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.     

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.     

The evolution of density-dependent dispersal

Despite a large body of empirical evidence suggesting that the dispersal rates of many species depend on population density, most metapopulation models assume a density-independent rate of dispersal. Similarly, studies investigating the evolution of dispersal have concentrated almost exclusively on density-independent rates of dispersal. We develop a model that allows density-dependent dispersal strategies to evolve. Our results demonstrate that a density-dependent dispersal strategy almost always evolves and that the form of the relationship depends on reproductive rate, type of competition, size of subpopulation equilibrium densities and cost of dispersal. We suggest that future metapopulation models should account for density-dependent dispersal     

Evolutionary suicide and evolution of dispersal in structured metapopulations

 We study the evolution of dispersal in a structured metapopulation model. The metapopulation consists of a large (infinite) number of local populations living in patches of habitable environment. Dispersal between patches is modelled by a disperser pool and individuals in transit between patches are exposed to a risk of mortality. Occasionally, local catastrophes eradicate a local population: all individuals in the affected patch die, yet the patch remains habitable. We prove that, in the absence of catastrophes, the strategy not to migrate is evolutionarily stable. Under a given set of environmental conditions, a metapopulation may be viable and yet selection may favor dispersal rates that drive the metapopulation to extinction. This phenomenon is known as evolutionary suicide. We show that in our model evolutionary suicide can occur for catastrophe rates that increase with decreasing local population size. Evolutionary suicide can also happen for constant catastrophe rates, if local growth within patches shows an Allee effect. We study the evolutionary bifurcation towards evolutionary suicide and show that a discontinuous transition to extinction is a necessary condition for evolutionary suicide to occur. In other words, if population size smoothly approaches zero at a boundary of viability in parameter space, this boundary is evolutionarily repelling and no suicide can occur. Received: 10 November 2000 / Revised version: 13 February 2002 / Published online: 17 July 2002     

Density-dependent dispersal complicates spatial synchrony in tri-trophic food chains

Spatial synchrony can increase extinction risk and undermines metapopulation persistence. Both dispersal and biotic interactions can strongly affect spatial synchrony. Here, we explore the spatial synchrony of a tri-trophic food chain in two patches connected by density-dependent dispersal, namely the strategies of prey evasion (PE) and predator pursuit (PP). The dynamics of the food chain are depicted by both the Hastings–Powell model and the chemostat model, with synchrony measured by the Pearson correlation coefficient. We use the density-independent dispersal in the system as a baseline for comparison. Results show that the density-independent dispersal of a species in the system can promote its dynamic synchrony. Dispersal of intermediate species in the tri-trophic food chain is the strongest synchronizer. In contrast, the density-dependent PP and PE of intermediate species can desynchronize the system. Highly synchronized dynamics emerged when the basal species has a strong PE strategy or when the top species has a moderate PP strategy. Our results reveal the complex relationship between density-dependent dispersal and spatial synchrony in tri-trophic systems.     

Metapopulation persistence in heterogeneous landscapes: lessons about the effect of stochasticity

This article addresses an important aspect of the analysis of metapopulation persistence. It highlights some consequences of ignoring and including stochasticity in the sequence of extinction and colonization events. The results are based on a comparative analysis of the outcomes of two (one deterministic, one stochastic) spatially realistic metapopulation models and a search for common effects and differences. One key result of the article is that, under certain conditions, there are extra effects of the landscape structure (number and configuration of patches, patch size distribution) on metapopulation persistence if stochasticity is included. In these cases, ignoring or including stochasticity can change conclusions about the persistence status but also ranking orders, relative results, and qualitative trends. A list of conditions is provided under which including stochasticity is vital to prevent counterproductive conclusions about metapopulation persistence. The results of the overall study are condensed in five lessons about the effect of stochasticity. A number of implications for ecological theory and conservation management are discussed. The study demonstrates the potential of three recently published approximation formulas (metapopulation capacity lambdaM, mean lifetime Tm, and effective number of patches N) to serve as tools for ecological analysis and thinking.     

Density-dependent migration and synchronism in metapopulations

A spatially explicit metapopulation model with density-dependent dispersal is proposed in order to study the stability of synchronous dynamics. A stability criterion is obtained based on the computation of the transversal Liapunov number of attractors on the synchronous invariant manifold. We examine in detail a special case of density-dependent dispersal rule where migration does not occur if the patch density is below a certain critical density, while the fraction of individuals that migrate to other patches is kept constant if the patch density is above the threshold level. Comparisons with density-independent migration models indicate that this simple density-dependent dispersal mechanism reduces the stability of synchronous dynamics. We were able to quantify exactly this loss of stability through the frequency that synchronous trajectories are above the critical density.     

Metapopulation persistence in fragmented landscapes: significant interactions between genetic and demographic processes

We formulated a mathematical model in order to study the joint influence of demographic and genetic processes on metapopulation viability. Moreover, we explored the influence of habitat structure, matrix quality and disturbance on the interplay of these processes. We showed that the conditions that allow metapopulation persistence under the synergistic action of genetic and demographic processes depart significantly from predictions based on a mere superposition of the effects of each process separately. Moreover, an optimal dispersal rate exists that maximizes the range of survival rates of dispersers under which metapopulation persists and at the same time allows the largest sustainable patch removal and patch‐size reduction. The relative impact of patch removal and patch‐size reduction depends both on matrix quality and the dispersal strategy of the species: metapopulation persistence is more affected by patch‐size reduction (patch removal) for low (high)‐dispersing species, in presence of a low (high) quality matrix. Avoidance of inbreeding, through increased dispersal when the rate of inbreeding in a population is large, has positive effects on low‐dispersing species, but impairs the persistence of high‐dispersing species. Finally, size heterogeneity between patches largely influences metapopulation dynamics; the presence of large patches, even at the expense of other patches being smaller, can have positive effects on persistence in particular for species of low dispersing ability.     

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 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.     

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.     

Contributions of high- and low-quality patches to a metapopulation with stochastic disturbance

Studies of time-invariant matrix metapopulation models indicate that metapopulation growth rate is usually more sensitive to the vital rates of individuals in high-quality (i.e., good) patches than in low-quality (i.e., bad) patches. This suggests that, given a choice, management efforts should focus on good rather than bad patches. Here, we examine the sensitivity of metapopulation growth rate for a two-patch matrix metapopulation model with and without stochastic disturbance and found cases where managers can more efficiently increase metapopulation growth rate by focusing efforts on the bad patch. In our model, net reproductive rate differs between the two patches so that in the absence of dispersal, one patch is high quality and the other low quality. Disturbance, when present, reduces net reproductive rate with equal frequency and intensity in both patches. The stochastic disturbance model gives qualitatively similar results to the deterministic model. In most cases, metapopulation growth rate was elastic to changes in net reproductive rate of individuals in the good patch than the bad patch. However, when the majority of individuals are located in the bad patch, metapopulation growth rate can be most elastic to net reproductive rate in the bad patch. We expand the model to include two stages and parameterize the patches using data for the softshell clam, Mya arenaria. With a two-stage demographic model, the elasticities of metapopulation growth rate to parameters in the bad patch increase, while elasticities to the same parameters in the good patch decrease. Metapopulation growth rate is most elastic to adult survival in the population of the good patch for all scenarios we examine. If the majority of the metapopulation is located in the bad patch, the elasticity to parameters of that population increase but do not surpass elasticity to parameters in the good patch. This model can be expanded to include additional patches, multiple stages, stochastic dispersal, and complex demography.     

Migration and Allee effects in the six-spot burnet moth Zygaena filipendulae

Abstract 1. Migration into local populations may increase the likelihood of persistence but emigration may decrease the persistence of small and isolated populations. The dispersal behaviour of a day-flying moth Zygaena filipendulae was examined to determine whether emigration is correlated positively or negatively with population size and host plant density.
2. A mark–release–recapture study showed that most moths moved small distances (< 40 m on average) and only 6% of movements were > 100 m.
3. Twenty-five individuals moved between populations, a measured exchange rate of 8%. Moths were more likely to move between patches that were close together and they moved to relatively large patches.
4. The fraction of residents increased with increasing population size in the patch and increasing host plant cover. Relatively high proportions of individuals left small patches with small moth populations.
5. Moths released in grassland lacking Lotus corniculatus (the host plant) tended to leave the area and biased their movement towards host plant areas, whereas those released within an area containing L. corniculatus tended to stay in that area.
6. Biased movement away from small populations and areas of low host plant density (normally with low population density) was found. This migration-mediated Allee effect is likely to decrease patch occupancy in metapopulations, the opposite of the rescue effect. The effects on metapopulation persistence are not known.     

The ability of individuals to assess population density influences the evolution of emigration propensity and dispersal distance

We analyze the simultaneous evolution of emigration and settlement decisions for actively dispersing species differing in their ability to assess population density. Using an individual-based model we simulate dispersal as a multi-step (patch to patch) movement in a world consisting of habitat patches surrounded by a hostile matrix. Each such step is associated with the same mortality risk. Our simulations show that individuals following an informed strategy, where emigration (and settlement) probability depends on local population density, evolve a lower (natal) emigration propensity but disperse over significantly larger distances - i.e. postpone settlement longer - than individuals performing density-independent emigration. This holds especially when variation in environmental conditions is spatially correlated. Both effects can be traced to the informed individuals' ability to better exploit existing heterogeneity in reproductive chances. Yet, already moderate distance-dependent dispersal costs prevent the evolution of multi-step (long-distance) dispersal, irrespective of the dispersal strategy.     

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.     

Simulating viability of a spadefoot toad Pelobates fuscus metapopulation in a landscape fragmented by a road

A stochastic simulation model allowing for demographic and environmental stochasticity was developed in order to predict the dynamics of a Pelobates fuscus metapopulation. The metapopulation (consisting of ca 1000 adult individuals) was intensively studied in the field for a period of four years and the simulation model was parameterised (sex ratio, age‐specific survival rates, fecundity and dispersal between subpopulations) using field data. A sensitivity analysis revealed that a change in the juvenile yearly survival rate has a relatively larger effect on subpopulation persistence than adult survival rate and fecundity rate have. The probability of subpopulation persistence for one hundred years increased from 0 to 0.6 with a change in juvenile yearly survival rate from 0.35 to 0.40. Varying dispersal rate (from 0 to 1% of the individuals in a subpopulation moving to another subpopulation within a year) showed that four of the five subpopulations are dependent on the last one for persistence, indicating a source‐sink structure of the metapopulation. The subpopulation with the highest estimated juvenile survival has a far higher persistence probability than the others; they in turn would go extinct were it not for the occasional input of individuals from the source subpopulation. The source‐sink structure was also apparent when simulating the isolation effect of the road: persistence of the subpopulation isolated by the road decreases markedly with only a 20% decrease in the number of individuals dispersing to this pond. Environmental stochasticity decreases persistence time of the source subpopulation, but increases persistence time of the unstable ones. This is probably due to the presence of overcompensating density‐dependent factors affecting the subpopulations and to the more general effect of stochasticity: it may temporarily change reproduction and mortality rates, increase time to extinction for unstable subpopulations through a rescue effect; and decrease time to extinction for the more stable subpopulations.     

Demographic consequences of population subdivision on the long-furred woolly mouse opossum (Micoureus paraguayanus) from the Atlantic Forest

Habitat destruction and fragmentation severely affected the Atlantic Forest. Formerly contiguous populations may become subdivided into a larger number of smaller populations, threatening their long-term persistence. The computer package VORTEX was used to simulate the consequences of habitat fragmentation and population subdivision on Micoureus paraguayanus, an endemic arboreal marsupial of the Atlantic Forest. Scenarios simulated hypothetical populations of 100 and 2000 animals being partitioned into 1–10 populations, linked by varying rates of inter-patch dispersal, and also evaluated male-biased dispersal. Results demonstrated that a single population was more stable than an ensemble of populations of equal size, irrespective of dispersal rate. Small populations (10–20 individuals) exhibited high instability due to demographic stochasticity, and were characterized by high rates of extinction, smaller values for metapopulation growth and larger fluctuations in population size and growth rate. Dispersal effects on metapopulation persistence were related to the size of the populations and to the sexes that were capable of dispersing. Male-biased dispersal had no noticeable effects on metapopulation extinction dynamics, whereas scenarios modelling dispersal by both sexes positively affected metapopulation dynamics through higher growth rates, smaller fluctuations in growth rate, larger final metapopulation sizes and lower probabilities of extinction. The present study highlights the complex relationships between metapopulation size, population subdivision, habitat fragmentation, rate of inter-patch dispersal and sex-biased dispersal and indicates the importance of gaining a better understanding of dispersal and its interactions with correlations between disturbance events.     

A persistence criterion for metapopulations

Simple conditions to evaluate the persistence of populations living in fragmented habitats are of primary importance in ecology. We address this need here using a spatially implicit approach that accounts for discrete individuals in a metapopulation. Demographic stochasticity is incorporated into a Markovian model in a natural way, as local extinction is characterized by the death or the dispersal of the last individual inhabiting a patch. The variables of the model are the probabilities p(i) (i=0, 1, 2...) that a patch be occupied by a finite, integer number i of individuals at a given time. We compare the stationary distributions predicted by the model with field data and discuss the role of dispersal in determining different distributions of local abundances. The analysis of the model leads to a persistence criterion which is equivalent to a condition formerly proved by Chesson (Z. Wahrscheinlichkeitstheor. 66, 97-107, 1984) namely that E(0)>1, where E(0) is the expected number of successful dispersers from a patch begun with one individual and to which immigration is excluded. We provide an analytic way of computing E(0) as a function of the main biological characteristics of the species (natality, mortality and dispersal rates, and colonizing ability). We can thus obtain persistence-extinction boundaries in the space of model parameters.     

The evolution of an 'intelligent' dispersal strategy: biased, correlated random walks in patchy landscapes

Theoretical work exploring dispersal evolution focuses on the emigration rate of individuals and typically assumes that movement occurs either at random to any other patch or to one of the nearest‐neighbour patches. There is a lack of work exploring the process by which individuals move between patches, and how this process evolves. This is of concern because any organism that can exert control over dispersal direction can potentially evolve efficiencies in locating patches, and the process by which individuals find new patches will potentially have major effects on metapopulation dynamics and gene flow. Here, we take an initial step towards filling this knowledge gap. To do this we constructed a continuous space population model, in which individuals each carry heritable trait values that specify the characteristics of the biased correlated random walk they use to disperse from their natal patch. We explore how the evolution of the random walk depends upon the cost of dispersal, the density of patches in the landscape, and the emigration rate. The clearest result is that highly correlated walks always evolved (individuals tended to disperse in relatively straight lines from their natal patch), reflecting the efficiency of straight‐line movement. In our models, more costly dispersal resulted in walks with higher correlation between successive steps. However, the exact walk that evolved also depended upon the density of suitable habitat patches, with low density habitat evolving more biased walks (individuals which orient towards suitable habitat at quite large distances from that habitat). Thus, low density habitat will tend to develop individuals which disperse efficiently between adjacent habitat patches but which only rarely disperse to more distant patches; a result that has clear implications for metapopulation theory. Hence, an understanding of the movement behaviour of dispersing individuals is critical for robust long‐term predictions of population dynamics in fragmented landscapes.