Attractive sinks, or how individual behavioural decisions determine source–sink dynamics

Gundersen et al . (2001 , Source-sink dynamics: how sinks affect demography of sources. Ecol. Lett. , 4, 14–21.) suggested that sinks can severely affect the demography of populations in source habitats. We propose this is a common result when animals lack cues associated with reduced fitness inside sinks and consequently select habitat inappropriately. These attractive sinks can result either from undetected risks of mortality (as in the experiment of Gundersen et al . 2001 ) or from undetected poor breeding probabilities (due to bioaccumulation of pesticides, for instance). Thus, individual habitat choice is a key process underlying source–sink dynamics.     

Potential ‘Ecological Traps’ of Restored Landscapes: Koalas Phascolarctos cinereus Re-Occupy a Rehabilitated Mine Site

With progressively increasing anthropogenic habitat disturbances, restoration of impacted landscapes is becoming a critical element of biodiversity conservation. Evaluation of success in restoration ecology rarely includes faunal components, usually only encompassing abiotic and floral components of the ecosystems. Even when fauna is explicitly included, it is usually only species presence/absence criteria that are considered. If restoration is to have a positive outcome, however, populations in restored habitats should exhibit comparable survival and reproductive rates to populations found in undisturbed surroundings. If a species recolonises restored areas but later experiences decreased fitness, restored areas could become ecological sinks or traps. We investigated this possibility in a case study of koalas Phascolarctos cinereus occupying rehabilitated mining areas on North Stradbroke Island, Australia. Our holistic approach compared rehabilitated and undisturbed areas on the basis of their vegetation characteristics, of koalas'' body condition, roosting trees, diet, as well as predator index. Koalas using rehabilitated areas appeared to be able to access an adequate supply of roosting and fodder trees, were in good condition and had high reproductive output. We did not find any significant differences in predator density between rehabilitated areas and undisturbed surroundings. The results presented in this study showed there was no evidence that the post-mining rehabilitated areas constitute ecological sinks or traps. However, to reach a definitive conclusion as to whether areas rehabilitated post-mining provide at least equivalent habitat to undisturbed locations, additional research could be undertaken to assess foliar nutrient/water/toxin differences and predation risk in rehabilitated areas compared with undisturbed areas. More generally, the evaluation of whether restoration successfully produces a functional ecological community should include criteria on the fitness of faunal populations reoccupying such sites, so as to ensure functioning ecosystems, rather than ecological sinks or traps, are the outcome.     

Are urban habitats ecological traps for a native songbird? Season‐long productivity,apparent survival,and site fidelity in urban and rural habitats

The northern mockingbird Mimus polyglottos is a native species that is more abundant in urban than non‐urban habitats (i.e. an urban‐positive species). Abundance alone, however, is not an accurate index of habitat quality because urban habitats could represent ecological traps (attractive sink habitat) for urban‐positive species. We compared mockingbird nesting productivity, apparent survival, and decision rules governing site fidelity in urban and rural habitats. If the higher abundance of mockingbirds in urban habitats is driven by higher quality urban habitat, then we predicted that productivity of urban mockingbirds would exceed the estimated source‐sink threshold and productivity of non‐urban mockingbirds. If, on the other hand, urban habitats act as ecological traps, productivity would be lower in urban habitats and would fall below the estimated source‐sink threshold. Productivity of urban pairs exceeded that of non‐urban pairs and more than offset estimated adult mortality, which makes urban habitat a likely source habitat. Apparent adult survival was higher in urban habitats than in non‐urban habitats, although this could be driven by dispersal more than mortality. Decision rules also appeared to differ between urban and non‐urban populations. Females in urban habitats with successful nests were more likely to return than those with unsuccessful nests, whereas return rates of females in nonurban habitats were unrelated to nesting success and may be more related to nesting habitat availability. We conclude that urban habitats do not act as ecological traps that lure mockingbirds into sink habitat and that increased breeding productivity contributes to their success in urban habitats.     

Experimental demonstration of accelerated extinction in source‐sink metapopulations

Population extinction is a fundamental ecological process which may be aggravated by the exchange of organisms between productive (source) and unproductive (sink) habitat patches. The extent to which such source‐sink exchange affects extinction rates is unknown. We conducted an experiment in which metapopulation effects could be distinguished from source‐sink effects in laboratory populations of Daphnia magna. Time‐to‐extinction in this experiment was maximized at intermediate levels of habitat fragmentation, which is consistent with a minority of theoretical models. These results provided a baseline for comparison with experimental treatments designed to detect effects of concentrating resources in source patches. These treatments showed that source‐sink configurations increased population variability (the coefficient of variation in abundance) and extinction hazard compared with homogeneous environments. These results suggest that where environments are spatially heterogeneous, accurate assessments of extinction risk will require understanding the exchange of organisms among population sources and sinks. Such heterogeneity may be the norm rather than the exception because of both the intrinsic heterogeneity naturally exhibited by ecosystems and increasing habitat fragmentation by human activity.     

Reciprocating dispersal by habitat-selecting white-footed mice

Theories of dispersal driven by density-dependent habitat selection demonstrate that putative examples of source–sink dynamics and balanced dispersal may also be explained by a more general pattern of bi-directional, reciprocating dispersal. Analyses of 19 years of data on dispersal by white-footed mice confirm the theory. Fitness of territorial white-footed mice living in an agricultural mosaic is higher in forest habitat than it is in either edge or fencerows. Density-dependent habitat selection theory predicts that if net emigration by mice flows from the forest to forest-edge during periods of population growth, animals should subsequently move from the edge to forest during population decline. The pattern of mouse dispersal varies between seasons as populations wax and wane in abundance. Mice tend, as predicted, to move from high-density forest habitat into low-density edge during periods of population increase, and from the low-density edge into high-density forest during periods of population decline. Over all years combined, dispersal by white-footed mice was balanced. Each habitat tended to gain as many dispersing individuals as it lost. The results support a conditional dispersal strategy linked to density-dependent habitat selection, but also suggest the possibility of multiple coexisting strategies.     

The effects of habitat fragmentation on persistence of source-sink metapopulations in systems with predators and prey or apparent competitors.

We consider systems with one predator and one prey, or a common predator and two prey species (apparent competitors) in source and sink habitats. In both models, the predator species is vulnerable to extinction, if productivity in the source is insufficient to rescue demographically deficient sink populations. Conversely, in the model with two prey species, if the source is too rich, one of the prey species may be driven extinct by apparent competition, since the predator can maintain a large population because of the alternative prey. Increasing the rate of predator movement from the source population has opposite effects on prey and predator persistence. High emigration rate exposes the predator population to danger of extinction, reducing the number of individuals that breed and produce offspring in the source habitat. This may promote coexistence of prey by relaxing predation pressure and apparent competition between the two prey species. The number of sinks and spatial arrangement of patches, or connectivity between patches, also influence persistence of the species. More sinks favor the prey and fewer sinks are advantageous to the predator. A linear pattern with the source at one end is profitable for the predator, and a centrifugal pattern in which the source is surrounded by sinks is advantageous to the prey. When the dispersal rate is low, effects of the spatial structure may exceed those of the number of sinks. In brief, productivity in patches and patterns of connectivity between patches differentially influence persistence of populations in different trophic levels.     

Virus population extinction via ecological traps

Populations are at risk of extinction when unsuitable or when sink habitat exceeds a threshold frequency in the environment. Sinks that present cues associated with high-quality habitats, termed ecological traps, have especially detrimental effects on net population growth at metapopulation scales. Ecological traps for viruses arise naturally, or can be engineered, via the expression of viral-binding sites on cells that preclude viral reproduction. We present a model for virus population growth in a heterogeneous host community, parameterized with data from populations of the RNA bacteriophage Φ6 presented with mixtures of suitable host bacteria and either neutral or trap cells. We demonstrate that viruses can sustain high rates of population growth in the presence of neutral non-hosts as long as some host cells are present, whereas trap cells dramatically reduce viral fitness. In addition, we demonstrate that the efficacy of traps for viral elimination is frequency dependent in spatially structured environments such that population viability is a nonlinear function of habitat loss in dispersal-limited virus populations. We conclude that the ecological concepts applied to species conservation in altered landscapes can also contribute to the development of trap cell therapies for infectious human viruses.     

Temporal autocorrelation can enhance the persistence and abundance of metapopulations comprised of coupled sinks

In spatially heterogeneous landscapes, some habitats may be persistent sources, providing immigrants to sustain populations in unfavorable sink habitats (where extinction is inevitable without immigration). Recent theoretical and empirical studies of source-sink systems demonstrate that temporally variable local growth rates in sinks can substantially increase average abundance of a persisting population, provided that the variation is positively autocorrelated--in effect, temporal variation inflates average abundance. Here we extend these results to a metapopulation in which all habitat patches are sinks. Using numerical studies of a population with discrete generations (buttressed by analytic results), we show that temporal variation and moderate dispersal can jointly permit indefinite persistence of the metapopulation and that positive autocorrelation both lowers the magnitude of variation required for persistence and increases the average abundance of persisting metapopulations. These effects are weakened--but not destroyed--if variation in local growth rates is spatially synchronized and dispersal is localized. We show that the inflationary effect is robust to a number of extensions of the basic model, including demographic stochasticity and density dependence. Because ecological and environmental processes contributing to temporally variable growth rates in natural populations are typically autocorrelated, these observations may have important implications for species persistence.     

Assessing habitat suitability for tiger in the fragmented Terai Arc Landscape of India and Nepal

Tiger Panthera tigris populations have declined dramatically in the Terai Arc Landscape (TAL; India and Nepal), and remaining populations are highly fragmented and endangered. As part of a research program to aid tiger management by identifying critical areas for conservation, we aimed to 1) identify the factors which affect the distribution of tigers in the TAL; 2) explore the role of spatial scale in habitat selection; 3) map potentially suitable habitats; and 4) assess the quality of potential corridors linking suitable habitats. We used an approach based on presence and pseudo‐absence data, combining ecological niche factor analysis and generalized linear models. We used an information‐theoretic approach to compare our data on tiger presence with different hypotheses on tiger habitat selection (i.e. protective habitat, prey species, human disturbance), and spatial scales. All hypotheses yielded models with high prediction accuracy (>79%). The most parsimonious model included variables characterizing habitat suitability of the 2 main prey species. More detailed assessment of potentially suitable areas using an extended source‐sink approach suggested that most of the habitats outside the protected areas were attractive sink‐like habitats (i.e. they suffered high levels of human disturbance in otherwise good habitats). Overall, 24% (ca 18 500 km²) of the study area was predicted as suitable (probability cut‐off p>0.5), approximately 7% of which is under protection. Our models showed that protecting the remaining concentrations of tigers requires focusing management efforts on specific areas outside the currently protected areas. These are characterized by good natural suitability; however, they suffer from a high level of human disturbance. Our models underscore the importance of minimizing human disturbances in these areas to avoid that they act as attractive sinks but act as corridors between existing subpopulations.     

Dancing between the devil and deep blue sea: the stabilizing effect of enemy-free and victimless sinks

Theoretical and empirical studies have shown that enemy–victim interactions in spatially homogenous environments can exhibit diverging oscillations which result in the extinction of one or both species. For enemy–victim models with overlapping generations, we investigate the dynamical implications of spatial heterogeneity created by enemy-free sinks or victimless sinks. An enemy-free sink is a behavioral, physiological or ecological state that reduces or eliminates the victim's vulnerability to the enemy but cannot sustain the victim population. For victims that move in an ideal-free manner, we prove that the inclusion of an enemy-free sink shifts the population dynamics from diverging oscillations to stable oscillations. During these stable oscillations, the victim disperses in an oscillatory manner between the enemy-free sink and the enemy-occupied patch. Enemy-free sinks with lower mortality rates exhibit oscillations with smaller amplitudes and longer periods. A victimless sink, on the other hand, is a behavioral, physiological or ecological state in which the enemy has limited (or no) access to its victims. For enemies that move in an ideal-free manner, we prove that victimless sinks also stabilize diverging oscillations. Simulations suggest that suboptimal behavior due to information gathering or learning limitations amplify oscillations for systems with enemy-free sinks and dampen oscillations for systems with victimless sinks. These results illustrate that the coupling of a sink created by unstable enemy–victim interactions and a sink created by unsuitable environmental conditions can result in population persistence at the landscape level.     

Effects of an attractive sink leading into maladaptive habitat selection

Habitat sinks can attract dispersing animals if high mortality or breeding failure are difficult to detect (e.g., when due to human hunting or pollution). Using a simple deterministic model, we explore the dynamics of such source-sink systems considering three scenarios: an avoided sink, no habitat preference, and an attractive sink. In the second two scenarios, there is a threshold proportion of sink habitat above which the whole population decreases to extinction, but this extinction threshold varies with habitat preference and the relative qualities of the two habitat types. Hence, it would be necessary to know the habitat preferences of any species in a source-sink system to interpret data on population increases and declines. In the attractive sink scenario, small changes in the proportion of sink habitat may have disproportionate effects on the population persistence. Also, small changes in growth rates at the source and the sink severely affect the threshold and the time of extinction. For some combinations of demographic parameters and proportion of habitat sink, the decline affects the source first; thus, during some time, it will be hidden to population monitoring at the sink, where numbers can even increase. The extinction threshold is also very sensitive to the initial population sizes relative to carrying capacity. Attractive sinks represent a novel aspect of source-sink dynamics with important conservation and management implications.     

Ecological traps and species distribution models: a challenge for prioritizing areas of conservation importance

Species distribution models analyse how species use different types of habitats. Their spatial predictions are often used to prioritize areas for conservation. Individuals may, however, prefer settling in habitat types of low quality compared to other available habitats. This ecological trap phenomenon is usually studied in a small number of habitat patches and consequences at the landscape level are largely unknown. It is therefore often unclear whether the spatial pattern of habitat use is aligned with the behavioural decisions made by the individuals during habitat selection or reflects actual variation in the quality of different habitat types. As species distribution models analyse the pattern of occurrence in different habitats, there is a conservation interest in examining what their predictions mean in terms of habitat quality when ecological traps are operating. Previous work in Belgium showed that red-backed shrikes Lanius collurio are more attracted to newly available clear-cut habitat in plantation forests than to the traditionally used farmland habitat. We developed models with shrike distribution data and compared their predictions with spatial variation in shrike reproductive performance used as a proxy for habitat quality. Models accurately predicted shrike distribution and identified the preferred clear-cut patches as the most frequently used habitat, but reproductive performance was lower in clear-cut areas than in farmland. With human-induced rapid environmental changes, organisms may indeed be attracted to low-quality habitats and occupy them at high densities. Consequently, the predictions of statistical models based on occurrence records may not align with variation in significant population parameters for the maintenance of the species. When species expand their range to novel habitats, such models are useful to document the spatial distribution of the organisms, but data on population growth rates are worth collecting before using model predictions to guide the spatial prioritization of conservation actions.     

On the evolutionary stability of sink populations

The evolution of adaptive behaviours can influence population dynamics. Conversely, population dynamics can affect both the rate and direction of adaptive evolution. This paper examines reasons why sink populations – populations maintained by immigration, preventing local extinction – might persist in the habitat repertoire of a species over evolutionary time-scales. Two such reasons correspond to standard explanations for deviations from an ideal free habitat distribution: organisms may not be free to settle in whichever habitat has the highest potential fitness, and may be constrained by costs, perceptual limitations, or mode of dispersal in the acuity of their habitat selectivity. Here, I argue that a third general reason for persistent sink populations is provided by unstable population dynamics in source habitats. I present a simple model illustrating how use of a sink habitat may be selectively advantageous, when a source population has unstable dynamics (which necessarily reflects temporal variation in local fitnesses). Species with unstable local dynamics in high-quality habitats should be selected to utilize a broader range of habitats than species with stable local dynamics, and in particular in some circumstances should utilize sink habitats. This observation has implications for the direction of niche evolution, and the likelihood of niche conservatism.     

Impacts of human‐induced environmental change in wetlands on aquatic animals

Many wetlands harbour highly diverse biological communities and provide extensive ecosystem services; however, these important ecological features are being altered, degraded and destroyed around the world. Despite a wealth of research on how animals respond to anthropogenic changes to natural wetlands and how they use created wetlands, we lack a broad synthesis of these data. While some altered wetlands may provide vital habitat, others could pose a considerable risk to wildlife. This risk will be heightened if such wetlands are ecological traps – preferred habitats that confer lower fitness than another available habitat. Wetlands functioning as ecological traps could decrease both local and regional population persistence, and ultimately lead to extinctions. Most studies have examined how animals respond to changes in environmental conditions by measuring responses at the community and population levels, but studying ecological traps requires information on fitness and habitat preferences. Our current lack of knowledge of individual‐level responses may therefore limit our capacity to manage wetland ecosystems effectively since ecological traps require different management practices to mitigate potential consequences. We conducted a global meta‐analysis to characterise how animals respond to four key drivers of wetland alteration: agriculture, mining, restoration and urbanisation. Our overarching goal was to evaluate the ecological impacts of human alterations to wetland ecosystems, as well as identify current knowledge gaps that limit both the current understanding of these responses and effective wetland management. We extracted 1799 taxon‐specific response ratios from 271 studies across 29 countries. Community‐ (e.g. richness) and population‐level (e.g. density) measures within altered wetlands were largely comparable to those within reference wetlands. By contrast, individual fitness measures (e.g. survival) were often lower, highlighting the potential limitations of using only community‐ and population‐level measures to assess habitat quality. Only four studies provided habitat‐preference data, preventing investigation of the potential for altered wetlands to function as ecological traps. This is concerning because attempts to identify ecological traps may detect previously unidentified conservation risks. Although there was considerable variability amongst taxa, amphibians were typically the most sensitive taxon, and thus, may be a valuable bio‐indicator of wetland quality. Despite suffering reduced survival and reproduction, measures such as time to and mass at metamorphosis were similar between altered and reference wetlands, suggesting that quantifying metamorphosis‐related measures in isolation may not provide accurate information on habitat quality. Our review provides the most detailed evaluation to date of the ecological impacts of human alterations to wetland ecosystems. We emphasise that the role of wetlands in human‐altered ecosystems can be complex, as they may represent important habitat but also pose potential risks to animals. Reduced availability of natural wetlands is increasing the importance of altered wetlands for aquatic animals. Consequently, we need to define what represents habitat quality from the perspective of animals, and gain a greater understanding of the underlying mechanisms of habitat selection and how these factors could be manipulated. Furthermore, strategies to enhance the quality of these wetlands should be implemented to maximise their conservation potential.     

Understanding the contribution of habitats and regional variation to long‐term population trends in tricolored blackbirds

Population trends represent a minimum amount of information required to assess the conservation status of a species. However, understanding and detecting trends can be complicated by variation among habitats and regions, and by dispersal connecting habitats through source‐sink dynamics. We analyzed trends in breeding populations between habitats and regions to better understand the overall dynamics of a species' decline. Specifically, we analyzed historical trends in breeding populations of tricolored blackbirds (Agelaius tricolor) using breeding records from 1907 to 2009. The species breeds itinerantly and ephemerally uses multiple habitat types and breeding areas, which make interpretation of trends complex. We found overall abundance declines of 63% between 1935 and 1975. Since 1980 overall declines became nonsignificant and obscure despite large amounts of data from 1980 to 2009. Temporal trends differed between breeding habitat types and were associated with regional differences in population declines. A new habitat, triticale crops (a wheat‐rye hybrid grain) produced colonies 40× larger, on average, than other breeding habitats, and contributed to a change in regional distribution since it primarily occurred in a single region. The mechanism for such an effect is not clear, but could represent the local availability of foodstuffs in the landscape rather than something specific to triticale crops. While variation in trends among habitats clearly occurred, they could not easily be ascribed to source‐sink dynamics, ecological traps, habitat selection or other detailed ecological mechanisms. Nonetheless, such exchanges provide valuable information to guide management of dynamic systems.     

Habitat selection,interspecific interactions and landscape composition

Summary I argue here that, from the perspective of any individual, most landscapes are composed of only three basic types of habitats. These are: (1) source habitat in which reproduction exceeds mortality and the expected per capita growth rate is greater than one; (2) sink habitat, in which limited, reproduction is possible but will not on average, compensate for mortality and the per capita rate of growth is between zero and one; and (3) unusable habitat, which comprises the matrix of all habitats that are never exploited by the species in question, and in which patches of source and sink habitats are embedded. Unlike earlier source-sink models, this model explicitly considers the effects that substituting one type of habitat for another has on the equilibrium size of a population and the interactions between species which can use both source and sink habitats. The model demonstrates that the equilibrium size of a species' population can sometimes be increased by substituting unusable habitat for sink habitat. Thus, even though the average patch quality in the landscape may be decreased, the overall quality of the landscape can increase. For two species with distinct habitat preferences, interactions between species can vary qualitatively as well as quantitatively as a function of the relative abundances of each of the habitat types. The model also shows that the interactions between species are particularly sensitive to the relative costs of moving between patches and sampling patches to determine their quality. Recent fragmentation of natural landscapes may increase the cost of searching for usable (source or sink) patches. Under some conditions, the interspecific interactions may be substantially more negative (competitive) than the interactions that evolved in the original natural landscape, further reducing population sizes and increasing the likelihood of competitive exclusion in fragmented modern landscapes.     

The influence of potential stressors on oviposition site selection and subsequent growth,survival and emergence of the non‐biting midge (Chironomus tepperi)

Theory predicts that animals should prefer habitats where their fitness is maximized but some mistakenly select habitats where their fitness is compromised, that is, ecological traps. Understanding why this happens requires knowledge of the habitat selection cues animals use, the habitats they prefer and why, and the fitness costs of habitat selection decisions. We conducted experiments with a freshwater insect, the non‐biting midge Chironomus tepperi to ask: (a) whether females respond to potential oviposition cues, (b) to explore whether oviposition is adaptive in relation to metal pollution and conductivity, and (c) whether individuals raised in poor quality sites are more likely to breed in similarly poor locations. We found the following: (a) females responded to some cues, especially conductivity and conspecifics, (b) females preferred sites with higher concentrations of bioavailable metals but suffered no consequences to egg/larval survival, (c) females showed some avoidance of high conductivities, but they still laid eggs resulting in reduced egg hatching, larval survival, and adult emergence, and (d) preferences were independent of natal environment. Our results show that C. tepperi is susceptible to ecological traps, depending on life stage and the relative differences in conductivities among potential oviposition sites. Our results highlight that (a) the fitness outcomes of habitat selection need to be assessed across the life cycle and (b) the relative differences in preference/suitability of habitats need to be considered in ecological trap research. This information can help determine why habitat preferences and their fitness consequences differ among species, which is critical for determining which species are susceptible to ecological traps.     

Modeling ecological traps for the control of feral pigs

Ecological traps are habitat sinks that are preferred by dispersing animals but have higher mortality or reduced fecundity compared to source habitats. Theory suggests that if mortality rates are sufficiently high, then ecological traps can result in extinction. An ecological trap may be created when pest animals are controlled in one area, but not in another area of equal habitat quality, and when there is density‐dependent immigration from the high‐density uncontrolled area to the low‐density controlled area. We used a logistic population model to explore how varying the proportion of habitat controlled, control mortality rate, and strength of density‐dependent immigration for feral pigs could affect the long‐term population abundance and time to extinction. Increasing control mortality, the proportion of habitat controlled and the strength of density‐dependent immigration decreased abundance both within and outside the area controlled. At higher levels of these parameters, extinction was achieved for feral pigs. We extended the analysis with a more complex stochastic, interactive model of feral pig dynamics in the Australian rangelands to examine how the same variables as the logistic model affected long‐term abundance in the controlled and uncontrolled area and time to extinction. Compared to the logistic model of feral pig dynamics, the stochastic interactive model predicted lower abundances and extinction at lower control mortalities and proportions of habitat controlled. To improve the realism of the stochastic interactive model, we substituted fixed mortality rates with a density‐dependent control mortality function, empirically derived from helicopter shooting exercises in Australia. Compared to the stochastic interactive model with fixed mortality rates, the model with the density‐dependent control mortality function did not predict as substantial decline in abundance in controlled or uncontrolled areas or extinction for any combination of variables. These models demonstrate that pest eradication is theoretically possible without the pest being controlled throughout its range because of density‐dependent immigration into the area controlled. The stronger the density‐dependent immigration, the better the overall control in controlled and uncontrolled habitat combined. However, the stronger the density‐dependent immigration, the poorer the control in the area controlled. For feral pigs, incorporating environmental stochasticity improves the prospects for eradication, but adding a realistic density‐dependent control function eliminates these prospects.     

Genetic differentiation within and between two habitats.

We investigate the usefulness of analyses of population differentiation between different ecological types, such as host races of parasites or sources and sink habitats. To that aim, we formulate a model of population structure involving two classes of subpopulations found in sympatry. Extensions of previous results for Wright''s F-statistics in island and isolation-by-distance models of dispersal are given. It is then shown that source and sinks cannot in general be distinguished by F-statistics nor by their gene diversities. The excess differentiation between two partially isolated classes with respect to differentiation within classes is shown to decrease with distance, and for a wide range of parameter values it should be difficult to detect. In the same circumstances little differentiation will be observed in "hierarchical" analyses between pools of samples from each habitat, and differences between levels of differentiation within each habitat will only reflect differences between levels of gene diversity within each habitat. Exceptions will indicate strong isolation between the different classes or habitat-related divergent selection.     

Population dynamics in two-patch environments: Some anomalous consequences of an optimal habitat distribution

The effect of dispersal on population size and stability is explored for a population that disperses passively between two discrete habitat patches. Two basic models are considered. In the first model, a single population experiences density-dependent growth in both patches. A graphical construction is presented which allows one to determine the spatial pattern of abundance at equilibrium for most reasonable growth models and rates of dispersal. It is shown under rather general conditions that this equilibrium is unique and globally stable. In the second model, the dispersing population is a food-limited predator that occurs in both a source habitat (which contains a prey population) and a sink habitat (which does not). Passive dispersal between source and sink habitats can stabilize an otherwise unstable predator-prey interaction. The conditions allowing this are explored in some detail. The theory of optimal habitat selection predicts the evolutionarily stable distribution of a population, given that individuals can freely move among habitats so as to maximize individual fitness. This theory is used to develop a heuristic argument for why passive dispersal should always be selectively disadvantageous (ignoring kin effects) in a spatially heterogeneous but temporally constant environment. For both the models considered here, passive dispersal may lead to a greater number of individuals in both habitats combined than if there were no dispersal. This implies that the evolution of an optimal habitat distribution may lead to a reduction in population size; in the case of the predator-prey model, it may have the additional effect of destabilizing the interaction. The paper concludes with a discussion of the disparate effects habitat selection might have on the geographical range occupied by a species.