Integrodifference models for persistence in fragmented habitats

Integrodifference models of growth and dispersal are analyzed on finite domains to investigate the effects of emigration, local growth dynamics and habitat heterogeneity on population persistence. We derive the bifurcation structure for a range of population dynamics and present an approximation that allows straighforward calculation of the equilibrium populations in terms of local growth dynamics and dispersal success rates. We show how population persistence in a heterogeneous environment depends on the scale of the heterogeneity relative to the organism's characteristic dispersal distance. When organisms tend to disperse only a short distance, population persistence is dominated by local conditions in high quality patches, but when dispersal distance is relatively large, poor quality habitat exerts a greater influence.     

Empirical evidence for source–sink populations: a review on occurrence,assessments and implications

Assessing the role of local populations in a landscape context has become increasingly important in the fields of conservation biology and ecology. A growing number of studies attempt to determine the source–sink status of local populations. As the source–sink concept is commonly used for management decisions in nature conservation, accurate assessment approaches are crucial. Based on a systematic literature review of studies published between 2002 and 2013, we evaluated a priori predictions on methodological and biological factors that may influence the occurrence of source or sink populations. The review yielded 90 assessments from 73 publications that included qualitative and quantitative evidence for either source or sink population(s) for one or multiple species. Overall, sink populations tended to occur more often than source populations. Moreover, the occurrence of source or sink populations differed among taxonomic classes. Sinks were more often found than sources in mammals, while there was a non‐significant trend for the opposite to be true for amphibians. Univariate and multivariate analyses showed that the occurrence of sources was positively related to connectivity of local populations. Our review furthermore highlights that more than 25 years after Pulliam's widely cited publication on ‘sources, sinks, and population regulation’, in‐depth assessments of the source–sink status of populations based on combined consideration of demographic parameters such as fecundity, survival, emigration and immigration are still scarce. To increase our understanding of source–sink systems from ecological, evolutionary and conservation‐related perspectives, we recommend that forthcoming studies on source–sink dynamics should pay more attention to the study design (i.e. connectivity of study populations) and that the assessment of the source–sink status of local populations is based on λ values calculated from demographic rates.     

Coexistence in streams: do source–sink dynamics allow salamanders to persist with fish predators?

Theory suggests that source–sink dynamics can allow coexistence of intraguild predators and prey, but empirical evidence for this coexistence mechanism is limited. We used capture–mark–recapture, genetic methods, and stable isotopes to test whether source–sink dynamics promote coexistence between stream fishes, the intraguild predator, and stream salamanders (Dicamptodon aterrimus), the intraguild prey. Salamander populations from upstream reaches without fish were predicted to maintain or supplement sink populations in downstream reaches with fish. We found instead that downstream reaches with fish were not sinks even though fish consumed salamander larvae—apparent survival, recruitment, and population growth rate did not differ between upstream and downstream reaches. There was also no difference between upstream and downstream reaches in net emigration. We did find that D. aterrimus moved frequently along streams, but believe that this is a response to seasonal habitat changes rather than intraguild predation. Our study provides empirical evidence that local-scale mechanisms are more important than dispersal dynamics to coexistence of streams salamanders and fish. More broadly, it shows the value of empirical data on dispersal and gene flow for distinguishing between local and spatial mechanisms of coexistence.     

Metapopulation dynamics: Does it help to have more of the same?

With the interest in conservation biology shifting towards processes from patterns, and to populations from communities, the theory of metapopulation dynamics is replacing the equilibrium theory of island biogeography as the population ecology paradigm in conservation biology. The simplest models of metapopulation dynamics make predictions about the effects of habitat fragmentation - size and isolation of habitat patches - on metapopulation persistence. The simple models may be enriched by considerations of the effects of demographic and environmental stochasticity on the size and extinction probability of local populations. Environmental stochasticity affects populations at two levels: it makes local extinctions more probable, and it also decreases metapopulation persistence time by increasing the correlation of extinction events across populations. Some controversy has arisen over the significance of correlated extinctions, and how they may affect the optimal subdivision of metapopulations to maximize their persistence time.     

Dynamics of mutualist populations that are demographically open

1. Few theoretical studies have examined the impact of immigration and emigration on mutualist population dynamics, but a recent empirical study (A.R. Thompson Oecologia, 143, 61-69) on mutualistic fish and shrimp showed that immigration can prevent population collapse, and that intraspecific competition for a mutualistic partner can curb population expansion. To understand in a theoretical context the implications of these results, and to assess their generality, we present a two-species model that accounts explicitly for immigration and emigration, as well as distinguishing the impacts of mutualism on birth rates, death rates and habitat acquisition. 2. The model confirms that immigration can stabilize mutualistic populations, and predicts that high immigration, along with enhanced reproduction and/or reduced mortality through mutualism, can cause population sizes to increase until habitat availability curbs further expansion. 3. We explore in detail the effects of different forms of habitat limitation on mutualistic populations. Habitat availability commonly limits the density of both populations if mutualists acquire shelter independently. If a mutualist depends on a partner for habitat, densities of that mutualist are capped by the amount of space provided by that partner. The density of the shelter-provider is limited by the environment. 4. If a mutualism solely augments reproduction, and most locally produced individuals leave the focal patch, then the mutualism will have a minimal effect on local dynamics. If the mutualism operates by reducing rates of death or enhancing habitat availability, and there is at least some immigration, then mutualism will affect local dynamics. This finding may be particularly relevant in marine systems, where there is high variability (among species and locations) in the extent to which progeny disperse from natal locations. 5. Overall, our results demonstrate that the consequences of immigration and emigration for the dynamics of mutualists depend strongly on which demographic rate is influenced by mutualism. 6. By relating our model to a variety of terrestrial and aquatic systems, we provide a general framework to guide future empirical studies of the dynamics of mutualistic populations.     

Movements and source–sink dynamics of a Masai giraffe metapopulation

Spatial variation in habitat quality and anthropogenic factors, as well as social structure, can lead to spatially structured populations of animals. Demographic approaches can be used to improve our understanding of the dynamics of spatially structured populations and help identify subpopulations critical for the long-term persistence of regional metapopulations. We provide a regional metapopulation analysis to inform conservation management for Masai giraffes (Giraffa camelopardalis tippelskirchi) in five subpopulations defined by land management designations. We used data from an individual-based mark–recapture study to estimate subpopulation sizes, subpopulation growth rates, and movement probabilities among subpopulations. We assessed the source–sink structure of the study population by calculating source–sink statistics, and we created a female-based matrix metapopulation model composed of all subpopulations to examine how variation in demographic components of survival, reproduction, and movement affected metapopulation growth rate. Movement data indicated no subpopulation was completely isolated, but movement probabilities varied among subpopulations. Source–sink statistics and net flow of individuals indicated three subpopulations were sources, while two subpopulations were sinks. We found areas with higher wildlife protection efforts and fewer anthropogenic impacts were sources, and less-protected areas were identified as sinks. Our results highlight the importance of identifying source–sink dynamics among subpopulations for effective conservation planning and emphasize how protected areas can play an important role in sustaining metapopulations.     

Patterns of dispersal and dynamics among habitat patches varying in quality

Both source-sink theory and extensions of optimal foraging theory ("balanced dispersal" theory) address dispersal and population dynamics in landscapes where habitat patches vary in quality. However, studying dispersal mechanisms empirically has proven difficult, and dispersal is rarely tied back to long-term spatial dynamics. We used a manipulable laboratory system consisting of bacteria and protozoa to investigate the ability of source-sink and optimal foraging theories to explain both dispersal and emergent spatial dynamics. Consistent with source-sink models and contrary to balanced dispersal models, there was a consistent net flux of protist individuals from high to low resource patches. However, unlike the simplest source-sink models, intermediate rates of dispersal led to highest abundances in low resource patches. Side experiments found strong density dependence in local population dynamics and differences in average protist body size in high and low resource patches. Parameterization and analysis of a two-patch model showed that high migration from high to low resource patches could have depressed population density in low resource patches, creating pseudosinks. The movement of individuals and biomass from sources to sinks (a form of ecosystem subsidy) resulted in the convergence of body size and population densities in sources and sinks. Our results indicate a need to carefully consider movement patterns and interaction with local dynamics in potential source-sink systems.     

Finite metapopulation models with density-dependent migration and stochastic local dynamics

The effects of small density-dependent migration on the dynamics of a metapopulation are studied in a model with stochastic local dynamics. We use a diffusion approximation to study how changes in the migration rate and habitat occupancy affect the rates of local colonization and extinction. If the emigration rate increases or if the immigration rate decreases with local population size, a positive expected rate of change in habitat occupancy is found for a greater range of habitat occupancies than when the migration is density-independent. In contrast, the reverse patterns of density dependence in respective emigration and immigration reduce the range of habitat occupancies where the metapopulation will be viable. This occurs because density-dependent migration strongly influences both the establishment and rescue effects in the local dynamics of metapopulations.     

The role of density-dependent dispersal in source-sink dynamics

I investigate two aspects of source-sink theory that have hitherto received little attention: density-dependent dispersal and the cost of dispersal to sources. The cost arises because emigration reduces the per capita growth rate of sources, thus predisposing them to extinction. I show that source-sink persistence depends critically on the interplay between these two factors. When the emigration rate increases with abundance at an accelerating rate, dispersal costs to sources is the lowest and risk of source-sink extinction the least. When the emigration rate increases with abundance at a decelerating rate, dispersal costs to sources is the highest and the risk of source-sink extinction the greatest. Density-independent emigration has an intermediate effect. Thus, density-dependent dispersal per se does not increase or decrease source-sink persistence relative to density-independent dispersal. The exact mode of dispersal is crucial. A key point to appreciate is that these effects of dispersal on source-sink extinction arise from the temporal density-dependence that dispersal induces in the per capita growth rates of source and sink populations. Temporal density-dependence due to dispersal is beneficial at low abundances because it rescues sinks from extinction, and detrimental at high abundances because it drives otherwise viable sources to extinction. These results are robust to the nature of population dynamics in the sink, whether exponential or logistic. They provide a means of assessing the relative costs and benefits of preserving sink habitats given three biological parameters.     

Natal habitat effects drive density—dependent scaling of dispersal decisions

The dispersal behavior of a species is critical for the stability and persistence of its populations across a landscape. How population density affects dispersal decisions is important for predicting these dynamics, as the form of density‐dependent dispersal influences the stability and persistence of populations. Natal habitat experience often has strong impacts on individual dispersal behavior as well, but its influence on density‐dependent dispersal behaviors remains unexplored. Here we address this conceptual gap in two experiments separately examining habitat selection and emigration from recently colonized patches for two species of flour beetle Tribolium sp. We found that interactions between the quality of habitat experienced during natal development and current habitat for dispersal capable adults can strongly affect the form of density dependence, including reversing the direction of nonlinearities (accelerating to decelerating), or even negating the influence of population density for individual dispersal decisions. Across heterogeneous landscapes, where individuals from different populations may experience different natal habitats, this altering of density‐dependent relationships is predicted by theory to fundamentally influence regional population dynamics. Our results indicate that species which occur across heterogeneous environments, such as during conservation reintroductions, or as invasive species spread, have much potential for natal experience to interact with density dependence and influence local and regional population dynamics.     

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.     

Metapopulation dynamics with quasi-local competition

Stepping-stone models for the ecological dynamics of metapopulations are often used to address general questions about the effects of spatial structure on the nature and complexity of population fluctuations. Such models describe an ensemble of local and spatially isolated habitat patches that are connected through dispersal. Reproduction and hence the dynamics in a given local population depend on the density of that local population, and a fraction of every local population disperses to neighboring patches. In such models, interesting dynamic phenomena, e.g. the persistence of locally unstable predator-prey interactions, are only observed if the local dynamics in an isolated patch exhibit non-equilibrium behavior. Therefore, the scope of these models is limited. Here we extend these models by making the biologically plausible assumption that reproductive success in a given local habitat not only depends on the density of the local population living in that habitat, but also on the densities of neighboring local populations. This would occur if competition for resources occurs between neighboring populations, e.g. due to foraging in neighboring habitats. With this assumption of quasi-local competition the dynamics of the model change completely. The main difference is that even if the dynamics of the local populations have a stable equilibrium in isolation, the spatially uniform equilibrium in which all local populations are at their carrying capacity becomes unstable if the strength of quasi-local competition reaches a critical level, which can be calculated analytically. In this case the metapopulation reaches a new stable state, which is, however, not spatially uniform anymore and instead results in an irregular spatial pattern of local population abundance. For large metapopulations, a huge number of different, spatially non-uniform equilibrium states coexist as attractors of the metapopulation dynamics, so that the final state of the system depends critically on the initial conditions. The existence of a large number of attractors has important consequences when environmental noise is introduced into the model. Then the metapopulation performs a random walk in the space of all attractors. This leads to large and complicated population fluctuations whose power spectrum obeys a red-shifted power law. Our theory reiterates the potential importance of spatial structure for ecological processes and proposes new mechanisms for the emergence of non-uniform spatial patterns of abundance and for the persistence of complicated temporal population fluctuations.     

Spatial population structure of a specialist leaf-mining moth

1. The spatial structure of natural populations may profoundly influence their dynamics. Depending on the frequency of movements among local populations and the consequent balance between local and regional population processes, earlier work has attempted to classify metapopulations into clear-cut categories, ranging from patchy populations to sets of remnant populations. In an alternative, dichotomous scheme, local populations have been classified as self-sustaining populations generating a surplus of individuals (sources) and those depending on immigration for persistence (sinks). 2. In this paper, we describe the spatial population structure of the leaf-mining moth Tischeria ekebladella, a specialist herbivore of the pedunculate oak Quercus robur. We relate moth dispersal to the distribution of oaks on Wattkast, a small island (5 km(2)) off the south-western coast of Finland. 3. We build a spatially realistic metapopulation model derived from assumptions concerning the behaviour of individual moths, and show that the model is able to explain part of the variation in observed patterns of occurrence and colonization. 4. While the species was always present on large trees, a considerable proportion of the local populations associated with small oaks showed extinction-recolonization dynamics. The vast majority of moth individuals occur on large trees. 5. According to model predictions, the dominance of local vs. regional processes in tree-specific moth dynamics varies drastically across the landscape. Most local populations may be defined broadly as 'sinks', as model simulations suggest that in the absence of immigration, only the largest oaks will sustain viable moth populations. Large trees in areas of high oak density will contribute most to the overall persistence of the metapopulation by acting as sources of moths colonizing other trees. 6. No single 'metapopulation type' will suffice to describe the oak-moth system. Instead, our study supports the notion that real populations are often a mix of earlier identified categories. The level to which local populations may persist after landscape modification will vary across the landscape, and sweeping classifications of metapopulations into single categories will contribute little to understanding how individual local populations contribute to the overall persistence of the system.     

Dispersal-mediated coexistence of competing predators

Models of metapopulations have often ignored local community dynamics and spatial heterogeneity among patches. However, persistence of a community as a whole depends both on the local interactions and the rates of dispersal between patches. We study a mathematical model of a metacommunity with two consumers exploiting a resource in a habitat of two different patches. They are the exploitative competitors or the competing predators indirectly competing through depletion of the shared resource. We show that they can potentially coexist, even if one species is sufficiently inferior to be driven extinct in both patches in isolation, when these patches are connected through diffusive dispersal. Thus, dispersal can mediate coexistence of competitors, even if both patches are local sinks for one species because of the interactions with the other species. The spatial asynchrony and the competition-colonization trade-off are usual mechanisms to facilitate regional coexistence. However, in our case, two consumers can coexist either in synchronous oscillation between patches or in equilibrium. The higher dispersal rate of the superior prompts rather than suppresses the inferior. Since differences in the carrying capacity between two patches generate flows from the more productive patch to the less productive, loss of the superior by emigration relaxes competition in the former, and depletion of the resource by subsidized consumers decouples the local community in the latter.     

Cyclic dynamics in simulated plant populations

Despite the general interest in nonlinear dynamics in animal populations, plant populations are supposed to show a stable equilibrium that is attributed to fundamental differences compared with animals. Some studies find more complex dynamics, but empirical studies usually are too short and most modelling studies ignore important spatial aspects of local competition and establishment. Therefore, we used a spatially explicit individual-based model of a hypothetical, non-clonal perennial to explore which mechanisms might generate complex dynamics, i.e. cycles. The model is based on the field-of-neighbourhood approach that describes local competition and establishment in a phenomenological manner. We found cyclic population dynamics for a wide spectrum of model variants, provided that mortality is determined by local competition and recruitment is virtually completely suppressed within the zone of influence of established plants. This destabilizing effect of local processes within plant populations might have wide-ranging implications for the understanding of plant community dynamics and coexistence.     

Effects of landscape and patch-level attributes on regional population persistence

Species responses are influenced by processes operating at multiple scales, yet many conservation studies and management actions are focused on a single scale. Although landscape-level habitat conditions (i.e., habitat amount, fragmentation and landscape quality) are likely to drive the regional persistence of spatially structured populations, patch-level factors (i.e., patch size, isolation, and quality) may also be important. To determine the spatial scales at which habitat factors influence the regional persistence of endangered Ord's kangaroo rats (Dipodomys ordii) in Alberta, Canada, we simulated population dynamics under a range of habitat conditions. Using a spatially-explicit population model, we removed groups of habitat patches based on their characteristics and measured the resulting time to extinction. We used proportional hazards models to rank the influence of landscape and interacting patch-level variables. Landscape quality was the most influential variable followed by patch quality, with both outweighing landscape- and patch-level measures of habitat quantity and fragmentation/proximity. Although habitat conservation and restoration priorities for this population should be in maximizing the overall quality of the landscape, population persistence depends on how this goal is achieved. Patch quality exerted a significant influence on regional persistence, with the removal of low quality road margin patches (sinks) reducing the risk of regional extinction. Strategies for maximizing overall landscape quality that omit patch-level considerations may produce suboptimal or detrimental results for regional population persistence, particularly where complex local population dynamics (e.g., source-sink dynamics) exist. This study contributes to a growing body literature that suggests that the prediction of species responses and future conservation actions may best be assessed with a multi-scale approach that considers habitat quality and that the success of conservation actions may depend on assessing the influences of habitat factors at multiple scales.     

Stabilization through spatial pattern formation in metapopulations with long-range dispersal

Many studies of metapopulation models assume that spatially extended populations occupy a network of identical habitat patches, each coupled to its nearest neighbouring patches by density-independent dispersal. Much previous work has focused on the temporal stability of spatially homogeneous equilibrium states of the metapopulation, and one of the main predictions of such models is that the stability of equilibrium states in the local patches in the absence of migration determines the stability of spatially homogeneous equilibrium states of the whole metapopulation when migration is added. Here, we present classes of examples in which deviations from the usual assumptions lead to different predictions. In particular, heterogeneity in local habitat quality in combination with long-range dispersal can induce a stable equilibrium for the metapopulation dynamics, even when within-patch processes would produce very complex behaviour in each patch in the absence of migration. Thus, when spatially homogeneous equilibria become unstable, the system can often shift to a different, spatially inhomogeneous steady state. This new global equilibrium is characterized by a standing spatial wave of population abundances. Such standing spatial waves can also be observed in metapopulations consisting of identical habitat patches, i.e. without heterogeneity in patch quality, provided that dispersal is density dependent. Spatial pattern formation after destabilization of spatially homogeneous equilibrium states is well known in reaction–diffusion systems and has been observed in various ecological models. However, these models typically require the presence of at least two species, e.g. a predator and a prey. Our results imply that stabilization through spatial pattern formation can also occur in single-species models. However, the opposite effect of destabilization can also occur: if dispersal is short range, and if there is heterogeneity in patch quality, then the metapopulation dynamics can be chaotic despite the patches having stable equilibrium dynamics when isolated. We conclude that more general metapopulation models than those commonly studied are necessary to fully understand how spatial structure can affect spatial and temporal variation in population abundance.     

The role of habitat selection behavior in population dynamics: source–sink systems and ecological traps

Ecological traps, poor-quality habitat that nonetheless attract individuals, have been observed in both natural and human-altered settings. Until recently, ecological traps were considered a kind of source–sink system, but source–sink theory does not model maladaptive habitat choice, and therefore cannot accurately represent ecological traps or predict their population-level consequences. Although recent models of ecological traps addressed this problem, they used patch-based models containing only two habitats that were very different from one another, but were internally homogeneous. These sorts of patch models may not apply to many real populations, and using them for populations in landscapes with mosaic or gradient habitat structures may be misleading. I developed models that treat source–sink dynamics and ecological traps as special cases of a single process, in which the attractiveness and quality of the habitat are separate variables that can be either positively or negatively related, and in which habitat quality varies continuously throughout the landscape. As expected, sinks are less detrimental to populations than ecological traps, in which preferential use of poor habitat elevates extinction risk. Furthermore, ecological traps may be undetected, and may even appear to be sources, when population sizes are large, but may still prevent recovery in spite of the availability of high-quality habitat when populations drop below threshold levels. Conservation biologists do not routinely consider the possibility that apparent sinks are actually traps, but since traps should be associated with the rapidly changing and novel habitat characteristics primarily produced by human activities, ecological traps should be considered an important and potentially widespread conservation concern.     

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.