represent a blueprint for the potential of brown trout invasiveness in pristine environments. Our conclusions shed light on the future of polar regions where, because of climate change, fish-free ecosystems become increasingly accessible to invasion by fish species.
... They also permit to simplify the dynamics of a population into its basic components: recruitment or birth, growth or ageing, and mortality. Matrix models have been widely used in ecology to deal with invasive species [18, 29], population viability [5, 3, 26, 28, 15], or the management of the harvested populations [13, 7, 16]. The most general matrix model was proposed by [21], and allows any transition from one stage to another. ...
A stochastic forestry model with a density-dependence structure is studied. The population evolves in discrete-time through stage-structured processes, in a way that its temporal evolution is described by a stochastic Markov chain. For adequate scalings of the transition rates, it is shown to converge to the deterministic matrix model, known as the Usher model, as a parameter n, interpreted as the population size roughly speaking, becomes large. From the perspective of the analysis of forestry data and predict the forestry population evolution, this approximation result may serve as a key tool for exploring the asymptotic properties of standard inference methods such as maximum likelihood estimation. We state preliminary statistical results in this context. Eventually, relation of the model to the available data of a tropical rain forest in French Guiana is investigated and numerical applications are carried out.
Dynamics of predator-prey systems are affected by life history attributes of both predator and prey. We compare performance of several different models of one specific type of predator-prey interaction in which both predator and prey exhibit seasonal reproduction and predation is continuous. We show that use of a discrete-time model that preserves seasonal reproduction, whether stage-structured or non-stage-structured, always produces equilibria that are locally stable, whereas use of a continuous-time predator-prey model with an instantaneous approximation of seasonal reproduction can produce a limit cycle (self-sustained population fluctuations). This difference in dynamics results from the mismatch of life history properties between the mathematical model and the biological system under the continuous time model. We conclude that seasonal reproduction may be an important stabilizing factor in predator-prey interactions. Finally, with stage-structured predator-prey models, we show how life history parameters affect asymptotic dynamics of the system. Discrete-time models provide a more natural match to the biology of these systems. Our results suggest that discrete-time models have the potential for reducing the gap between theoretical models and empirical observations for these systems. (c) 2013 Elsevier B.V. All rights reserved.
In the subantarctic French territory of the Kerguelen Islands, Atlantic salmon Salmo salar was stocked to create a new population in the Korrigans drainage system. The analysis of historical scale collections showed that hybrids were inadvertently introduced with the original Atlantic salmon stocks. Later colonization of the Korrigans system by brown trout Salmo trutta was followed by interspecific hybridization between the two species. Our results highlight the importance of both routine genetic monitoring of hatchery stocks and considering the possible influence of other species when stocking is envisaged.
A mathematical model representing the long-term change in a trout population under different river management scenarios is presented. It describes the structure of a population broken down into age classes based on the Leslie matrix; if the population structure for any given month is known, the model should be able to estimate that of the following month. The passage from one month to the next takes into account various relevant factors: survival rate of individuals in the different age classes; fertility rate of females; linear and weighted growth rates; displacement linked to habitat fluctuations using weighted usable area (WUA) values. The model was applied to two French rivers. Regular monitoring of trout populations on the River Kernec enabled comparison of the response of the model with no displacement, with actual variations in fish stocks on the first river. In addition, the knowledge of WUA chronologies on the River Echez made it possible to carry out initial simulations of the response of a fish population to different river management scenarios at the second site.
The Leslie matrix model for discrete population theory is examined for the assessment of the effects of environmental alterations on a species population using an eigenvalue analysis. This analysis provides estimates of population growth rate and stable age distribution. A sensitivity analysis is conducted for changes in elements of the population matrix and the resultant effect on population growth rate and stable age distribution. An example of this technique is presented for the cunner (Tautogolabrus adspersus). This example considers the effect of entrainment of cunner eggs and larvae at the intakes of power stations.
The normal approach to management of Atlantic salmon (Salmo
salar L.) is to develop stock-recruitment relationships. Target spawning criteria can be estimated from such relationships and a river system can be managed by allowing specified escapement to achieve the required ova deposition.
Brown trout populations acclimatized in freshwater ecosystems of the Kerguelen Islands are the only ones south of the Antarctic Convergence. Even though the introduction was realized with a hatchery strain, adaptation to this new freshwater environment with limited capacity is expressed by the spontaneous appearance of trophic catadromous migratory behavior. Subpopulations of resident and migratory trout are compared with respect to demographic structure, growth, feeding, reproductive and migratory behavior in relation to main environment parameters. Temporal evolution of these populations is characterized by upstream extension of their distribution, increase in density, and steady progression of maximum size, which indicate better exploitation of the environment by better fit individuals. -from Current Antarctic Literature
Matrix population models are discrete-time structured population models in which individuals are classified into discrete stages (age classes, size classes, developmental stages, spatial locations, etc.).
The Leslie matrix model for discrete population theory is examined for the assessment of the effects of environmental alterations on a species population using an eigenvalue analysis. This analysis provides estimates of population growth rate and stable age distribution. A sensitivity analysis is conducted for changes in elements of the population matrix and the resultant effect on population growth rate and stable age distribution. An example of this technique is presented for the cunner (Tautogolabrus adspersus). This example considers the effect of entrainment of cunner eggs and larvae at the intakes of power stations.