Demographic effects of aggregation in the presence of a component Allee effect

The component Allee effect (AE) is the positive correlation between an organism's fitness component and population density. Depending on the population spatial structure, which determines the interactions between organisms, a component AE might lead to positive density dependence in the population per-capita growth rate and establish a demographic AE. However, existing spatial models impose a fixed population spatial structure, which limits the understanding of how a component AE and spatial dynamics jointly determine the existence of demographic AEs. We introduce a spatially explicit theoretical framework where spatial structure and population dynamics are emergent properties of the individual-level demographic and movement rates. This framework predicts various spatial patterns depending on its specific parametrization, including evenly spaced aggregates of organisms, which determine the demographic-level by-products of the component AE. We find that aggregation increases population abundance and allows population survival in harsher environments and at lower global population densities when compared with uniformly distributed organisms. Moreover, aggregation can prevent the component AE from manifesting at the population level or restrict it to the level of each independent aggregate. These results provide a mechanistic understanding of how component AEs might operate for different spatial structures and manifest at larger scales.

Reproductive ecology of the black rat (Rattus rattus) in Madagascar: the influence of density-dependent and -independent effects

The black rat (Rattus rattus) poses a severe threat to food security and public health in Madagascar, where it is a major cause of pre- and post-harvest crop losses and an important reservoir for many zoonotic diseases, including plague. Elsewhere, ecologically based rodent management (EBRM) strategies have been developed using ecological information to inform decisions on where and when to target control. EBRM could deliver improved health and well-being outcomes in Madagascar if adapted to the local ecological context. Using data collected from removal studies, we explored spatio-temporal patterns in the breeding activity of the black rat (R. rattus) in domestic and agricultural habitats across Madagascar and investigated to what extent these trends are influenced by rainfall and rat density. We identified clear spatio-temporal variation in the seasonality of R. rattus reproduction. Reproduction was highly seasonal both inside and outside of houses, but seasonal trends varied between these two habitats. Seasonal trends were explained, in part, by variation in rainfall; however, the effect of rainfall on reproductive rates did itself vary by season and habitat type. A decline in breeding intensity with increasing rat density was recorded outside of houses. This has important implications for control, as populations may compensate for removal through increased reproduction. We recommend that sustained control initiated before the main breeding season, combined with improved hygiene and adequate rodent-proofing in homes and grain stores, could curtail population growth and reduce pre- and post-harvest losses provided that these measures overcome the compensatory response of rodent populations.

Bayesian inference on the Allee effect in cancer cell line populations using time-lapse microscopy images

The Allee effect describes the phenomenon that the per capita reproduction rate increases along with the population density at low densities. Allee effects have been observed at all scales, including in microscopic environments where individual cells are taken into account. This is great interest to cancer research, as understanding critical tumour density thresholds can inform treatment plans for patients. In this paper, we introduce a simple model for cell division in the case where the cancer cell population is modelled as an interacting particle system. The rate of the cell division is dependent on the local cell density, introducing an Allee effect. We perform parameter inference of the key model parameters through Markov Chain Monte Carlo, and apply our procedure to two image sequences from a cervical cancer cell line. The inference method is verified on in silico data to accurately identify the key parameters, and results on the in vitro data strongly suggest an Allee effect.

Density-dependent habitat selection alters drivers of population distribution in northern Yellowstone elk

Although it is well established that density dependence drives changes in organismal abundance over time, relatively little is known about how density dependence affects variation in abundance over space. We tested the hypothesis that spatial trade-offs between food and safety can change the drivers of population distribution, caused by opposing patterns of density-dependent habitat selection (DDHS) that are predicted by the multidimensional ideal free distribution. We addressed this using winter aerial survey data of northern Yellowstone elk (Cervus canadensis) spanning four decades. Supporting our hypothesis, we found positive DDHS for food (herbaceous biomass) and negative DDHS for safety (openness and roughness), such that the primary driver of habitat selection switched from food to safety as elk density decreased from 9.3 to 2.0 elk/km² . Our results demonstrate how population density can drive landscape-level shifts in population distribution, confounding habitat selection inference and prediction and potentially affecting community-level interactions.

Extinction transition of hantavirus-infected rodents in a hostile environment

The spatial critical shelter sizes above which populations would survive are investigated for the infection of hantavirus among rodent populations surrounded by a deadly environment. We show that the critical shelter sizes for the infected population and the susceptible population are different due to symmetry breaking in the reproduction and the transmission processes. Therefore, there exists a shelter size gap within which the infected population becomes extinct while only the susceptible population survives. With the field data reported in the literature, we estimate that, if one confines the rodent population within a stripe region surrounded by a deadly environment with the shorter dimension between 335.5±27.2m and 547.9±78.3m, the infected population would become extinct. In addition, we introduce two factors that influence the movement of rodents, namely, the spatial asymmetry of the landscape and the sociality of rodents, to study their effects on the shelter size gap. The effects on the critical size due to environmental bias are twofold: it enhances the overall competition among rodents which increases the critical size, but on the other hand it promotes the spread of the hantavirus which reduces the critical size for the infected population. On the contrary, the sociality of rodents gives rise to a more localized population profile which promotes the spread of the hantavirus and reduces the shelter size gap. The results shed light on a possible strategy of eliminating hantavirus while preserving the integrity of food webs in ecosystems.

Effects of Prey's Diffusion on Predator-Prey Systems with Two Patches

This paper considers predator-prey systems in which the prey can move between source and sink patches. First, we give a complete analysis on global dynamics of the model. Then, we show that when diffusion from the source to sink is not large, the species would coexist at a steady state; when the diffusion is large, the predator goes to extinction, while the prey persists in both patches at a steady state; when the diffusion is extremely large, both species go to extinction. It is derived that diffusion in the system could lead to results reversing those without diffusion. That is, diffusion could change species' coexistence if non-diffusing, to extinction of the predator, and even to extinction of both species. Furthermore, we show that intermediate diffusion to the sink could make the prey reach total abundance higher than if non-diffusing, larger or smaller diffusion rates are not favorable. The total abundance, as a function of diffusion rates, can be both hump-shaped and bowl-shaped, which extends previous theory. A novel finding of this work is that there exist diffusion scenarios which could drive the predator into extinction and make the prey reach the maximal abundance. Diffusion from the sink to source and asymmetry in diffusion could also lead to results reversing those without diffusion. Meanwhile, diffusion always leads to reduction of the predator's density. The results are biologically important in protection of endangered species.

Cooperation and Cheating among Germinating Spores

Many microbes produce stress-resistant spores to survive unfavorable conditions [1-4] and enhance dispersal [1, 5]. Cooperative behavior is integral to the process of spore formation in some species [3, 6], but the degree to which germination of spore populations involves social interactions remains little explored. Myxococcus xanthus is a predatory soil bacterium that upon starvation forms spore-filled multicellular fruiting bodies that often harbor substantial diversity of endemic origin [7, 8]. Here we demonstrate that germination of M. xanthus spores formed during fruiting-body development is a social process involving at least two functionally distinct social molecules. Using pairs of natural isolates each derived from a single fruiting body that emerged on soil, we first show that spore germination exhibits positive density dependence due to a secreted "public-good" germination factor. Further, we find that a germination defect of one strain under saline stress in pure culture is complemented by addition of another strain that germinates well in saline environments and mediates cheating by the defective strain. Glycine betaine, an osmo-protectant utilized in all domains of life, is found to mediate saline-specific density dependence and cheating. Density dependence in non-saline conditions is mediated by a distinct factor, revealing socially complex spore germination involving multiple social molecules.

Population Dynamics with Threshold Effects Give Rise to a Diverse Family of Allee Effects

The Allee effect describes populations that deviate from logistic growth models and arises in applications including ecology and cell biology. A common justification for incorporating Allee effects into population models is that the population in question has altered growth mechanisms at some critical density, often referred to as a threshold effect. Despite the ubiquitous nature of threshold effects arising in various biological applications, the explicit link between local threshold effects and global Allee effects has not been considered. In this work, we examine a continuum population model that incorporates threshold effects in the local growth mechanisms. We show that this model gives rise to a diverse family of Allee effects, and we provide a comprehensive analysis of which choices of local growth mechanisms give rise to specific Allee effects. Calibrating this model to a recent set of experimental data describing the growth of a population of cancer cells provides an interpretation of the threshold population density and growth mechanisms associated with the population.

Fire mosaics and habitat choice in nomadic foragers

In the mid-1950s Western Desert of Australia, Aboriginal populations were in decline as families left for ration depots, cattle stations, and mission settlements. In the context of reduced population density, an ideal free-distribution model predicts landscape use should contract to the most productive habitats, and people should avoid areas that show more signs of extensive prior use. However, ecological or social facilitation due to Allee effects (positive density dependence) would predict that the intensity of past habitat use should correlate positively with habitat use. We analyzed fire footprints and fire mosaics from the accumulation of several years of landscape use visible on a 35,300-km2 mosaic of aerial photographs covering much of contemporary Indigenous Martu Native Title Lands imaged between May and August 1953. Structural equation modeling revealed that, consistent with an Allee ideal free distribution, there was a positive relationship between the extent of fire mosaics and the intensity of recent use, and this was consistent across habitats regardless of their quality. Fire mosaics build up in regions with low cost of access to water, high intrinsic food availability, and good access to trade opportunities; these mosaics (constrained by water access during the winter) then draw people back in subsequent years or seasons, largely independent of intrinsic habitat quality. Our results suggest that the positive feedback effects of landscape burning can substantially change the way people value landscapes, affecting mobility and settlement by increasing sedentism and local population density.

Stress response and population dynamics: Is Allee effect hormesis?

Hormesis is a fundamental notion in ecotoxicology while competition between organisms is an essential notion in population ecology and species adaptation and evolution. Both sub-disciplines of ecology deal with the response of organisms to abiotic and biotic stresses. In ecotoxicology, the Linear-non-Threshold (LNT), Threshold and Hormetic models are used to describe the dominant responses of a plethora of endpoints to abiotic stress. In population ecology, the logistic, theta-logistic and the Allee effect models are used to describe the growth of populations under different responses to (biotic) stress induced by population density. The per capita rate of population increase (r) measures species fitness. When it is used as endpoint, the responses to population density seem to perfectly correspond to LNT, Threshold and Hormetic responses to abiotic stress, respectively. Our analysis suggests the Allee effect is a hormetic-like response of r to population density, an ultimate biotic stress. This biphasic dose-response model appears across different systems and situations (from molecules to tumor growth to population dynamics), is highly supported by ecological and evolutionary theory, and has important implications in most sub-disciplines of biology as well as in environmental and earth sciences. Joined multi-disciplinary efforts would facilitate the development and application of advanced research approaches for better understanding potential planetary-scale implications.

The role of density-dependent and -independent processes in spawning habitat selection by salmon in an Arctic riverscape

Density-dependent (DD) and density-independent (DI) habitat selection is strongly linked to a species’ evolutionary history. Determining the relative importance of each is necessary because declining populations are not always the result of altered DI mechanisms but can often be the result of DD via a reduced carrying capacity. We developed spatially and temporally explicit models throughout the Chena River, Alaska to predict important DI mechanisms that influence Chinook salmon spawning success. We used resource-selection functions to predict suitable spawning habitat based on geomorphic characteristics, a semi-distributed water-and-energy balance hydrologic model to generate stream flow metrics, and modeled stream temperature as a function of climatic variables. Spawner counts were predicted throughout the core and periphery spawning sections of the Chena River from escapement estimates (DD) and DI variables. Additionally, we used isodar analysis to identify whether spawners actively defend spawning habitat or follow an ideal free distribution along the riverscape. Aerial counts were best explained by escapement and reference to the core or periphery, while no models with DI variables were supported in the candidate set. Furthermore, isodar plots indicated habitat selection was best explained by ideal free distributions, although there was strong evidence for active defense of core spawning habitat. Our results are surprising, given salmon commonly defend spawning resources, and are likely due to competition occurring at finer spatial scales than addressed in this study.

Climatic variation modulates the indirect effects of large herbivores on small-mammal habitat use

Large mammalian herbivores (LMH) strongly shape the composition and architecture of plant communities. A growing literature shows that negative direct effects of LMH on vegetation frequently propagate to suppress the abundance of smaller consumers. Indirect effects of LMH on the behaviour of these consumers, however, have received comparatively little attention despite their potential ecological significance. We sought to understand (i) how LMH indirectly shape small-mammal habitat use by altering the density and distribution of understorey plants; (ii) how these effects vary with climatic context (here, seasonality in rainfall); and (iii) the extent to which behavioural responses of small mammals are contingent upon small-mammal density. We tested the effects of a diverse LMH community on small-mammal habitat use using 4 years of spatially explicit small-mammal trapping and vegetation data from the UHURU Experiment, a replicated set of LMH exclosures in semi-arid Kenyan savanna. Small-mammal habitat use was positively associated with tree density and negatively associated with bare (unvegetated) patches in all plots and seasons. In the presence of LMH, and especially during the dry season, small mammals consistently selected tree cover and avoided bare patches. In contrast, when LMH were excluded, small mammals were weakly associated with tree cover and did not avoid bare patches as strongly. These behavioural responses of small mammals were largely unaffected by changes in small-mammal density associated with LMH exclusion. Our results show that LMH indirectly affect small-mammal behaviour, and that these effects are influenced by climate and can arise via density-independent mechanisms. This raises the possibility that anthropogenic LMH declines might interact with changing patterns of rainfall to alter small-mammal distribution and behaviour, independent of numerical responses by small mammals to these perturbations. For example, increased rainfall in East Africa (as predicted in many recent climate-model simulations) may relax constraints on small-mammal distribution where LMH are rare or absent, whereas increased aridity and/or drought frequency may tighten them.

Density dependence in demography and dispersal generates fluctuating invasion speeds

Density dependence plays an important role in population regulation and is known to generate temporal fluctuations in population density. However, the ways in which density dependence affects spatial population processes, such as species invasions, are less understood. Although classical ecological theory suggests that invasions should advance at a constant speed, empirical work is illuminating the highly variable nature of biological invasions, which often exhibit nonconstant spreading speeds, even in simple, controlled settings. Here, we explore endogenous density dependence as a mechanism for inducing variability in biological invasions with a set of population models that incorporate density dependence in demographic and dispersal parameters. We show that density dependence in demography at low population densities-i.e., an Allee effect-combined with spatiotemporal variability in population density behind the invasion front can produce fluctuations in spreading speed. The density fluctuations behind the front can arise from either overcompensatory population growth or density-dependent dispersal, both of which are common in nature. Our results show that simple rules can generate complex spread dynamics and highlight a source of variability in biological invasions that may aid in ecological forecasting.

Thresholds for impaired species recovery

Studies on small and declining populations dominate research in conservation biology. This emphasis reflects two overarching frameworks: the small-population paradigm focuses on correlates of increased extinction probability; the declining-population paradigm directs attention to the causes and consequences of depletion. Neither, however, particularly informs research on the determinants, rate or uncertainty of population increase. By contrast, Allee effects (positive associations between population size and realized per capita population growth rate, r(realized), a metric of average individual fitness) offer a theoretical and empirical basis for identifying numerical and temporal thresholds at which recovery is unlikely or uncertain. Following a critique of studies on Allee effects, I quantify population-size minima and subsequent trajectories of marine fishes that have and have not recovered following threat mitigation. The data suggest that threat amelioration, albeit necessary, can be insufficient to effect recovery for populations depleted to less than 10% of maximum abundance (N(max)), especially when they remain depleted for lengthy periods of time. Comparing terrestrial and aquatic vertebrates, life-history analyses suggest that population-size thresholds for impaired recovery are likely to be comparatively low for marine fishes but high for marine mammals.Articulation of a 'recovering population paradigm' would seem warranted. It might stimulate concerted efforts to identify generic impaired recovery thresholds across species. It might also serve to reduce the confusion of terminology, and the conflation of causes and consequences with patterns currently evident in the literature on Allee effects, thus strengthening communication among researchers and enhancing the practical utility of recovery-oriented research to conservation practitioners and resource managers.

The replicator equation and other game dynamics

The replicator equation is the first and most important game dynamics studied in connection with evolutionary game theory. It was originally developed for symmetric games with finitely many strategies. Properties of these dynamics are briefly summarized for this case, including the convergence to and stability of the Nash equilibria and evolutionarily stable strategies. The theory is then extended to other game dynamics for symmetric games (e.g., the best response dynamics and adaptive dynamics) and illustrated by examples taken from the literature. It is also extended to multiplayer, population, and asymmetric games.

Estimating Allee dynamics before they can be observed: polar bears as a case study

Allee effects are an important component in the population dynamics of numerous species. Accounting for these Allee effects in population viability analyses generally requires estimates of low-density population growth rates, but such data are unavailable for most species and particularly difficult to obtain for large mammals. Here, we present a mechanistic modeling framework that allows estimating the expected low-density growth rates under a mate-finding Allee effect before the Allee effect occurs or can be observed. The approach relies on representing the mechanisms causing the Allee effect in a process-based model, which can be parameterized and validated from data on the mechanisms rather than data on population growth. We illustrate the approach using polar bears (Ursus maritimus), and estimate their expected low-density growth by linking a mating dynamics model to a matrix projection model. The Allee threshold, defined as the population density below which growth becomes negative, is shown to depend on age-structure, sex ratio, and the life history parameters determining reproduction and survival. The Allee threshold is thus both density- and frequency-dependent. Sensitivity analyses of the Allee threshold show that different combinations of the parameters determining reproduction and survival can lead to differing Allee thresholds, even if these differing combinations imply the same stable-stage population growth rate. The approach further shows how mate-limitation can induce long transient dynamics, even in populations that eventually grow to carrying capacity. Applying the models to the overharvested low-density polar bear population of Viscount Melville Sound, Canada, shows that a mate-finding Allee effect is a plausible mechanism for slow recovery of this population. Our approach is generalizable to any mating system and life cycle, and could aid proactive management and conservation strategies, for example, by providing a priori estimates of minimum conservation targets for rare species or minimum eradication targets for pests and invasive species.

The Allee-type ideal free distribution

The ideal free distribution (IFD) in a two-patch environment where individual fitness is positively density dependent at low population densities is studied. The IFD is defined as an evolutionarily stable strategy of the habitat selection game. It is shown that for low and high population densities only one IFD exists, but for intermediate population densities there are up to three IFDs. Population and distributional dynamics described by the replicator dynamics are studied. It is shown that distributional stability (i.e., IFD) does not imply local stability of a population equilibrium. Thus distributional stability is not sufficient for population stability. Results of this article demonstrate that the Allee effect can strongly influence not only population dynamics, but also population distribution in space.

Consequences of local Allee effects in spatially structured populations

The ideal free distribution model incorporating the Allee effect was published by Fretwell and Lucas (1970), but went almost unnoticed within the ecological literature. The model is relevant to populations distributed among patchy habitats. It predicts a sporadic but substantial decline in populations at high densities, which in turn induces the rapid growth of new populations. In this paper, I show that the simple process explained by this model can be used to change our view of several phenomena within the field of population ecology, behavioural ecology and conservation. The ecological consequences of the model are well known. A key feature of Fretwell and Lucas's model is what I call the "Allee paradox:" there is a range of local population densities at which local individual fitness is less than the potential mean gain that could be obtained in the environment; however, individuals cannot disperse. This paradox can be used to explain why helping appears before suitable breeding areas are fully occupied, and why breeding females aggregate when male coercion is a reproductive cost. The model also predicts high clustering between related populations, and, in conservation biology, it can identify unfounded concerns about the dangers of extinction, delays in recolonisation processes after human-induced population decline, and latency periods in the initial phases of expansion of invasive species.

An appraisal of the fitness consequences of forest disturbance for wildlife using habitat selection theory

Isodar theory can help to unveil the fitness consequences of habitat disturbance for wildlife through an evaluation of adaptive habitat selection using patterns of animal abundance in adjacent habitats. By incorporating measures of disturbance intensity or variations in resource availability into fitness-density functions, we can evaluate the functional form of isodars expected under different disturbance-fitness relationships. Using this framework, we investigated how a gradient of forest harvesting disturbance and differences in resource availability influenced habitat quality for snowshoe hares (Lepus americanus) and red-backed voles (Myodes gapperi) using pairs of logged and uncut boreal forest. Isodars for both species had positive intercepts, indicating reductions to maximum potential fitness in logged stands. Habitat selection by hares depended on both conspecific density and differences in canopy cover between harvested and uncut stands. Fitness-density curves for hares in logged stands were predicted to shift from diverging to converging with those in uncut forest across a gradient of high to low disturbance intensity. Selection for uncut forests thus became less pronounced with increasing population size at low levels of logging disturbance. Voles responded to differences in moss cover between habitats which reflected moisture availability. Lower moss cover in harvested stands either reduced maximum potential fitness or increased the relative rate of decline in fitness with density. Differences in vole densities between harvested and uncut stands were predicted, however, to diminish as populations increased. Our findings underscore the importance of accounting for density-dependent behaviors when evaluating how changing habitat conditions influence animal distribution.

Allee effect limits colonization success of sexually reproducing zooplankton

Understanding the dynamics of populations at low density and the role of Allee effects is a priority due to concern about the decline of rare species and interest in colonization/invasion dynamics. Despite well-developed theory and observational support, experimental examinations of the Allee effect in natural systems are rare, partly because of logistical difficulties associated with experiments at low population density. We took advantage of fish introduction and removal in alpine lakes to experimentally test for the Allee effect at the whole-ecosystem scale. The large copepod Hesperodiaptomus shoshone is often extirpated from the water column by fish and sometimes fails to recover following fish disappearance, despite the presence of a long-lived egg bank. Population growth rate of this dioecious species may be limited by mate encounter rate, such that below some critical density a colonizing population will fail to establish. We conducted a multi-lake experiment in which H. shoshone was stocked at densities that bracketed our hypothesized critical density of 0.5-5 copoepods/m3. Successful recovery by the copepod was observed only in the lake with the highest initial density (3 copepods/m3). Copepods stocked into small cages at 3000 copepods/m3 survived and reproduced at rates comparable to natural populations, confirming that the lakes were suitable habitat for this species. In support of mate limitation as the mechanism underlying recovery failure, we found a significant positive relationship between mating success and density across experimental and natural H. shoshone populations. Furthermore, a mesocosm experiment provided evidence of increased per capita population growth rate with increasing population density in another diaptomid species, Skistodiaptomus pallidus. Together, these lines of evidence support the importance of the Allee effect to population recovery of H. shoshone in the Sierra Nevada, and to diaptomid copepods in general.

Modelling the mating system of polar bears: a mechanistic approach to the Allee effect

Allee effects may render exploited animal populations extinction prone, but empirical data are often lacking to describe the circumstances leading to an Allee effect. Arbitrary assumptions regarding Allee effects could lead to erroneous management decisions so that predictive modelling approaches are needed that identify the circumstances leading to an Allee effect before such a scenario occurs. We present a predictive approach of Allee effects for polar bears where low population densities, an unpredictable habitat and harvest-depleted male populations result in infrequent mating encounters. We develop a mechanistic model for the polar bear mating system that predicts the proportion of fertilized females at the end of the mating season given population density and operational sex ratio. The model is parametrized using pairing data from Lancaster Sound, Canada, and describes the observed pairing dynamics well. Female mating success is shown to be a nonlinear function of the operational sex ratio, so that a sudden and rapid reproductive collapse could occur if males are severely depleted. The operational sex ratio where an Allee effect is expected is dependent on population density. We focus on the prediction of Allee effects in polar bears but our approach is also applicable to other species.

How predator functional responses and Allee effects in prey affect the paradox of enrichment and population collapses

In Rosenzweig-MacArthur models of predator-prey dynamics, Allee effects in prey usually destabilize interior equilibria and can suppress or enhance limit cycles typical of the paradox of enrichment. We re-evaluate these conclusions through a complete classification of a wide range of Allee effects in prey and predator's functional response shapes. We show that abrupt and deterministic system collapses not preceded by fluctuating predator-prey dynamics occur for sufficiently steep type III functional responses and strong Allee effects (with unstable lower equilibrium in prey dynamics). This phenomenon arises as type III functional responses greatly reduce cyclic dynamics and strong Allee effects promote deterministic collapses. These collapses occur with decreasing predator mortality and/or increasing susceptibility of the prey to fall below the threshold Allee density (e.g. due to increased carrying capacity or the Allee threshold itself). On the other hand, weak Allee effects (without unstable equilibrium in prey dynamics) enlarge the range of carrying capacities for which the cycles occur if predators exhibit decelerating functional responses. We discuss the results in the light of conservation strategies, eradication of alien species, and successful introduction of biocontrol agents.

The role of predation in the decline and extirpation of woodland caribou

To select appropriate recovery strategies for endangered populations, we must understand the dynamics of small populations and distinguish between the possible causes that drive such populations to low numbers. It has been suggested that the pattern of population decline may be inversely density-dependent with population growth rates decreasing as populations become very small; however, empirical evidence of such accelerated declines at low densities is rare. Here we analyzed the pattern of decline of a threatened population of woodland caribou (Rangifer tarandus caribou) in British Columbia, Canada. Using information on the instantaneous rate of increase relative to caribou density in suitable winter foraging habitat, as well as on pregnancy rates and on causes and temporal distribution of mortalities from a sample of 349 radiocollared animals from 15 subpopulations, we tested 3 hypothesized causes of decline: (a) food regulation caused by loss of suitable winter foraging habitat, (b) predation-sensitive foraging caused by loss of suitable winter foraging habitat and (c) predation with caribou being secondary prey. Population sizes of caribou subpopulations ranged from < 5 to > 500 individuals. Our results showed that the rates of increase of these subpopulations varied from -0.1871 to 0.0496 with smaller subpopulations declining faster than larger subpopulations. Rates of increase were positively related to the density of caribou in suitable winter foraging habitat. Pregnancy rates averaged 92.4% +/-2.24 and did not differ among subpopulations. In addition, we found predation to be the primary cause of mortality in 11 of 13 subpopulations with known causes of mortality and predation predominantly occurred during summer. These results are consistent with predictions that caribou subpopulations are declining as a consequence of increased predation. Recovery of these woodland caribou will thus require a multispecies perspective and an appreciation for the influence of inverse density dependence on population trajectories.

Habitat selection and population regulation in temporally fluctuating environments

Understanding and predicting the distribution of organisms in heterogeneous environments lies at the heart of ecology, and the theory of density-dependent habitat selection (DDHS) provides ecologists with an inferential framework linking evolution and population dynamics. Current theory does not allow for temporal variation in habitat quality, a serious limitation when confronted with real ecological systems. We develop both a stochastic equivalent of the ideal free distribution to study how spatial patterns of habitat use depend on the magnitude and spatial correlation of environmental stochasticity and also a stochastic habitat selection rule. The emerging patterns are confronted with deterministic predictions based on isodar analysis, an established empirical approach to the analysis of habitat selection patterns. Our simulations highlight some consistent patterns of habitat use, indicating that it is possible to make inferences about the habitat selection process based on observed patterns of habitat use. However, isodar analysis gives results that are contingent on the magnitude and spatial correlation of environmental stochasticity. Hence, DDHS is better revealed by a measure of habitat selectivity than by empirical isodars. The detection of DDHS is but a small component of isodar theory, which remains an important conceptual framework for linking evolutionary strategies in behavior and population dynamics.

Allee effects, immigration, and the evolution of species' niches

Theoretical studies of adaptation to sink environments (with conditions outside the niche requirements of a species) have shown that immigration from source habitats can either facilitate or inhibit local adaptation. Here, we examine the influence of immigration on the evolution of local adaptation, given an Allee effect (i.e., at low densities, absolute fitness increases with population density). We consider a deterministic model for evolution at a haploid locus, and a stochastic individual-based model for evolution of a quantitative trait, and several kinds of Allee effects. We demonstrate that increased immigration can greatly facilitate adaptive evolution in the sink; with greater immigration, local population sizes rise, and because of the Allee effect, there is a positive indirect effect of immigration on local fitness. This makes it easier for alleles of modest effect to be captured by natural selection, transforming the sink into a locally adapted population that can persist without immigration.