Metapopulation persistence in dynamic landscapes: the role of dispersal distance

Species associated with transient habitats need efficient dispersal strategies to ensure their regional survival. Using a spatially explicit metapopulation model, we studied the effect of the dispersal range on the persistence of a metapopulation as a function of the local population and landscape dynamics (including habitat patch destruction and subsequent regeneration). Our results show that the impact of the dispersal range depends on both the local population and patch growth. This is due to interactions between dispersal and the dynamics of patches and populations via the number of potential dispersers. In general, long-range dispersal had a positive effect on persistence in a dynamic landscape compared to short-range dispersal. Long-range dispersal increases the number of couplings between the patches and thus the colonisation of regenerated patches. However, long-range dispersal lost its advantage for long-term persistence when the number of potential dispersers was low due to small population growth rates and/or small patch growth rates. Its advantage also disappeared with complex local population dynamics and in a landscape with clumped patch distribution.     

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.     

Metapopulation Persistence in Random Fragmented Landscapes

Habitat destruction and land use change are making the world in which natural populations live increasingly fragmented, often leading to local extinctions. Although local populations might undergo extinction, a metapopulation may still be viable as long as patches of suitable habitat are connected by dispersal, so that empty patches can be recolonized. Thus far, metapopulations models have either taken a mean-field approach, or have modeled empirically-based, realistic landscapes. Here we show that an intermediate level of complexity between these two extremes is to consider random landscapes, in which the patches of suitable habitat are randomly arranged in an area (or volume). Using methods borrowed from the mathematics of Random Geometric Graphs and Euclidean Random Matrices, we derive a simple, analytic criterion for the persistence of the metapopulation in random fragmented landscapes. Our results show how the density of patches, the variability in their value, the shape of the dispersal kernel, and the dimensionality of the landscape all contribute to determining the fate of the metapopulation. Using this framework, we derive sufficient conditions for the population to be spatially localized, such that spatially confined clusters of patches act as a source of dispersal for the whole landscape. Finally, we show that a regular arrangement of the patches is always detrimental for persistence, compared to the random arrangement of the patches. Given the strong parallel between metapopulation models and contact processes, our results are also applicable to models of disease spread on spatial networks.     

Does colonization asymmetry matter in metapopulations?

Despite the considerable evidence showing that dispersal between habitat patches is often asymmetric, most of the metapopulation models assume symmetric dispersal. In this paper, we develop a Monte Carlo simulation model to quantify the effect of asymmetric dispersal on metapopulation persistence. Our results suggest that metapopulation extinctions are more likely when dispersal is asymmetric. Metapopulation viability in systems with symmetric dispersal mirrors results from a mean field approximation, where the system persists if the expected per patch colonization probability exceeds the expected per patch local extinction rate. For asymmetric cases, the mean field approximation underestimates the number of patches necessary for maintaining population persistence. If we use a model assuming symmetric dispersal when dispersal is actually asymmetric, the estimation of metapopulation persistence is wrong in more than 50% of the cases. Metapopulation viability depends on patch connectivity in symmetric systems, whereas in the asymmetric case the number of patches is more important. These results have important implications for managing spatially structured populations, when asymmetric dispersal may occur. Future metapopulation models should account for asymmetric dispersal, while empirical work is needed to quantify the patterns and the consequences of asymmetric dispersal in natural metapopulations.     

Size and genetic composition of the colonizing propagules in a butterfly metapopulation

The amount and spatial distribution of genetic variation that is maintained in a metapopulation depends critically on the colonization process. Here, we use molecular markers to determine the number and genetic relatedness of individuals establishing new local populations in a large metapopulation of the Glanville fritillary butterfly Melitaea cinxia. The empirical results are compared with the predictions of a dispersal model based on a diffusion approximation of correlated random walk, which serves as a base‐line hypothesis about the rate and pattern of colonization. The results show that half of the new local populations consisted of a single larval group of full sibs and hence necessarily of the offspring of a single female. If the colonization involved two or more larval groups, these were usually oviposited by two different females that were unrelated to each other. The pattern of colonizations is thus intermediate between the propagule pool and the migrant pool models. These results elucidate the generation of genetic stochasticity, which may influence the dynamics of small populations. The dispersal model predicted well the pattern of habitat occupancy and the pattern of colonizations in relation to landscape structure, though which particular habitat patches became colonized was influenced also by measures of habitat quality not included in the model.     

Evolution of Complex Density-Dependent Dispersal Strategies

The question of how dispersal behavior is adaptive and how it responds to changes in selection pressure is more relevant than ever, as anthropogenic habitat alteration and climate change accelerate around the world. In metapopulation models where local populations are large, and thus local population size is measured in densities, density-dependent dispersal is expected to evolve to a single-threshold strategy, in which individuals stay in patches with local population density smaller than a threshold value and move immediately away from patches with local population density larger than the threshold. Fragmentation tends to convert continuous populations into metapopulations and also to decrease local population sizes. Therefore we analyze a metapopulation model, where each patch can support only a relatively small local population and thus experience demographic stochasticity. We investigated the evolution of density-dependent dispersal, emigration and immigration, in two scenarios: adult and natal dispersal. We show that density-dependent emigration can also evolve to a nonmonotone, “triple-threshold” strategy. This interesting phenomenon results from an interplay between the direct and indirect benefits of dispersal and the costs of dispersal. We also found that, compared to juveniles, dispersing adults may benefit more from density-dependent vs. density-independent dispersal strategies.     

Potential metapopulation structure and the effects of habitat quality on population size of the endangered False Ringlet butterfly

The False Ringlet (Coenonympha oedippus) is a European butterfly species, endangered due to the severe loss and fragmentation of its habitat. In Hungary, two remaining populations of the butterfly occur in lowland Purple Moorgrass meadows. We studied a metapopulation occupying twelve habitat patches in Central Hungary. Our aim was to reveal what measures of habitat quality affect population size and density of this metapopulation, estimate dispersal parameters and describe phenology of subpopulations. Local population sizes and dispersal parameters were estimated from an extensive mark–release–recapture dataset, while habitat quality was characterized by groundwater level, cover of grass tussocks, bush cover, height of vegetation and grass litter at each habitat patch. The estimated size of the metapopulation was more than 3,000 individuals. We estimated a low dispersal capacity, especially for females, indicating a very low probability of (re)colonization. Butterfly abundance and density in local populations increased with higher grass litter, lower groundwater level and larger area covered by tussocks. We suppose that these environmental factors affect butterfly abundance by determining the microclimatic conditions for both larvae and adult butterflies. Our results suggest that the long-term preservation of the studied metapopulation needs the maintenance of high quality habitat patches by appropriate mowing regime and water regulation. Management also should facilitate dispersal to strengthen metapopulation structure with creating stepping-stones or gradually increase habitat quality in present matrix.     

Do invasive species undergo metapopulation dynamics? A case study of the invasive Caspian gull,Larus cachinnans,in Poland

Aim The mechanisms of initial dispersal and habitat occupancy by invasive alien species are fundamental ecological problems. Most tests of metapopulation theory are performed on local population systems that are stable or in decline. In the current study we were interested in the usefulness of metapopulation theory to study patch occupancy, local colonization, extinction and the abundance of the invasive Caspian gull (Larus cachinnans) in its initial invasion stages. Location Waterbodies in Poland. Methods Characteristics of the habitat patches (waterbodies, 35 in total) occupied by breeding pairs of Caspian gulls and an equal sample of randomly selected unoccupied patches were compared with t‐tests. Based on presence–absence data from 1989 to 2006 we analysed factors affecting the probability of local colonization, extinction and the size of local populations using generalized linear models. Results Occupied habitat patches were significantly larger and less isolated (from other habitat patches and other local populations) and were located closer to rivers than empty patches. The proximity of local food resources (fish ponds, refuse dumps) positively affected the occurrence of breeding pairs. The probability of colonization was positively affected by patch area, and negatively by distances to fish ponds, nearest habitat patch, nearest breeding colony and to a river, and by higher forest cover around the patch boundaries. The probability of extinction was lower in patches with a higher number of breeding pairs and with a greater area of islets. The extinction probability increased with distances to other local populations, other habitat patches, fish ponds and to refuse dumps and with a higher cover of forest around the patch boundaries. The size of the local population decreased with distances to the nearest habitat patch, local population, river, fish pond and refuse dump. Local abundance was also positively affected by the area of islets in the patch. Main conclusions During the initial stages of the invasion of Caspian gulls in Poland the species underwent metapopulation‐like dynamics with frequent extinctions from colonized habitat patches. The results prove that metapopulation theory may be a useful conceptual framework for predicting which habitats are more vulnerable to invasion.     

The effect of conspecific attraction on metapopulation dynamics

Random dispersal direction is assumed in all current metapopulation models. This assumption is called into question by recent experiments demonstrating that some species disperse preferentially to sites occupied by conspecifies. We incorporate conspecific attraction into two metapopulation models which differ in type of dispersal, the Levins model and a two-dimensional stepping-stone model. In both models, conspecific attraction lowers the proportion of occupied habitat patches within a metapopulation at equilibrium.     

Viability analyses with habitat-based metapopulation models

Population viability analysis (PVA) models incorporate spatial dynamics in different ways. At one extreme are the occupancy models that are based on the number of occupied populations. The simplest occupancy models ignore the location of populations. At the other extreme are individual-based models, which describe the spatial structure with the location of each individual in the population, or the location of territories or home ranges. In between these are spatially structured metapopulation models that describe the dynamics of each population with structured demographic models and incorporate spatial dynamics by modeling dispersal and temporal correlation among populations. Both dispersal and correlation between each pair of populations depend on the location of the populations, making these models spatially structured. In this article, I describe a method that expands spatially structured metapopulation models by incorporating information about habitat relationships of the species and the characteristics of the landscape in which the metapopulation exists. This method uses a habitat suitability map to determine the spatial structure of the metapopulation, including the number, size, and location of habitat patches in which subpopulations of the metapopulation live. The habitat suitability map can be calculated in a number of different ways, including statistical analyses (such as logistic regression) that find the relationship between the occurrence (or, density) of the species and independent variables which describe its habitat requirements. The habitat suitability map is then used to calculate the spatial structure of the metapopulation, based on species-specific characteristics such as the home range size, dispersal distance, and minimum habitat suitability for reproduction. Received: April 1, 1999 / Accepted: October 29, 1999     

Metapopulation dynamics of the bog fritillary butterfly: experimental changes in habitat quality induced negative density‐dependent dispersal

Habitat quality and habitat geometry are two crucial factors driving metapopulation dynamics. However, their intricacy has prevented so far a reliable test of their relative impact on local population dynamics and persistence. Here we report on a long‐term study in which we manipulated habitat quality within a butterfly metapopulation, whereas habitat geometry was kept constant. The treatment consisted in lowering the quality of certain habitat patches while others were kept untreated, using the same spatial design over years. The effect of the treatment on metapopulation dynamics was assessed by comparing residence probability and dispersal rates within the same habitat network on 11 and 6 independent butterfly generations before and after treatment, respectively. Results showed that the experimental decrease in habitat quality generated significantly higher emigration rates from treated patches. This increase was associated with a significant decrease in dispersal rates out of untreated patches, and a significant higher residence probability in these patches. The direct relation between lower habitat quality and higher dispersal propensity in treated patches was expected. However, the lower dispersal from untreated patches after treatment was opposite to the expectation of positive density dependent dispersal generally observed in butterflies. Such negative density‐dependent dispersal would allow a rapid fine‐tuning of dispersal rates to changes in habitat quality, particularly when the spatial autocorrelation of the environmental is low. Accordingly, dispersal would promote an ideal free distribution of individuals in the landscape according to their fitness expectation.     

Metapopulation dynamics of the bog fritillary butterfly: modelling the effect of habitat fragmentation

Population viability analysis (PVA) and metapopulation theory are valuable tools to model the dynamics of spatially structured populations. In this article we used a spatially realistic population dynamic model to simulate the trajectory of a Proclossiana eunomia metapopulation in a network of habitat patches located in the Belgian Ardenne. Sensitivity analysis was used to evaluate the relative influence of the different parameters on the model output. We simulated habitat loss by removing a percentage of the original habitat, proportionally in each habitat patch. Additionally, we evaluated isolation and fragmentation effects by removing and dividing habitat patches from the network, respectively. The model predicted a slow decline of the metapopulation size and occupancy. Extinction risks predicted by the model were highly sensitive to environmental stochasticity and carrying capacity. For a determined level of habitat destruction, the expected lifetime of the metapopulation was highly dependent on the spatial configuration of the landscape. Moreover, when the proportion of removed habitat is above 40% of the original habitat, the loss of whole patches invariably leads to the strongest reduction in metapopulation viability.     

描述Meta-种群动态的耦合映象格子模型

Ｍｅｔａ－种群观点为在局部种群之上的空间尺度上描述种群的生态学过程提供了一种途径。但是由于植物所拥有的若干特殊性质（如种子休眠、有限扩散和局部适应）使得对某些植物种使用原有的Ｍｅｔａ－种群概念和模型存在许多困难。因此,为了能更精确地反映植物Ｍｅｔａ－种群动态,本文将Ｍｅｔａ－种群动态分解为斑块内局部种群动态和斑块间的扩散过程两个分量。用Ｌｏｇｉｓｔｉｃ方程表述每个斑块内的局部种群动态,用扩散系数ε表示斑块间的扩散,建立了描述Ｍｅｔａ－种群动态的耦合映象格子模型。对单峰映象ｘｎ＋１＝１－ａｘ２ｎ给出了耦合映象格子的时空行为,这对Ｍｅｔａ－种群动态的研究可能是非常重要的。     

Heterogeneity in patch quality buffers metapopulations from pathogen impacts

Many wildlife species persist on a network of ephemerally occupied habitat patches connected by dispersal. Provisioning of food and other resources for conservation management or recreation is frequently used to improve local habitat quality and attract wildlife. Resource improvement can also facilitate local pathogen transmission, but the landscape-level consequences of provisioning for pathogen spread and habitat occupancy are poorly understood. Here, we develop a simple metapopulation model to investigate how heterogeneity in patch quality resulting from resource improvement influences long-term metapopulation occupancy in the presence of a virulent pathogen. We derive expressions for equilibrium host–pathogen outcomes in terms of provisioning effects on individual patches (through decreased patch extinction rates) and at the landscape level (the fraction of high-quality, provisioned patches), and highlight two cases of practical concern. First, if occupancy in the unprovisioned metapopulation is sufficiently low, a local maximum in occupancy occurs for mixtures of high- and low-quality patches, such that further increasing the number of high-quality patches both lowers occupancy and allows pathogen invasion. Second, if the pathogen persists in the unprovisioned metapopulation, further provisioning can result in all patches becoming infected and in a global minimum in occupancy. This work highlights the need for more empirical research on landscape-level impacts of local resource provisioning on pathogen dynamics.     

The dispersal rate of a beetle, Osmoderma eremita, living in tree hollows

The dispersal of an endangered beetle, Osmoderma eremita, that lives in tree hollows, was studied by mark-release-recapture with pitfall traps. As only a small proportion of all dispersals is observed by this method, a simulation model was constructed to estimate the dispersal rate per individual. The model results suggest that 15% of the adults leave the original tree for another hollow tree, and consequently most individuals remain in the same tree throughout their entire life. This suggests that each hollow tree sustains a local population with limited connection with the populations in surrounding trees. It supports the view that O. eremita has a metapopulation structure, with each tree possibly sustaining a local population, and with the population in an assemblage of trees forming a metapopulation. Low dispersal rate and range make the species vulnerable to habitat fragmentation, probably at a scale of only a few hundred meters.     

Metapopulation viability analysis of the bog fritillary butterfly using RAMAS/GIS

Many species living in man-shaped landscapes are restricted to small natural habitat patches and form metapopulations; predicting their future is a central issue in applied ecology. We examined the viability of the bog fritillary butterfly Proclossiana eunomia Esper, a specialist glacial relict species, in a highly fragmented landscape (<1% of suitable habitat in 10 km²), by way of population viability analysis. We used comprehensive data from a long-term study in which a patchy population was monitored during ten consecutive years to parameterise a spatially structured metapopulation model using commercially available platform RAMAS/GIS 3.0. Population growth rate was density-dependent and modulated by various climatic variables acting on different developmental stages of the butterfly. Density dependence was probably related to larval parasitism by a specific parasitoid. Population size was negatively affected by an increase in the mean temperature. Dispersal was modelled as the observed proportion of movements between patches, taking into account the probability of emigration out of a given patch. Our model provided results close to the picture of the system drawn from the field data and was considered as useful in making predictions about the metapopulation. Demographic parameters proved to have a far higher impact on metapopulation persistence than dispersal or correlation of local dynamics. Scenarios simulating both global warming and management of habitat patches by rustic herbivore grazing indicated a decrease in the viability of the metapopulation. Our results prompted the regional nature conservation agency to modify the planned management regime. We urge conservation biologists to use structured population models including local population dynamics for viability analysis targeted to such threatened metapopulations in highly fragmented landscapes.     

Metapopulation dynamics for spatially extended predator–prey interactions

Traditional metapopulation theory classifies a metapopulation as a spatially homogeneous population that persists on neighboring habitat patches. The fate of each population on a habitat patch is a function of a balance between births and deaths via establishment of new populations through migration to neighboring patches. In this study, we expand upon traditional metapopulation models by incorporating spatial heterogeneity into a previously studied two-patch nonlinear ordinary differential equation metapopulation model, in which the growth of a general prey species is logistic and growth of a general predator species displays a Holling type II functional response. The model described in this work assumes that migration by generalist predator and prey populations between habitat patches occurs via a migratory corridor. Thus, persistence of species is a function of local population dynamics and migration between spatially heterogeneous habitat patches. Numerical results generated by our model demonstrate that population densities exhibit periodic plane-wave phenomena, which appear to be functions of differences in migration rates between generalist predator and prey populations. We compare results generated from our model to results generated by similar, but less ecologically realistic work, and to observed population dynamics in natural metapopulations.     

Spatial Heterogeneity in Habitat Quality and Cross-Scale Interactions in Metapopulations

Abstract Integration of habitat heterogeneity into spatially realistic metapopulation approaches reveals the potential for key cross-scale interactions. Broad-scale environmental gradients and land-use practices can create autocorrelation of habitat quality of suitable patches at intermediate spatial scales. Patch occupancy then depends not only on habitat quality at the patch scale but also on feedbacks from surrounding neighborhoods of autocorrelated patches. Metapopulation dynamics emerge from how demographic and dispersal processes interact with relevant habitat heterogeneity. We provide an empirical example from a metapopulation of round-tailed muskrats (Neofiber alleni) in which habitat quality of suitable patches was spatially autocorrelated most strongly within 1,000 m, which was within the expected dispersal range of the species. After controlling for factors typically considered in metapopulation studies—patch size, local patch quality, patch connectivity—we use a cross-variogram analysis to demonstrate that patch occupancy by muskrats was correlated with habitat quality across scales ≤1,171 m. We also discuss general consequences of spatial heterogeneity of habitat quality for metapopulations related to potential cross-scale interactions. We focus on spatially correlated extinctions and metapopulation persistence, hierarchical scaling of source–sink dynamics, and dispersal decisions by individuals in relation to information constraints.     

Congruent population structure inferred from dispersal behaviour and intensive genetic surveys of the threatened Florida scrub-jay (Aphelocoma coerulescens)

The delimitation of populations, defined as groups of individuals linked by gene flow, is possible by the analysis of genetic markers and also by spatial models based on dispersal probabilities across a landscape. We combined these two complimentary methods to define the spatial pattern of genetic structure among remaining populations of the threatened Florida scrub-jay, a species for which dispersal ability is unusually well-characterized. The range-wide population was intensively censused in the 1990s, and a metapopulation model defined population boundaries based on predicted dispersal-mediated demographic connectivity. We subjected genotypes from more than 1000 individual jays screened at 20 microsatellite loci to two Bayesian clustering methods. We describe a consensus method for identifying common features across many replicated clustering runs. Ten genetically differentiated groups exist across the present-day range of the Florida scrub-jay. These groups are largely consistent with the dispersal-defined metapopulations, which assume very limited dispersal ability. Some genetic groups comprise more than one metapopulation, likely because these genetically similar metapopulations were sundered only recently by habitat alteration. The combined reconstructions of population structure based on genetics and dispersal-mediated demographic connectivity provide a robust depiction of the current genetic and demographic organization of this species, reflecting past and present levels of dispersal among occupied habitat patches. The differentiation of populations into 10 genetic groups adds urgency to management efforts aimed at preserving what remains of genetic variation in this dwindling species, by maintaining viable populations of all genetically differentiated and geographically isolated populations.     

The evolution of dispersal – the importance of information about population density and habitat characteristics

The evolution of mobility patterns and dispersal strategies depend on different population, habitat and life history characteristics. The ability to perceive and make use of information about the surrounding environment for dispersal decisions will also differ between organisms. To investigate the evolutionary consequences of such differences, we have used a simulation model with nearest-neighbour dispersal in a metapopulation to study how variation in the ability to obtain and make use of information about habitat quality and conspecific density affects the evolution of dispersal strategies. We found a rather strong influence of variation in information on the overall rate of dispersal in a metapopulation. The highest emigration rate evolved in organisms with no information about either density or habitat quality and the lowest rate was found in organisms with information about both the natal and the neighbouring patches. For organisms that can make use of information about conspecific density, positively density-dependent dispersal evolved in the majority of cases, with the strongest density dependence occurring when an individual only has information about density in the natal patch. However, we also identified situations, involving strong local population fluctuations and frequent local extinctions, where negatively density-dependent dispersal evolved.