Article

Comparative population dynamics of large and small mammals in the Northern Hemisphere: Deterministic and stochastic forces

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Abstract

Deterministic feedbacks within populations interact with extrinsic, stochastic processes to generate complex patterns of animal abundance over time and space. Animals inherently differ in their responses to fluctuating environments due to differences in body sizes and life history traits. However, controversy remains about the relative importance of deterministic and stochastic forces in shaping population dynamics of large and small mammals. We hypothesized that effects of environmental stochasticity and density dependence are stronger in small mammal populations relative to their effects in large mammal populations and thus differentiate the patterns of population dynamics between them. We conducted an extensive, comparative analysis of population dynamics in large and small mammals to test our hypothesis, using seven population parameters to describe general dynamic patterns for 23 (14 species) time series of observations of abundance of large mammals and 38 (21 species) time series for small mammals. We used state-space models to estimate the strength of direct and delayed density dependence as well as the strength of environmental stochasticity. We further used phylogenetic comparative analysis to detect differences in population dynamic patterns and individual population parameters, respectively, between large and small mammals. General population dynamic patterns differed between large and small mammals. However, the strength of direct and delayed density dependence was comparable between large and small mammals. Moreover, the variances of population growth rates and environmental stochasticity were greater in small mammals than in large mammals. Therefore, differences in population response to stochastic forces and strength of environmental stochasticity are the primary factor that differentiates population dynamic patterns between large and small mammal species.

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... We plotted the coefficients of direct and delayed density dependence derived from the AR(2) skeleton model for each population within the Royama parameter plane to estimate their stability properties. The relative locations within the Royama parameter plane of the estimates of the coefficients of statistical direct and delayed density dependence derived from the skeleton AR(2) model ( Fig. 2a) indicate the stability properties of a population (Royama 1992, Bjornstad et al. 1995, Forchhammer et al. 1998, Stenseth et al. 2003, Wang et al. 2013 as follows: Region I, point stability characterized by moderate direct and weak delayed density dependence, and assumed to be steadily converging to carrying capacity; Region II, variable point stability characterized by strong direct and weak delayed density dependence, and assumed to fluctuate with a small amplitude over short intervals (~1-2 yr) while converging toward carrying capacity eventually; Region III, short-term fluctuations characterized by moderate to strong direct and strong delayed density dependence; and Region IV, longer-term fluctuations characterized by moderate to weak direct and strong delayed density dependence. Hence, populations occurring within the triangle but above the parabola are stable, while those within the triangle but below the parabola are variable, with the degree of variability increasing downward and to the right within the parabola (Royama 1992, Bjornstad et al. 1995. ...
... Our results complement two other studies that have analyzed the population dynamics of large herbivores using the Royama framework (Forchhammer et al. 1998, Wang et al. 2013. Both of these studies also failed to detect populations characterized by short periodicity, i.e., a complete absence of populations in region II of the Royama parameter plane. ...
... Highly stable dynamics, which in a completely deterministic environment would result in point stability, were uncommon among populations included in this analysis. In contrast, Wang et al. (2013) detected dynamics approximating point stability in all 23 of the populations of large herbivores they analyzed. A direct comparison to our results is complicated, however, by the fact that our analysis focused on a single species complex, while that of Wang et al. (2013) incorporated 14 species. ...
Article
Stability in population dynamics is an emergent property of the interaction between direct and delayed density dependence, the strengths of which vary with environmental covariates. Analysis of variation across populations in the strength of direct and delayed density dependence can reveal variation in stability properties of populations at the species level. We examined the stability properties of 22 elk/red deer populations in a two-stage analysis. First, we estimated direct and delayed density dependence applying an AR(2) model in a Bayesian hierarchical framework. Second, we plotted the coefficients of direct and delayed density dependence in the Royama parameter plane. We then used a hierarchical approach to test the significance of environmental covariates of direct and delayed density dependence. Three populations exhibited highly stable and convergent dynamics with strong direct, and weak delayed, density dependence. The remaining 19 populations exhibited more complex dynamics characterized by multi-annual fluctuations. Most (15 of 19) of these exhibited a combination of weak to moderate direct and delayed density dependence. Best-fit models included environmental covariates in 17 populations (77% of the total). Of these, interannual variation in growing-season primary productivity and interannual variation in winter temperature were the most common, performing as the best-fit covariate in six and five populations, respectively. Interannual variation in growing-season primary productivity was associated with the weakest combination of direct and delayed density dependence, while interannual variation in winter temperature was associated with the strongest combination of direct and delayed density dependence. These results accord with a classic theoretical prediction that environmental variability should weaken population stability. They furthermore suggest that two forms of environmental variability, one related to forage resources and the other related to abiotic conditions, both reduce stability but in opposing fashion: one through weakened direct density dependence and the other through strengthened delayed density dependence. Importantly, however, no single abiotic or biotic environmental factor emerged as generally predictive of the strengths of direct or delayed density dependence, nor of the stability properties emerging from their interaction. Our results emphasize the challenges inherent to ascribing primacy to drivers of such parameters at the species level and distribution scale. This article is protected by copyright. All rights reserved.
... Thus, population variability is the variance of the log population growth rate across years due to environmental stochasticity (Morris & Doak, 2003). We ran sets of simulations to explore a reasonable span of natural population values that encapsulate the basic dynamics of a broad range of species (Table 1; e.g., Herrera, 1998;Liebhold, 1992;Morris & Doak, 2003;Nicholls et al., 1996;Saether & Engen, 2002;Wang et al., 2013). Ranges of population variability (0-2) are based on known variability from the literature (e.g., Davidson, 1938;Davidson & Andrewartha, 1948;Varley, 1949;Davis, 1964;Harper, 1977;Uvarov, 1977;Perrins et al., 1991;Liebhold, 1992;Nicholls et al., 1996; Clutton-Brock et al., 1997;Herrera, 1998;Matlack et al., 2002;Saether & Engen, 2002;Morris & Doak, 2003;Huxman et al., 2008) as well as empirical population variability calculated among small mammals from a 30-year mark and recapture study in Kansas (Brady & Slade, 2004;Wang et al., 2013; Slade pers. ...
... We ran sets of simulations to explore a reasonable span of natural population values that encapsulate the basic dynamics of a broad range of species (Table 1; e.g., Herrera, 1998;Liebhold, 1992;Morris & Doak, 2003;Nicholls et al., 1996;Saether & Engen, 2002;Wang et al., 2013). Ranges of population variability (0-2) are based on known variability from the literature (e.g., Davidson, 1938;Davidson & Andrewartha, 1948;Varley, 1949;Davis, 1964;Harper, 1977;Uvarov, 1977;Perrins et al., 1991;Liebhold, 1992;Nicholls et al., 1996; Clutton-Brock et al., 1997;Herrera, 1998;Matlack et al., 2002;Saether & Engen, 2002;Morris & Doak, 2003;Huxman et al., 2008) as well as empirical population variability calculated among small mammals from a 30-year mark and recapture study in Kansas (Brady & Slade, 2004;Wang et al., 2013; Slade pers. comm.: population variability = 0.59-1.88). ...
Article
The rush to assess species' responses to anthropogenic climate change (CC) has underestimated the importance of interannual population variability (PV). Researchers assume sampling rigor alone will lead to an accurate detection of response regardless of the underlying population fluctuations of the species under consideration. Using population simulations across a realistic, empirically-based gradient in PV, we show that moderate to high PV can lead to opposite and biased conclusions about CC responses. Between pre- and post-CC sampling bouts of modeled populations as in resurvey studies, there is (1) a 50% probability of erroneously detecting the opposite trend in population abundance change and nearly zero probability of detecting no change. (2) Across multiple years of sampling, it is nearly impossible to accurately detect any directional shift in population sizes with even moderate PV. (3) There is up to 50% probability of detecting a population extirpation when the species is present, but in very low natural abundances. (4) Under scenarios of moderate to high PV across a species' range or at the range edges, there is a bias towards erroneous detection of range shifts or contractions. Essentially, the frequency and magnitude of population peaks and troughs greatly impact the accuracy of our CC response measurements. Species with moderate to high PV (many small vertebrates, invertebrates, and annual plants) may be inaccurate 'canaries in the coal mine' for CC without pertinent demographic analyses and additional repeat sampling. Variation in PV may explain some idiosyncrasies in CC responses detected so far, and urgently needs more careful consideration in design and analysis of CC responses This article is protected by copyright. All rights reserved.
... The first deals with the ability of species to adapt to rapid environmental change. The second depends on the ability of evolutionary ecologists to predict the future ecological and also appear simply because unstable systems lack direct density-dependent feedback in response to environmental stochasticity (Wang et al., 2011). Less appreciated, perhaps, are the differential effects that climate-induced environmental stochasticity can evoke on habitat quality and habitat selection (Morris, 2003b(Morris, , 2004Schreiber, 2012). ...
... We can thus conclude that, at least during early summer for lemmings at Walker Bay, continued climate change will have pervasive, quick influences on lemming dynamics and the relative quality of their habitats, as well as short-and long-term effects on lemming distribution. Indeed, analyses of 61 time series representing 35 different species of northern mammals showed that the high dependence of small-mammal dynamics on environmentally stochastic events, such as climatic variability, is related to both direct and delayed densitydependent regulation (Wang et al., 2011). This conclusion mirrors the results of our path analysis, which suggested that changes in the abundance of Dicrostonyx in its preferred upland habitat were caused by both direct effects of habitat change as well as indirect effects mediated through changes in its abundance in meadows. ...
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Questions: Can we merge theories of habitat selection with changes in habitat and habitat use to predict future strategies of habitat selection? If so, do changes in the frequency of upland and meadow habitats exploited by two species of lemmings confirm that their strategies of habitat selection have also changed? Field methods: We measured habitat at 300 permanent stations on 12 study plots in 1996 and in 2010. We classified habitat into upland versus meadow categories and estimated population abundances of the two lemming species in both habitats in eight different years. Statistical and conceptual methods: Logistic regression, path analysis, isodars, invader strategy landscapes. Assumptions: Lemmings are ideal density-dependent habitat selectors. Habitat selection strategies vary with density and depend on the frequency of alternative strategies. Results: Meadow habitat became more frequent while the proportion of upland habitat declined. Habitat selection strategies shifted with changes in habitat even though lemming abundance was lower in warm years than in cool years. Shallow selection gradients, which yield a small fitness advantage for the optimum strategy at low density, become increasingly steep at high densities. Conclusion: Analysis of altered patterns of habitat selection can forecast future strategies of habitat use with changing climate. But reductions in lemming abundance with global warming portend an increasing role for stochasticity in their future habitat selection.
... Variation in an environment has temporal and spatial components, which both vary in their patterning and degree of heterogeneity (Boyce et al. 2006). Temporal variability has been associated with an increase in herbivore density dependence, most probably due to more frequent per capita forage deficits (Wang et al. 2006(Wang et al. , 2013. In contrast, spatial heterogeneity can buffer populations against temporal variability by increasing the asynchrony in plant phenology, allowing herbivores to access a greater proportion of the forage resource while in its most nutritious state (Wang et al. 2006, 2009, Hobbs and Gordon 2010 and dispersing them before they critically deplete these preferred resources (Walker et al. 1987, Owen-Smith 2004. ...
... Temporal variation that impacts the availability and duration of reliance on the key resource will increase the role of density in regulating the population (Wang et al. 2006(Wang et al. , 2013 by increasing the frequency of large mismatches between population size and riparian browse availability. Greater temporal variability of the key resource will also reduce mean population size, because populations decline more rapidly in poor years than they can recover in good years O'Connor 2000, Davis et al. 2002). ...
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Large-mammal herbivore populations are subject to the interaction of internal density-dependent processes and external environmental stochasticity. We disentangle these processes by linking consumer population dynamics, in a highly stochastic environment, to the availability of their key forage resource via effects on body condition and subsequent fecundity and mortality rates. Body condition and demographic rate data were obtained by monitoring 500 tagged female goats in the Richtersveld National Park, South Africa, over a three-year period. Identifying the key resource and pathway to density dependence for a population allows environmental stochasticity to be partitioned into that which has strong feedbacks to population stability, and that which does not. Our data reveal a density-dependent seasonal decline in goat body condition in response to concomitant density-dependent depletion of the dry-season forage resource. The loss in body condition reduced density-dependent pregnancy rates, litter sizes, and pre-weaning survival. Survival was lowest following the most severe dry season and for juveniles. Adult survival in the late-dry season depended on body condition in the mid-dry season. Population growth was determined by the length of the dry season and the population size in the previous year. The RNP goat population is thereby dynamically coupled primarily to its dry-season forage resource. Extreme environmental variability thus does not decouple consumer resource dynamics, in contrast to the views of nonequilibrium protagonists.
... Population growth rates of shortlived species are sensitive to environment-driven variability (i.e., environmental stochasticity) of all vital rates (Morris et al., 2008). As a result, populations of small mammals have strong environmental stochasticity (Wang et al., 2013). Additionally, the effects of weather or climate on the demography of small mammals may be nonlinear Stenseth et al., 2002). ...
... Population growth rates may be related to densities in the year t−1 (i.e., direct density dependence) or in the year t−2 (i.e., indirect density dependence; Lima et al., 2006). Density dependence commonly occurs in small mammal populations (Wang et al., 2013). Direct density dependence may reduce reproduction and recruitment with increasing densities and subsequently stabilize population abundances of rodents (Ostfeld et al., 1993;Reed & Slade, 2008). ...
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Understanding differential and integral effects of weather and population density on vital rates (e.g., survival and recruitment rates) helps elucidate the ecological and demographic mechanisms underlying animal population dynamics. Nonlinear responses of vital rates to changes in weather conditions, such as precipitation, are important for predicting the effects of climate changes on small herbivorous mammals. We aimed to test the hypotheses: 1) that small herbivore populations increase from low to intermediate precipitation with improved habitat conditions and decline beyond the intermediate or optimum precipitation due to increased mortality in semi-arid grassland; and 2) that increases in population size would result in stronger negative effects on recruitment than on survival of small mammals. We live-trapped a population of the Daurian pika (Ochotona dauurica), a small herbivorous mammal, in north central Inner Mongolia, China, biweekly between May and November from 2010 to 2012. We estimated the effects of temperature, precipitation, and population size on the survival probabilities and recruitment rates of O. dauurica using mark-recapture methods. Increases in temperature improved the recruitment but reduced the survival of O. dauurica, resulting in negative net effects on population growth rates. Increased precipitation initially resulted in positive effects, and then had negative effects on population growth rates primarily through nonlinear effects on survival probabilities, supporting the optimum habitat hypothesis. Changes in population size had stronger effects on recruitment than on survival of O. dauurica, suggesting that density-dependent feedback to recruitment may be a primary regulatory mechanism of small mammal populations.
... Population growth rates of shortlived species are sensitive to environment-driven variability (i.e., environmental stochasticity) of all vital rates (Morris et al., 2008). As a result, populations of small mammals have strong environmental stochasticity (Wang et al., 2013). Additionally, the effects of weather or climate on the demography of small mammals may be nonlinear Stenseth et al., 2002). ...
... Population growth rates may be related to densities in the year t−1 (i.e., direct density dependence) or in the year t−2 (i.e., indirect density dependence; Lima et al., 2006). Density dependence commonly occurs in small mammal populations (Wang et al., 2013). Direct density dependence may reduce reproduction and recruitment with increasing densities and subsequently stabilize population abundances of rodents (Ostfeld et al., 1993;Reed & Slade, 2008). ...
Conference Paper
Background/Question/Methods The relative importance of intrinsic and extrinsic forces has been a central theme of animal population ecology. Densities and climate may have different effects on different demographic processes of animal populations. Small mammal populations have substantial environmental variability, often exhibiting the boom-bust type of population dynamics. It is plausible to hypothesize that survival and recruitment of small mammals, as income breeders, are susceptible to changes in climate (hereafter, climatically labile demography hypothesis). Life history theory predicts that small mammal populations are more sensitive to changes in fecundity and recruitment than to those in other vital rates. Additionally, delayed effects of densities on sexual maturity have been ascribed to the occurrence of delayed density dependence in northern small mammals. Therefore, we hypothesize that density dependence would emerge first in recruitment or reproduction in small mammals (hereafter recruitment regulation hypothesis). We live trapped a population of Daurian pikas (Ochotona dauurica) in north central Inner Mongolia, China biweekly during the plant growing seasons (April to November) from 2009 to 2012 using capture-recapture methods. We fit Cormack-Jolly-Seber models to the trapping data with daily temperature and precipitation as well as minimum number of animals alive (MNA) as covariates to test our hypotheses. Results/Conclusions Our best approximating model with the lowest Akaike information criterion supports the climatically labile demography hypothesis. Survival probabilities of Daurian pikas were inversely related to daily temperatures; however, recruitment was positively related to daily temperatures. Additionally, survival was inversely related to daily precipitation. Our results showed opposite effects of warning on survival and recruitment of the pikas. On the contrary, increases in MNA only resulted in decreases in recruitment, supporting the recruitment regulation hypothesis. Effects of densities and climate on the demography of small mammals appeared to be complex. Therefore, studies of the demographic pathways of density dependence and climate effects are vital to understanding and forecasting the impacts of densities and climate on population dynamics.
... Thus, population variability is the variance of the log population growth rate across years due to environmental stochasticity (Morris & Doak, 2003). We ran sets of simulations to explore a reasonable span of natural population values that encapsulate the basic dynamics of a broad range of species (Table 1; e.g., Herrera, 1998; Liebhold, 1992; Morris & Doak, 2003; Nicholls et al., 1996; Saether & Engen, 2002; Wang et al., 2013 ). Ranges of population variability (0–2) are based on known variability from the literature (e.g., Davidson, 1938; Davidson & Andrewartha, 1948; Varley, 1949; Davis, 1964; Harper, 1977; Uvarov, 1977; Perrins et al., 1991; Liebhold, 1992; Nicholls et al., 1996; Clutton-Brock et al., 1997; Herrera, 1998; Matlack et al., 2002; Saether & Engen, 2002; Morris & Doak, 2003; Huxman et al., 2008) as well as empirical population variability calculated among small mammals from a 30-year mark and recapture study in Kansas (Brady & Slade, 2004; Wang et al., 2013; Slade pers. ...
... We ran sets of simulations to explore a reasonable span of natural population values that encapsulate the basic dynamics of a broad range of species (Table 1; e.g., Herrera, 1998; Liebhold, 1992; Morris & Doak, 2003; Nicholls et al., 1996; Saether & Engen, 2002; Wang et al., 2013 ). Ranges of population variability (0–2) are based on known variability from the literature (e.g., Davidson, 1938; Davidson & Andrewartha, 1948; Varley, 1949; Davis, 1964; Harper, 1977; Uvarov, 1977; Perrins et al., 1991; Liebhold, 1992; Nicholls et al., 1996; Clutton-Brock et al., 1997; Herrera, 1998; Matlack et al., 2002; Saether & Engen, 2002; Morris & Doak, 2003; Huxman et al., 2008) as well as empirical population variability calculated among small mammals from a 30-year mark and recapture study in Kansas (Brady & Slade, 2004; Wang et al., 2013; Slade pers. comm.: population variability = 0.59–1.88). ...
... Strong year to year variation in small mammal populations (Wang et al., 2013) can limit their value as indicators of forest condition. We found that red-backed voles, deer mice, and two shrew species exhibited distinct responses to various forms of understory structure and forest harvest across three years of data. ...
Article
Conservation of communities of wildlife may conflict with forestry due to the impacts of habitat alteration to wildlife and desire by the public for economic development. Identification of thresholds to disturbance and habitat conditions may improve our ability to find compromises between conservation and resource development, while also identifying sensitive indicators. We used the multivariate Threshold Indicator Taxa Analysis (TITAN) to assess the response of a wildlife community to disturbance from forest harvest, roads, and forest habitat affected by forest management. Significant thresholds were evident among birds, amphibians and mammals, and patterns in positive and negative responses appeared to vary in relation to life history adaptations. Birds typically had the strongest relationships to environmental gradients and provided good representation of a range of forest conditions useful in assessing sustainability in forestry. We found that negative indicator responses to forest habitat gradients were often more precise and synchronous among species than positive responses, potentially affected by the diversity of habitat niche space among species. Stronger responses among a greater range of species were evident for resource-providing habitat conditions than direct measures of disturbance (i.e. forest cuts and roads). Our approach demonstrates the value of identifying ecological community thresholds that can serve to set targets for conserving biodiversity and to characterize community dynamics in response to habitat change mediated by natural resource management.
... Understanding population dynamics is a central goal in ecology (Andreo et al. 2009;Wang et al. 2013Wang et al. , 2016Xiao et al. 2016). The role of endogenous and exogenous factors in population dynamics of animals is well-studied (Previtali et al. 2009;Wang et al. 2009;Ernest et al. 2010;Yan et al. 2013;Selås 2016a, b), but it is often difficult to determine exactly which factor or set of factors regulate natural populations (Stenseth et al. 2003;Ratikainen et al. 2008;Holyoak and Heath 2016;Bastille-Rousseau et al. 2018). ...
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Chemical compounds in seeds exert negative and even lethal effects on seed-consuming animals. Tannin-degrading bacteria in the guts of small mammals have been associated with the ability to digest seeds high in tannins. At the population level, it is not known if tannins influence rodent species differently according to the composition of their gut microbiota. Here, we test the hypothesis that sympatric tree species with different tannins exert contrasting effects on population fluctuations of seed-eating rodents. We collected a 10-year dataset of seed crops and rodent population sizes and sequenced 16S rRNA of gut microbes. The abundance of Apodemus peninsulae was not correlated with seed crop of either high-tannin Quercus mongolica or low-tannin Corylus mandshurica, but positively correlated with their total seed crops. Abundance of Tamias sibiricus was negatively correlated with seed crop of Q. mongolica but positively correlated with C. mandshurica. Body masses of A. peninsulae and T. sibiricus decreased when given high-tannin food; however, only the survival of T. sibiricus was reduced. The abundance of microbial genus Lactobacillus exhibiting potential tannin-degrading activity was significantly higher in A. peninsulae than in T. sibiricus. Our results suggest that masting tree species with different tannin concentrations may differentially influence population fluctuations of seed predators hosting different gut microbial communities. Although the conclusion is based on just correlational analysis of a short time-series, seeds with different chemical composition may influence rodent populations differently. Future work should examine these questions further to understand the complex interactions among seeds, gut microbes, and animal populations.
... A complex relationship between condition and the timing of ice-breakup likely also affects food resources and the female's ability to rebuild energy stores prior to moulting. Temporal variation that impacts the availability and duration of reliance on a key resource will increase the role of density in regulating the population (Wang et al., 2006(Wang et al., , 2013 by increasing the frequency of large mismatches between population size and food resources (Chamailllé-Jammes et al., 2008;Hempson et al., 2015). Among ungulates, greater temporal variability of the key resource will also reduce mean population size, because populations decline more rapidly in poor years than they can recover in good years (Illius and O'Connor, 2000;Davis et al., 2002). ...
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Life history theory predicts that resource competition increases as a population increases, leading to changes in life history traits such as growth, survival, and reproduction. The Northwest Atlantic (NWA) harp seal population has increased from a low of 1.1 million animals in 1971 to over 7 million animals in 2014. Given this 7-fold increase in abundance, we hypothesized that density-dependent regulation might be reflected by changes in body growth. Gompertz curves fitted to size at age data for harp seals collected in the Gulf of St Lawrence over a 40 year period show a decline in female asymptotic length and mass. Body mass and condition were negatively related to reproductive rates the previous year, while a quadratic relationship (‘inverse u’) was observed between body measures and the ratio of the March:April first year ice cover, a measure of ice breakup. Condition was also negatively related to January ice cover. At high densities, reproduction is likely to be relatively more expensive for Northwest Atlantic harp seals, underlining the importance of females being able to access high energy food during the winter foraging period to build-up condition prior to pupping. A complex relationship between condition and the timing of ice-breakup likely reflects the influence of the timing of ice retreat on food resources and hence female ability to rebuild energy stores prior to moulting.
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It has been hypothesized that animal populations respond nonlinearly to the environment, and such responses are important to understand the effects of climate change population dynamics of small mammals in arid environments at northern latitudes. The aim of this study was to test the following hypotheses: (1) that small rodent populations increase as their semiarid habitat conditions improve from low to intermediate levels of temperature or precipitation, and decline beyond the optimum climate because of decreased survival, and (2) that increased population density would result in stronger negative effects on recruitment than on survival. A wild population of Mongolian gerbils (Meriones unguiculatus), a granivorous rodent distributed in Inner Mongolia, China, was live-trapped half-monthly between April and October from 2014 to 2017 and the effects of climate and density on their apparent survival probabilities and recruitment rates were estimated using mark-recapture methods. Increased temperatures initially had a positive effect on population growth rates, and then had negative effects on population growth rates primarily, which was mediated by quadratic effects on survival probabilities, further supporting the optimum habitat hypothesis. Moreover, the increases in temperature had a positive effect on the recruitment of gerbils, whereas population density had a more markedly negative effect on recruitment than on survival. The results of this study suggested that the density-dependent feedback to recruitment may be a primary regulatory mechanism of small mammal populations, and the complex responses of populations to temperature, which is a limiting ecological factor, may raise concerns for the fate of populations of small mammals at northern latitudes, in view of the predicted global climate change scenarios.
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Age‐ and sex‐specific survival rates are essential for understanding animal population dynamics and discerning environmental influences on population parameters. To date, little research has been done on age‐ and sex‐specific survival of the Gunnison's prairie dog (Cynomys gunnisoni), a colonial ground‐dwelling squirrel inhabiting the sagebrush ecosystem of the southwestern United States. To discern impacts of the year of study, age, sex, and reproductive status on survival, we conducted a capture‐mark‐recapture analysis on a previously collected long‐term dataset of a population of Gunnison's prairie dogs (n = 2508) from 1989 to 1995. We implemented two models: age‐cohort Cormack–Jolly–Seber (CJS) models (to examine survival by age, sex, and year) and multistate mark‐recapture models (to analyze survival by age and year, as well as breeding status). Females had higher apparent survival than males. Yearlings had a low apparent survival rate (0.288 ± 0.022, [±SE]) compared to juveniles (0.461 ± 0.019) and adults (0.482 ± 0.055). Less than 50% (48.0 ± 2.7) of female yearlings successfully weaned litters each year. Yearling survival rate was lower than other highly social prairie dog species that do not reproduce as yearlings, suggesting that there may be a cost to reproduction. We also constructed a postbreeding matrix population model and associated elasticity analysis, which indicated that the reproductive output of yearlings was the most significant potential driver of population growth. Our findings provide more nuanced estimates for age‐ and sex‐specific survival in this species than were previously available and also more broadly inform linkages between demography and sociality in prairie dogs.
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In large-herbivore populations, environmental variation and density dependence co-occur and have similar effects on various fitness components. Our review aims to quantify the temporal variability of fitness components and examine how that variability affects changes in population growth rates. Regardless of the source of variation, adult female survival shows little year-to-year variation [coefficient of variation (CV<10%)], fecundity of prime-aged females and yearling survival rates show moderate year-to-year variation (CV<20%), and juvenile survival and fecundity of young females show strong variation (CV>30%). Old females show senescence in both survival and reproduction. These patterns of variation are independent of differences in body mass, taxonomic group, and ecological conditions. Differences in levels of maternal care may fine-tune the temporal variation of early survival. The immature stage, despite a low relative impact on population growth rate compared with the adult stage, may be the critical component of population dynamics of large herbivores. Observed differences in temporal variation may be more important than estimated relative sensitivity or elasticity in determining the relative demographic impact of various fitness components.
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It has recently been proposed that life-history evolution is subject to a fundamental size-dependent constraint. This constraint limits the rate at which biomass can be produced so that production per unit of body mass is inevitably slower in larger organisms than in smaller ones. Here we derive predictions for how changes in body size and production rates evolve in different lifestyles subject to this constraint. Predictions are tested by using data on the mass of neonate tissue produced per adult per year in 637 placental mammal species and are generally supported. Compared with terrestrial insectivores with generalized primitive traits, mammals that have evolved more specialized lifestyles have divergent mass-specific production rates: (i) increased in groups that specialize on abundant and reliable foods: grazing and browsing herbivores (artiodactyls, lagomorphs, perissodactyls, and folivorous rodents) and flesh-eating marine mammals (pinnipeds, cetaceans); and (ii) decreased in groups that have lifestyles with reduced death rates: bats, primates, arboreal, fossorial, and desert rodents, bears, elephants, and rhinos. Convergent evolution of groups with similar lifestyles is common, so patterns of productivity across mammalian taxa reflect both ecology and phylogeny. The overall result is that groups with different lifestyles have parallel but offset relationships between production rate and body size. These results shed light on the evolution of the fast–slow life-history continuum, suggesting that variation occurs along two axes corresponding to body size and lifestyle. • allometry • production rate • metabolic ecology • fast-slow
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In this book, Andrew Harvey sets out to provide a unified and comprehensive theory of structural time series models. Unlike the traditional ARIMA models, structural time series models consist explicitly of unobserved components, such as trends and seasonals, which have a direct interpretation. As a result the model selection methodology associated with structural models is much closer to econometric methodology. The link with econometrics is made even closer by the natural way in which the models can be extended to include explanatory variables and to cope with multivariate time series. From the technical point of view, state space models and the Kalman filter play a key role in the statistical treatment of structural time series models. The book includes a detailed treatment of the Kalman filter. This technique was originally developed in control engineering, but is becoming increasingly important in fields such as economics and operations research. This book is concerned primarily with modelling economic and social time series, and with addressing the special problems which the treatment of such series poses. The properties of the models and the methodological techniques used to select them are illustrated with various applications. These range from the modellling of trends and cycles in US macroeconomic time series to to an evaluation of the effects of seat belt legislation in the UK.
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We argue that a relationship between life history variation and population processes may form the foundation for developing a theory for variation in population growth rate. An examination of the distribution of 104 European bird species in relation to their clutch size and adult survival rate showed three different clusters. First, there is a large group of species which lay a large number of eggs and have low adult survival rate. The second cluster consists of species with very high survival rates and a clutch size of only one egg. The third group is characterized by species with high survival rates but still a relatively large clutch size. From these clusters of life history characteristics we argue that the species can be classified according to the quality of their survival and breeding habitats, respectively. The high-reproductive species live in favourable breeding habitats, but poor survival habitat. In contrast, the survival habitat of the survivorship species are very good, but the breeding habitats are poor. The bet-hedging species live in favourable breeding and survival habitats, but the annual variation in the quality of the breeding habitats is very large, favouring the evolution of a larger clutch size than in the survivorship species. In order to examine the effects of these patterns of covariation between life history traits on population dynamics we calculated the sensitivity and elasticity of population growth rate to a change in age-specific fecundity or mortality rates for one species from each of the three life history types. These analyses showed that population growth rates of high-reproductive species were more sensitive and elastic to changes in the fecundity among the younger age-classes, compared to the species from the two other groups. Furthermore, elasticity to variation in mortality rates was higher than to variation in fecundity rates in all three species. To provide a further link between life history variation and population dynamics the results from key-factor analyses of population fluctuations in birds and mammals were reviewed. In most altricial birds, the key-factor appears during the non-breeding season. In contrast, in precocial birds key-factors from the breeding season explained a higher proportion of the variance in the total losses than the losses during the non-breeding season. In the majority of the cases density-dependence was found in the losses during the non-breeding season. According to the Allee-effect, we would expect that the population growth rate should decrease with density at low population sizes. No evidence was found for the presence of an Allee-effect in the studies of 11 bird species which were reduced to very low population levels during the study period. We suggest however that such an Allee-effect still may be important due to a reduction in the defence efficiency among predators or parasites, reduction in mating efficiency, or reduction in the foraging efficiency at low population densities. These results may have some important implications for overall priorities in the development of strategies for conserving species diversity. In particular, we focus on the securing of survival habitats for especially longlived species outside the breeding season.
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Microtine rodents are known to show extreme population variations (cycles) but non-cyclic populations have also been recognized during recent years. The cyclic populations have been widely thought to be regulated by intrinsic mechanisms. However, such predictions for cyclic populations are usually not applicable to non-cyclic ones and extrinsic factors may have to be included in any explanation. A hypothesis that the degree of fluctuations in small rodent numbers is related to the sustainable number of generalist predators was tested on mainly literature data by computing “indices of cyclicity” for local populations. These indices were related to latitude and snow cover (two measures) as these variables will affect the amount of alternative prey available for these generalists. Within Fennoscandia such indices for Clethrionomys glareolus and Microtus agrestis were clearly positively related to latitude and snow cover. The fraction of populations with summer declines in numbers, characterizing highly cyclic populations, increased in the same way. Cyclicity indices in Great Britain were similar to those in southern Fennoscandia, both areas being poor in snow, but were higher at the same latitudes in eastern Europe with more snow. Indices of density variations were generally low in North American Clethrionomys species and very variable in Microtus species. The gradients observed and differences between continents are interpreted as due to microtine-vegetation interactions in northern European areas poor in generalist predators but with important small mustelid predation, and to similar snowshoe hare-vegetation interactions in mainly Canada-Alaska, where small rodents may serve as alternative prey for numerically fluctuating hare predators, at least in the forests. Western European microtine populations, and probably many others, seem to be regulated by generalist predators.
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Variation in the abundance of animals has traditionally been explained as the outcome of endogenous forcing from density dependence and exogenous forcing arising from variation in weather and predation. Emerging evidence suggests that the effects of density dependence interact with external influences on population dynamics. In particular, spatial heterogeneity in resources and the presence of capable predators may weaken feedbacks from density dependence to growth of populations. We used the Kalman filter to analyze 23 time series of estimates of abundance of northern ungulate populations arrayed along a latitudinal gradient (latitude range of 40°–70°N) to evaluate the influence of spatial heterogeneity in resources and predation on density dependence. We also used contingency tables to test whether density dependence was independent of the presence of carnivores (our estimate of predation) and multiple regressions to determine the effects of spatial heterogeneity in resources, predation, and latitude on the strength of density dependence. Our results showed that the strength of density dependence of ungulate populations was low in the presence of large carnivores, particularly at northern latitudes with low primary productivity. We found that heterogeneity in elevation, which we assume acted as a surrogate for spatial heterogeneity in plant phenology, also reduced effects of density dependence. Thus, we show that external forces created by heterogeneity in resources and predation interact with internal feedbacks from population density to shape dynamics of populations of northern ungulates.
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Temporal variation in population size is regulated by both exogenous forces and density-dependent feedbacks. Furthermore, accumulating evidence indicates that temporal and spatial variation in climate and resources can modify the strength of density dependence in animal populations. We analyzed six long-term time series estimates of Peromyscus leucopus (white-footed mouse) abundance from Kansas, Ohio, Pennsylvania, Virginia, Vermont, and Maine, USA, using the Kalman filter. Model-averaged estimates of the strength of delayed density dependence increased from west to east and from south to north. The strength of direct and delayed density dependence was positively related to the annual number of days with minimum temperature below −17.8°C. Annual population growth rates of P. leucopus at the Maine site were positively related to acorn abundance and P. leucopus populations tracked the changes in red-oak acorn abundance. The populations of P. leucopus living in northern latitudes might be more dependent on northern red oak (Quercus rubra) acorns for winter food than P. leucopus in southern latitudes. Furthermore, northern red oak trees mast every 4–5years. Thus, longer, colder winters in northerly latitudes might result in stronger delayed density dependence in mouse populations with a shortage of winter food. Mice might simply track the acorn fluctuations in a delayed autocorrelated manner; however, delayed density dependence remained in our models for the Maine mouse populations after accounting for acorns, suggesting additional sources for delayed density dependence. Our results suggest that, in seed-eating Peromyscus, cyclicity may be regulated, in part, from low to high trophic levels.
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Climate influences a variety of ecological processes. These effects operate through local weather parameters such as temperature, wind, rain, snow, and ocean currents, as well as interactions among these. In the temperate zone, local variations in weather are often coupled over large geographic areas through the transient behavior of atmospheric planetary-scale waves. These variations drive temporally and spatially averaged exchanges of heat, momentum, and water vapor that ultimately determine growth, recruitment, and migration patterns. Recently, there have been several studies of the impact of large-scale climatic forcing on ecological systems. We review how two of the best-known climate phenomena—the North Atlantic Oscillation and the El Niño–Southern Oscillation—affect ecological patterns and processes in both marine and terrestrial systems.
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Density‐dependence is a key concept in population dynamics. Here, we review how body mass and demographic parameters vary with population density in large herbivores. The demographic parameters we consider are age‐ and sex‐specific reproduction, survival and dispersal. As population density increases, the body mass of large herbivores typically declines, affecting individual performance traits such as age of first reproduction and juvenile survival. We documented density‐dependent variations in reproductive rates for many species from the Arctic to subtropical zones, both with and without predation. At high density, a trade‐off between growth and reproduction delays the age of primiparity and often increases the costs of reproduction, decreasing both survival and future reproductive success of adult females. Density‐dependent preweaning juvenile survival occurs more often in polytocous than monotocous species, while the effects of density on post‐weaning juvenile survival are independent of litter size. Responses of adult survival to density are much less marked than for juvenile survival, and may be exaggerated by density‐dependent changes in age structure. The role of density‐dependent dispersal in population dynamics remains uncertain, because very few studies have examined it. For sexually dimorphic species, we found little support for higher sensitivity to increasing density in the life history traits of males compared to females, except for young age classes. It remains unclear whether males of dimorphic species are sensitive to male density, female density or a combination of both. Eberhardt's model predicting a sequential effect of density on demographic parameters (from juvenile survival to adult survival) was supported by 9 of 10 case studies. In addition, population density at birth can also lead to cohort effects, including a direct effect on juvenile survival and long‐term effects on average cohort performance as adults. Density effects typically interact with weather, increasing in strength in years of harsh weather. For some species, the synchronization between plant phenology and reproductive cycle is a key process in population dynamics. The timing of late gestation as a function of plant phenology determines whether density‐dependence influences juvenile survival or adult female reproduction. The detection of density‐dependence can be made difficult by nonlinear relationships with density, high sampling variability, lagged responses to density changes, changes in population age structure, and temporal variation in the main factors limiting population growth. The negative feedbacks of population size on individual performance, and hence on life history traits, are thus only expected in particular ecological contexts and are most often restricted to certain age‐specific demographic traits.
Article
A knowledge of animal population dynamics is essential for the proper management of natural resources and the environment. This book, now available in paperback, develops basic concepts and a rigorous methodology for the analysis of animal population dynamics to identify the underlying mechanisms.
Chapter
Small mammals and rodents particularly are ideal subjects to study comparative and evolutionary aspects of life-history styles. They are common, species-rich, widely-distributed in diverse habitats, occupy numerous trophic niches and are easily sampled. Most mammals are viviparous, polytocous and suckle their young. This places constraints on the plasticity of their life-history styles, facilitating investigation of current hypotheses, and generalisation. Alternative strategies for the partitioning of energy by pregnant and lactating small mammals include (a) reducing litter size, (b) reducing growth rate of young, or (c) increasing time to weaning. Altricial species have a wide range of reproductive characteristics while precocial species are relatively uniform; precociality is likely associated with the early development of endothermy. Demography cannot be ignored when considering the evolution of life-history styles, and include fertility, fecundity and degree of iteroparity. Breeding seasons of mammalian species are strongly influenced by population density and dispersion, which in turn are affected by resource availability and distribution. It is possible to trace the evolutionary relationships between such parameters, r and K selection relates a population’s density/r max to resource availability/stability, but density relative to resources is not the sole criterion for understanding the evolution of life histories and the dualism of r and K is too simplistic to encompass all life-history traits. Adversity selection, temporally-dynamic selection and bet-hedging are invoked to extend/counter r and K theory (i) in habitats of predictable unfavourableness (ii) where regular temporal shifts occur in habitat/population density, (iii) or in variable habitats that influence mortality rates of juveniles/adults differentially, resulting in shifts in degree of iteroparity and predictions counter to r and K theory. Life-history styles may be regarded as a consequence of body mass since differentially mass-related constraints affect reproductive parameters, e.g. duration of pregnancy, relative foetal mass and growth rate. However, rodents with similar mass have markedly dissimilar life-history styles; allometry is not a total explanation. Holistic hypotheses are required to account for the evolution of ecological segregation of life-history styles in small mammals.
Chapter
When Keith (1963) published his ‘Wildlife’s 10-year cycle’, available information on the theme was minimal. Many theories were no more than conjectures. In 1961, realizing that further theorizing would get him nowhere, Keith and a team of researchers from the Wisconsin school of wildlife ecology, launched a long-term field study on snowshoe hare (Lepus americanus) populations near Rochester, Alberta. A number of important papers from this study have appeared since then, including the monograph (Keith and Windberg, 1978) that provides a nearly complete 15-year set of demographic data. I shall call this work ‘the Rochester study’.
Chapter
Nothing has so intrigued and fascinated many naturalists and ecologists as the persistent 10-year cycle of Canada lynx, Lynx canadensis. The well-known archives of the fur trade between the Hudson’s Bay Company and the Canadian trappers in the past two centuries have been a rich source of speculation about the cause of the cycle. As a result, diverse theories exist in the literature. However, many of these ideas were not substantiated by observations, and some statistical analyses ignored ecological mechanisms.
Article
I review the regular multiannual population fluctuations in voles and lemmings of northern latitudes. Periodically fluctuating small rodent populations all exhibit a clear two-dimensional density-dependent structure. This implies both a direct and a delayed annual density dependence, and suggests that either a predator-prey type of interaction or a specialised plant-herbivore type of interaction (but not both) may be the underlying cause of these multiannual density cycles. Clear-cut experimental testing relating to these propositions is, however, lacking. A two-dimensional annual density-dependent structure is typically non-linear in a way which may be modelled as a threshold type of non-linearity and interpreted as a phase dependence in the density-dependent structure (implying that the density-dependent structure is different in the increase and the decrease phase). Two clear geographic gradients in the annual density-dependent structure are reviewed: the Fennoscandian gradient and the Hokkaidian gradient. The seasonal nature of the annual density-dependent structure is furthermore reviewed: for voles in both Fennoscandia and Hokkaido the direct annual density dependence during the winter (measured per time unit) is concluded to be the strongest. I close with a survey of the main challenges within the field of 'small rodent cycles' - the greatest of which is suggested to be the integration of demography and population dynamics. I recommend to look at other populations for potentially applicable model systems. I conclude that multiannual population cycles seen in voles and lemmings will continue to be a strong source of conceptual and methodological developments within the field of population ecology.
Article
It has been suggested that specialist mammalian predators (small mustelids) maintain or at least significantly contribute to the regular multi-annual cycles of rodent populations in N Europe. Generalist predators are assumed to stabilize rodent populations in more southern localities. Combining the 2 kinds of predation in the same predator-prey model demonstrates that the generalist predators have a stabilizing effect on a cycle driven by specialist predators. In the model, the ratio of the maximum over the minimum prey population size and the length of the prey cycle decrease with increasing numbers of generalist predators. Sufficiently large numbers of generalist predators convert the limit cycle to a stable equilibrium point. The numbers of generalist predators greatly increase from N → S in Fennoscandia. In agreement with the model predictions, the ratio of the maximum over the minimum rodent density decreases by an order of magnitude, and the length of the cycle decreases from 5 to 3 yr, from the seventieth to the sixtieth parallel. There is no clear multiannual cycle below 60°N. -from Authors
Article
Multivariate Data and Multivariate Analysis.- Looking at Multivariate Data.- Principal Components Analysis.- Exploratory Factor Analysis.- Multidimensional Scaling and Correspondence Analysis.- Cluster Analysis.- Grouped Multivariate Data: Multivariate Analysis of Variance and Discriminant Function Analysis.- Multiple Regression and Canonical Correlation.- Analysis of Repeated Measures Data.
Article
Explicit consideration of timescales and dynamics is required for an understanding of fundamental issues in ecology. Endogenous dynamics can lead to transient states where asymptotic behavior is very different from dynamics on short timescales. The causes of these kinds of transients can be placed in one of three classes: linear systems with different timescales embedded or exhibiting reactive behavior, the potentially long times to reach synchrony across space for oscillating systems, and the complex dynamics of systems with strong density-dependent (nonlinear) interactions. It is also important to include the potentially disparate timescales inherent in ecological systems when determining the endogenous dynamics. I argue that the dynamics of ecological systems can best be understood as the response, which may include transient dynamics, to exogenous influences leading to the observed dynamics on ecologically relevant timescales. This view of ecosystem behavior as responses of ecological systems governed by endogenous dynamics to exogenous influences provides a synthetic way to unify different approaches to population dynamics, to understand mechanisms that determine the distribution and abundance of species, and to manage ecosystems on appropriate timescales. There are implications for theoretical approaches, empirical approaches, and the statistical approaches that bridge theory and observation.
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Article
Snow is a major determinant of forage availability for reindeer and caribou (Rangifer tarandus; hereafter Rangifer) in winter and is, consequently, a medium through which climate variation may influence population dynamics in this species. Periodic "icing" of winter ranges, where interludes of mild weather result in formation of crusted snow and basal ice that restrict access to forage, is held to be a cause of mass starvation, catastrophic declines in numbers, and even extirpation of local populations. It has been suggested that warming of the Arctic may result in increased frequency of winters with unfavorable snow and ice conditions, with serious consequences for Rangifer. This paper examines data on major declines in populations of Rangifer to determine the mechanism(s) of these events and the role of snow and ice conditions in them. Thirty-one declines, involving numerical decreases between 25% and 99%, were identified in 12 populations. Declines were of two types: the negative phase of irruptive oscillations, mainly associated with populations introduced into new habitat, and numerical fluctuation in persistently unstable established populations. The mechanisms of decline differed widely in both categories, ranging from wholly mortality to almost wholly emigration. In all cases, the observed dynamics are best interpreted as a product of interaction between internal processes (density dependence) and the external abiotic conditions (density independence). The strength and the form of density independence, parameterized in terms of local weather or large-scale climate, varies widely between populations, reflecting the enormous range of climate conditions across the circumpolar distribution of Rangifer. This complicates the search for abiotic components likely to be consistently important determinants of population growth in the species. There are few data demonstrating the presence of extensive hard snow or basal ice on ranges during winter(s) in which populations declined, and none confirming ice as a ubiquitous and potent agent in the dynamics of Rangifer. Instead, where the simultaneous effects of density-dependent and density-independent factors are examined across the full temporal record of dynamics, climatic conditions associated with increased amounts of snow or winter warming are generally found to enhance the abundance of animals, at least in established populations.
Article
In this book, Andrew Harvey sets out to provide a unified and comprehensive theory of structural time series models. Unlike the traditional ARIMA models, structural time series models consist explicitly of unobserved components, such as trends and seasonals, which have a direct interpretation. As a result the model selection methodology associated with structural models is much closer to econometric methodology. The link with econometrics is made even closer by the natural way in which the models can be extended to include explanatory variables and to cope with multivariate time series. From the technical point of view, state space models and the Kalman filter play a key role in the statistical treatment of structural time series models. The book includes a detailed treatment of the Kalman filter. This technique was originally developed in control engineering, but is becoming increasingly important in fields such as economics and operations research. This book is concerned primarily with modelling economic and social time series, and with addressing the special problems which the treatment of such series poses. The properties of the models and the methodological techniques used to select them are illustrated with various applications. These range from the modellling of trends and cycles in US macroeconomic time series to to an evaluation of the effects of seat belt legislation in the UK.
Article
Ecologists that study the population dynamics of large and small herbivorous mammals operate in two worlds that overlap only partly, and in this paper I address whether the conjecture that these worlds represent two distinct and valid paradigms is currently justified. I argue that large mammals fall into three groups depending on whether they have effective predators or not, and whether they are harvested by humans. Because of human persecution of large predators, more and more large herbivorous mammals are effectively predator-free and are controlled bottom-up by food. But in less disturbed systems, large herbivorous mammals should be controlled top-down by effective predators, and this can lead to a trophic cascade. Small herbivorous mammals have been suggested to be controlled top-down by predators but some experimental evidence has challenged this idea and replaced it with the notion that predation is one of several factors that may affect rates of population increase. Intrinsic control (territoriality, infanticide, social inhibition of breeding) appears to be common in small herbivorous mammals with altricial young but is absent in species with precocial young, in ecosystems with strong stochastic weather variation (deserts) and in areas of human-induced habitat fragmentation in agricultural monocultures. The extrinsic control of large herbivores with precocial young validates part of Graeme Caughley's Grand Vision, but the relative role of intrinsic and extrinsic mechanisms for small herbivores with altricial young is still controversial. An improved knowledge of population control mechanisms for large and small herbivores is essential for natural resource management.
Dear Sir, The frequent opportunities I have had of receiving pleasure from your writings and conversation, have induced me to prefer offering to the Royal Society through your medium, this Paper on Life Contingencies, which forms part of a continuation of my original paper on the same subject, published among the valuable papers of the Society, as by passing through your hands it may receive the advantage of your judgment.
Chapter
Examines the ideas of limitation, regulation and persistence in populations, and reviews the history of relevant concepts, viz the balance of nature; weather and population persistence; and extrinsic/intrinsic factors and group selection. There follows an examination of regulation and testing for density dependence, with various kinds of evidence for regulation being scrutinised. Density dependence in the life cycle is given particular attention, and causes of density-dependent mortality are discussed in insects, fish, large mammals, small mammals and birds. A final section discusses non-equilibrium conditions and multiple stable states. -P.J.Jarvis
Article
The intrinsic rate of increase is a fundamental concept in population ecology, and a variety of problems require that estimates of population growth rate be obtained from empirical data. However, depending on the extent and type of data available (e.g. time series, life tables, life history traits), several alternative empirical estimators of population growth rate are possible. Because these estimators make different assumptions about the nature of age-dependent mortality and density-dependence of population dynamics, among other factors, these quantities capture fundamentally different aspects of population growth and are not interchangeable. Nevertheless, they have been routinely commingled in recent ecoinformatic analyses relating to allometry and conservation biology. Here we clarify some of the confusion regarding the empirical estimation of population growth rate and present separate analyses of the frequency distributions and allometric scaling of three alternative, non-interchangeable measures of population growth. Studies of allometric scaling of population growth rate with body size are additionally sensitive to the statistical line fitting approach used, and we find that different approaches yield different allometric scaling slopes. Across the mix of population growth estimators and line fitting techniques, we find scattered and limited support for the key allometric prediction from the metabolic theory of ecology, namely that log10(population growth rate) should scale as −0.25 power of log10(body mass). More importantly, we conclude that the question of allometric scaling of population growth rate with body size is highly sensitive to previously unexamined assumptions regarding both the appropriate population growth parameter to be compared and the line fitting approach used to examine the data. Finally, we suggest that the ultimate test of allometric scaling of maximum population growth rates with body size has not been done and, moreover, may require data that are not currently available.
Article
In this paper, we critically evaluate the view that eutherian life history diversity arises because of constraints imposed by the allometric consequences of body size, rather than selection acting on a broad array of possible life histories. Using life history data from over 700 species of eutherians, we examine covariation of life history variables across the 18 orders represented. Eutherian orders can be arranged from those characterized by small rapidly reproducing, rapidly developing, short-lived species, such as lagomorphs, to large, slowly developing, slowly reproducing, long lived species, such as elephants. When the effect of body weight is controlled for, this pattern remains, but the relative positions ofthe orders on the new fast-slow continuum are very different. There is a trade-off between the weight and number of offspring in a litter which is independent of adult body weight. Maximum recorded lifespan is the best identified predictor of annual fecundity: high fecundity is associated with short lives. This is not easily explained as a cost of reproduction, because it is a function of the whole lifetime, rather than just the maximum reproductive lifespan. Those mechanisms said to underlie the allometric scaling of life histories, and which make testable predictions–growth constraints imposed by basal metabolic rate, brain weight and the rate of neuronal tissue growth–are not associated with life history variation once the effects of body weight are removed. Thus these variables have no greater explanatory power than body weight itself, since they cannot explain the variation in life histories which is not correlated with weight. Rates of litter growth rate are associated with life history variation independent of body weight, but until we understand why litter growth rates vary, they are unable, on their own, to explain considerable amounts of life history diversity. Differences in life histories among orders, whether or not the effect of body weight is controlled for, are associated with differences in mortality rates. We suggest that eutherian life histories are better thought of as adaptive strategies, and that mortality patterns offer considerably more promise in the understanding of eutherian life history diversity than loosely defined ideas about scaling principles and the allometric consequences of body size.
Article
Although there have been numerous life-history reviews of mammals at high taxonomic levels (e.g. among families within orders), there are far fewer studies at lower taxonomic levels (e.g. among species within genera). Data on adult weights, litter size, gestation length, neonate weight, age and weight at weaning, growth rate to weaning, maximum life span, and length of the breeding season were compiled from the literature on five species of Clethrionomys and 33 species of Microtus. Variability in litter size and male body weights was not significantly different when compared between cyclic and non-cyclic populations. Coefficients of variation were also calculated for the three species with the most data (C. gapperi, C. glareolus and M. pennsylvanicus). These values showed that the amount of intraspecific variation differed among traits as well as among species. Gestation length was the most invariable of all traits and variation in adult weights, neonate weight, gestation length, and litter size had similar values to those reported for Peromyscus maniculatus. Five and eight traits differed among Clethrionomys and Microtus species, respectively. Differences in litter size, adult weights and length of the breeding season were common to both genera. Male weight, gestation length and neonate weight as well as length of the breeding season were different between genera. Very few traits covaried within C. gapperi, C. glareolus or M. pennsylvanicus. Similarly, few traits covaried among all Clethrionomys populations. However, among all Microtus populations and Microtus species, 11 and 12 correlations were significant. Many of the patterns found in Microtus involved positive relationships between female weight and some other trait. These patterns have also been found by broader surveys at higher taxonomic levels. Large species of Microtus had larger offspring, a greater litter size and occurred in short-season environments relative to small species of this genus.
Book
Information theory and log-likelihood models - a basis for model selection and inference practical use of the information theoretic approach model selection uncertainty with examples Monte Carlo insights and extended examples statistical theory.
Article
Natural ecological communities are continuously buffeted by a varying en-vironment, often making it difficult to measure the stability of communities using concepts requiring the existence of an equilibrium point. Instead of an equilibrium point, the equi-librial state of communities subject to environmental stochasticity is a stationary distri-bution, which is characterized by means, variances, and other statistical moments. Here, we derive three properties of stochastic multispecies communities that measure different characteristics associated with community stability. These properties can be estimated from multispecies time-series data using first-order multivariate autoregressive (MAR(1)) models. We demonstrate how to estimate the parameters of MAR(1) models and obtain confidence intervals for both parameters and the measures of stability. We also address the problem of estimation when there is observation (measurement) error. To illustrate these methods, we compare the stability of the planktonic communities in three lakes in which nutrient loading and planktivorous fish abundance were experimentally manipulated. MAR(1) mod-els and the statistical methods we present can be used to identify dynamically important interactions between species and to test hypotheses about stability and other dynamical properties of naturally varying ecological communities. Thus, they can be used to integrate theoretical and empirical studies of community dynamics.
Article
Model selection is a necessary step in many practical regression analyses. But for methods based on estimating equations, such as the quasi-likelihood and generalized estimating equation (GEE) approaches, there seem to be few well-studied model selection techniques. In this article, we propose a new model selection criterion that minimizes the expected predictive bias (EPB) of estimating equations. A bootstrap smoothed cross-validation (BCV) estimate of EPB is presented and its performance is assessed via simulation for overdispersed generalized linear models. For illustration, the method is applied to a real data set taken from a study of the development of ewe embryos.
Article
Regular oscillations of northern small rodents (lemmings, voles and mice) have fascinated ecologists for decades. In particular, cycles exhibited by Fennoscandian voles have inspired population ecologists to propose several hypotheses for their underlying causes. Although there is now some agreement that the interaction with specialist predators is involved, many aspects remain enigmatic, one being the precise ecological mechanism involved in the first-order feedback effect (i.e. direct density dependence). In this paper we evaluate the relative importance of first and second-order negative feedback on small rodent dynamics in 64 data sets, assess the evidence of non-linearity in the feedback structure, and look for similarities and/or differences between species and places. A clear feature of our analysis was the highly consistent pattern of first-order dynamics across species and locations, suggesting the importance of intra-specific interactions independent of local environmental conditions. Second-order feedback generally showed a large degree of variation and appears to be strongly dependent on environmental conditions and locality. There seems to be no consistent latitudinal pattern or non-linearity in the feedback responses. We conclude that northern small rodent populations are basically regulated by both highly consistent first-order feedback (e.g. intra-specific competition, functional responses of generalist predators) and less consistent, site-specific second-order effects (e.g. numerical responses of specialist predators or food plants).
Article
We offer an evaluation of the Caughley and Krebs hypothesis that small mammals are more likely than large mammals to possess intrinsic population regulating mechanisms. Based on the assumption that intrinsic regulation will be manifest via direct density-dependent feedbacks, and extrinsic regulation via delayed density-dependent feedbacks, we fit autoregressive models to 30 time series of abundance for large and small mammals to characterize their dynamics. Delayed feedbacks characterizing extrinsic mechanisms, such as trophic-level interactions, were detected in most time series, including both small and large mammals. Spectral analyses indicated that the effect of such delayed feedbacks on the variability in population growth rates differed with body size, with large mammals exhibiting predominantly reddened and whitened spectra in contrast with predominantly blue spectra for small mammals. Large mammals showed less variance and more stable dynamics than small mammals, consistent with, among other factors, differences in their potential population growth rates. Patterns of population dynamics in small versus large mammals contradicted those predicted by the Caughley and Krebs hypothesis.
Article
Populations are regulated intrinsically (self-regulated) when the animals lower their rate of increase behaviorally or physiologically as a reaction to rising density. They are regulated extrinsically if the equilibrium is a mechanical consequence of interaction between the population and the organisms providing its food. We suggest that, at least for mammalian herbivores, self-regulation is unlikely to evolve unless the population's intrinsic rate of increase exceeds about 0.45 on a yearly basis. That value corresponds to a body weight of about 30 kg, the intrinsic rate being related inversely to body weight by r m=1.5 W-0.36 with W in kg.The two dynamic strategies, self-regulation and extrinsic regulation, should enforce a bimodality of the frequency distribution of observed intrinsic rates of increase. This in turn might be reflected in a bimodality of body sizes, the smaller herbivores constituting the lower mode generally showing intrinsic regulation and the larger herbivores of the upper mode generally being regulated by extrinsic mechanisms. There is some empirical support for these predictions but it is by no means clearcut.Mechanisms of self-regulation can evolve either by individual or group selection. Individual selection may act in two ways. By inhibiting their neighbours with some form of interference, individuals may increase their relative fitness without increasing their reproductive rate. Alternatively, individual selection may raise the absolute fitness of individuals and thereby raise the populations's intrinsic rate of increase. The population is destabilized if that process continues beyond a certain threshold and the population is then at significant risk of extinction at the troughs of the consequent oscillations. Selection between such populations will favour those carrying the beginnings of a self-regulating mechanism, and with that mechanism strengthened and fixed by continuing group selection, individual selection is again freed of the dynamic restraints on raising further the intrinsic rate of increase.
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The classical filtering and prediction problem is re-examined using the Bode-Sliannon representation of random processes and the “state-transition” method of analysis of dynamic systems. New results are: (1) The formulation and methods of solution of the problem apply without modification to stationary and nonstationary statistics and to growing-memory and infinitememory filters. (2) A nonlinear difference (or differential) equation is derived for the covariance matrix of the optimal estimation error. From the solution of this equation the coefficients of the difference (or differential) equation of the optimal linear filter are obtained without further calculations. (3) The filtering problem is shown to be the dual of the noise-free regulator problem. The new method developed here is applied to two well-known problems, confirming and extending earlier results. The discussion is largely self-contained and proceeds from first principles; basic concepts of the theory of random processes are reviewed in the Appendix.
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A broadly applicable algorithm for computing maximum likelihood estimates from incomplete data is presented at various levels of generality. Theory showing the monotone behaviour of the likelihood and convergence of the algorithm is derived. Many examples are sketched, including missing value situations, applications to grouped, censored or truncated data, finite mixture models, variance component estimation, hyperparameter estimation, iteratively reweighted least squares and factor analysis.
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Among ecologists, it is often believed that population abundance is lognormally distributed. To test this hypothesis, we analysed and compared 544 annual time-series of population abundance longer than 30 years (n≥30). Using Khamis’ modified KS test we found one-half of the long-term datasets were lognormally distributed (p-value=0.05). Among those deviating from lognormality, the most consistent feature was that the skewness was less than that expected under the lognormal hypothesis, implying a shorter upper tail (i.e. fewer extremely high values) than expected. There was little evidence of systematic extreme heavy-tail behaviour characteristic of the Lévy-stable distributions in long (n≥50 years) time series. Both the standard KS test and the Akaike information criterion (AIC) were used to compare a number of alternative distributions for goodness of fit. Distributions symmetric in logarithmic scale (lognormal and log-sech) were found to fit the data best according to the KS test. However, by the AIC the gamma distribution was most often the best model. Numbers of significant departures from lognormality varied among taxa, with insects having the highest departure from lognormality. There were also trophic differences, with herbivores deviating from lognormality more than carnivores. We found no habitat or geographic dependencies in the incidence of lognormality. The poor fit of the lognormal to real data means that it is not a good substitute for specific population dynamic and distributional information. However, being a superior “universal” descriptor of population abundance than other two-parameter models, it may be useful in applications where such detailed information is unavailable.