Density-dependent dispersal and relative dispersal affect the stability of predator-prey metacommunities

Although density-dependent dispersal and relative dispersal (the difference in dispersal rates between species) have been documented in natural systems, their effects on the stability of metacommunities are poorly understood. Here we investigate the effects of intra- and interspecific density-dependent dispersal on the regional stability in a predator-prey metacommunity model. We show that, when the dynamics of the populations reach equilibrium, the stability of the metacommunity is not affected by density-dependent dispersal. However, the regional stability, measured as the regional variability or the persistence, can be modified by density-dependent dispersal when local populations fluctuate over time. Moreover these effects depend on the relative dispersal of the predator and the prey. Regional stability is modified through changes in spatial synchrony. Interspecific density-dependent dispersal always desynchronizses local dynamics, whereas intraspecific density-dependent dispersal may either synchronize or desynchronize it depending on dispersal rates. Moreover, intra- and interspecific density-dependent dispersal strengthen the top-down control of the prey by the predator at intermediate dispersal rates. As a consequence the regional stability of the metacommunity is increased at intermediate dispersal rates. Our results show that density-dependent dispersal and relative dispersal of species are keys to understanding the response of ecosystems to fragmentation.     

Evolution of positive and negative density-dependent dispersal

Understanding the evolution of density-dependent dispersal strategies has been a major challenge for evolutionary ecologists. Some existing models suggest that selection should favour positive and others negative density-dependence in dispersal. Here, we develop a general model that shows how and why selection may shift from positive to negative density-dependence in response to key ecological factors, in particular the temporal stability of the environment. We find that in temporally stable environments, particularly with low dispersal costs and large group sizes, habitat heterogeneity selects for negative density-dependent dispersal, whereas in temporally variable environments, particularly with high dispersal costs and small group sizes, habitat heterogeneity selects for positive density-dependent dispersal. This shift reflects the changing balance between the greater competition for breeding opportunities in more productive patches, versus the greater long-term value of offspring that establish themselves there, the latter being very sensitive to the temporal stability of the environment. In general, dispersal of individuals out of low-density patches is much more sensitive to habitat heterogeneity than is dispersal out of high-density patches.     

Effect of predator density dependent dispersal of prey on stability of a predator-prey system

This work presents a predator-prey Lotka-Volterra model in a two patch environment. The model is a set of four ordinary differential equations that govern the prey and predator population densities on each patch. Predators disperse with constant migration rates, while prey dispersal is predator density-dependent. When the predator density is large, the dispersal of prey is more likely to occur. We assume that prey and predator dispersal is faster than the local predator-prey interaction on each patch. Thus, we take advantage of two time scales in order to reduce the complete model to a system of two equations governing the total prey and predator densities. The stability analysis of the aggregated model shows that a unique strictly positive equilibrium exists. This equilibrium may be stable or unstable. A Hopf bifurcation may occur, leading the equilibrium to be a centre. If the two patches are similar, the predator density dependent dispersal of prey has a stabilizing effect on the predator-prey system.     

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.     

Density-dependence across dispersal stages in a hermaphrodite land snail: insights from discrete choice models

Dispersal movements, i.e. movements leading to gene flow, are key behaviours with important, but only partially understood, consequences for the dynamics and evolution of populations. In particular, density-dependent dispersal has been widely described, yet how it is determined by the interaction with individual traits, and whether density effects differ between the three steps of dispersal (departure, transience, and settlement), remains largely unknown. Using a semi-natural landscape, we studied dispersal choices of Cornu aspersum land snails, a species in which negative effects of crowding are well documented, and analysed them using dispersal discrete choice models, a new method allowing the analysis of dispersal decisions by explicitly considering the characteristics of all available alternatives and their interaction with individual traits. Subadults were more dispersive than adults, confirming existing results. In addition, departure and settlement were both density dependent: snails avoided crowded patches at both ends of the dispersal process, and subadults were more reluctant to settle into crowded patches than adults. Moreover, we found support for carry-over effects of release density on subsequent settlement decisions: snails from crowded contexts were more sensitive to density in their subsequent immigration choices. The fact that settlement decisions were informed indicates that costs of prospecting are not as important as previously thought in snails, and/or that snails use alternative ways to collect information, such as indirect social information (e.g. trail following). The observed density-dependent dispersal dynamics may play an important role in the ability of C. aspersum to successfully colonise frequently human-disturbed habitats around the world.     

Intra- and interspecific density-dependent dispersal in an aquatic prey-predator system

1. Dispersal intensity is a key process for the persistence of prey-predator metacommunities. Consequently, knowledge of the ecological mechanisms of dispersal is fundamental to understanding the dynamics of these communities. Dispersal is often considered to occur at a constant per capita rate; however, some experiments demonstrated that dispersal may be a function of local species density. 2. Here we use aquatic experimental microcosms under controlled conditions to explore intra- and interspecific density-dependent dispersal in two protists, a prey Tetrahymena pyriformis and its predator Dileptus sp. 3. We observed intraspecific density-dependent dispersal for the prey and interspecific density-dependent dispersal for both the prey and the predator. Decreased prey density lead to an increase in predator dispersal, while prey dispersal increased with predator density. 4. Additional experiments suggest that the prey is able to detect its predator through chemical cues and to modify its dispersal behaviour accordingly. 5. Density-dependent dispersal suggests that regional processes depend on local community dynamics. We discuss the potential consequences of density-dependent dispersal on metacommunity dynamics and stability.     

The ideal free distribution as an evolutionarily stable strategy

We examine the evolutionary stability of strategies for dispersal in heterogeneous patchy environments or for switching between discrete states (e.g. defended and undefended) in the context of models for population dynamics or species interactions in either continuous or discrete time. There have been a number of theoretical studies that support the view that in spatially heterogeneous but temporally constant environments there will be selection against unconditional, i.e. random, dispersal, but there may be selection for certain types of dispersal that are conditional in the sense that dispersal rates depend on environmental factors. A particular type of dispersal strategy that has been shown to be evolutionarily stable in some settings is balanced dispersal, in which the equilibrium densities of organisms on each patch are the same whether there is dispersal or not. Balanced dispersal leads to a population distribution that is ideal free in the sense that at equilibrium all individuals have the same fitness and there is no net movement of individuals between patches or states. We find that under rather general assumptions about the underlying population dynamics or species interactions, only such ideal free strategies can be evolutionarily stable. Under somewhat more restrictive assumptions (but still in considerable generality), we show that ideal free strategies are indeed evolutionarily stable. Our main mathematical approach is invasibility analysis using methods from the theory of ordinary differential equations and nonnegative matrices. Our analysis unifies and extends previous results on the evolutionary stability of dispersal or state-switching strategies.     

Warming induces synchrony and destabilizes experimental pond zooplankton metacommunities

The spatial insurance hypothesis predicts that intermediate rates of dispersal between patches in a metacommunity allow species to track favourable conditions, preserving diversity and stabilizing biomass at local and regional scales. However, theory is unclear as to whether dispersal will provide spatial insurance when environmental conditions are changing directionally. In particular, increased temperatures as a result of climate change are expected to cause synchronous growth or decline across species and communities, and this has the potential to erode the stabilizing compensatory dynamics facilitated by dispersal. Here we report on an experimental test of how dispersal affects the diversity and stability of metacommunities under warming using replicate two‐patch pond zooplankton metacommunities. Initial differences in local community composition and abiotic conditions were established by seeding each patch in the metacommunities with plankton and sediment from one of two natural ponds that differed in water chemistry and species composition. We exposed metacommunities to a 2°C increase in average ambient temperature, crossed with three rates of dispersal (none, intermediate, high). In ambient conditions, intermediate dispersal rates preserved diversity and stabilized metacommunities by promoting spatially asynchronous fluctuations in biomass, especially between local populations of the dominant genus, Ceriodaphnia. However, warming synchronized their populations so that these effects of dispersal were lost. Furthermore, because the stabilizing effect of dispersal was primarily due to asynchronous fluctuations between populations of a single genus, metacommunity biomass was stabilized, but dispersal did not stabilize local community biomass. Our results show that dispersal can preserve diversity and provide stability to metacommunities, but also show that this benefit can be eroded when warming is directional and synchronous across patches of a metacommunity, as is expected with climate warming.     

Emergence of global behaviour in a host–parasitoid model with density-dependent dispersal in a chain of patches

We present a time discrete spatial host–parasitoid model. The environment is a chain of patches connected by dispersal events. Dispersal of parasitoids is host-density dependent. When the host density is small (resp. high), the proportion of migrant parasitoids is close to unity (resp. to zero). We assume fast patch to patch dispersal with respect to local interactions. Local host–parasitoid interactions are described by the classical Nicholson–Bailey model. By using time scales separation methods (or aggregation methods), we obtain a reduced model that governs the total host and parasitoid densities (obtained by addition over all patches). The aggregated model describes the time evolution of the total number of hosts and parasitoids of the system of patches. This global model is useful to make predictions of emerging behaviour regarding the dynamics of the complete system. We study the effects of number of patches and host density-dependent parasitoid dispersal on the overall stability of the host–parasitoid system. We finally compare our stability results with the CV² > 1 rule.     

Single species models with logistic growth and dissymmetric impulse dispersal

In this paper, two classes of single-species models with logistic growth and impulse dispersal (or migration) are studied: one model class describes dissymmetric impulsive bi-directional dispersal between two heterogeneous patches; and the other presents a new way of characterizing the aggregate migration of a natural population between two heterogeneous habitat patches, which alternates in direction periodically. In this theoretical study, some very general, weak conditions for the permanence, extinction of these systems, existence, uniqueness and global stability of positive periodic solutions are established by using analysis based on the theory of discrete dynamical systems. From this study, we observe that the dynamical behavior of populations with impulsive dispersal differs greatly from the behavior of models with continuous dispersal. Unlike models where the dispersal is continuous in time, in which the travel losses associated with dispersal make it difficult for such dispersal to evolve e.g., [25], [26], [28], in the present study it was relatively easy for impulsive dispersal to positively affect populations when realistic parameter values were used, and a rich variety of behaviors were possible. From our results, we found impulsive dispersal seems to more nicely model natural dispersal behavior of populations and may be more relevant to the investigation of such behavior in real ecological systems.     

Two-patch population models with adaptive dispersal: the effects of varying dispersal speeds

The population-dispersal dynamics for predator–prey interactions and two competing species in a two patch environment are studied. It is assumed that both species (i.e., either predators and their prey, or the two competing species) are mobile and their dispersal between patches is directed to the higher fitness patch. It is proved that such dispersal, irrespectively of its speed, cannot destabilize a locally stable predator–prey population equilibrium that corresponds to no movement at all. In the case of two competing species, dispersal can destabilize population equilibrium. Conditions are given when this cannot happen, including the case of identical patches.     

Effects of patch number and dispersal patterns on population dynamics and synchrony

In this paper, we examine the effects of patch number and different dispersal patterns on dynamics of local populations and on the level of synchrony between them. Local population renewal is governed by the Ricker model and we also consider asymmetrical dispersal as well as the presence of environmental heterogeneity. Our results show that both population dynamics and the level of synchrony differ markedly between two and a larger number of local populations. For two patches different dispersal rules give very versatile dynamics. However, for a larger number of local populations the dynamics are similar irrespective of the dispersal rule. For example, for the parameter values yielding stable or periodic dynamics in a single population, the dynamics do not change when the patches are coupled with dispersal. High intensity of dispersal does not guarantee synchrony between local populations. The level of synchrony depends also on dispersal rule, the number of local populations, and the intrinsic rate of increase. In our study, the effects of density-independent and density-dependent dispersal rules do not show any consistent difference. The results call for caution when drawing general conclusions from models of only two interacting populations and question the applicability of a large number of theoretical papers dealing with two local populations.     

Effects of matrix heterogeneity on animal dispersal: from individual behavior to metapopulation-level parameters

Mounting theoretical and empirical evidence shows that matrix heterogeneity may have contrasting effects on metapopulation dynamics by contributing to patch isolation in nontrivial ways. We analyze the movement properties during interpatch dispersal in a metapopulation of Iberian lynx (Lynx pardinus). On a daily temporal scale, lynx habitat selection defines two types of matrix habitats where individuals may move: open and dispersal habitats (avoided and used as available, respectively). There was a strong and complex impact of matrix heterogeneity on movement properties at several temporal scales (hourly and daily radiolocations and the entire dispersal event). We use the movement properties on the hourly temporal scale to build a simulation model to reconstruct individual dispersal events. The two most important parameters affecting model predictions at both the individual (daily) and metapopulation scales were related to the movement capacity (number of movement steps per day and autocorrelation in dispersal habitat) followed by the parameters representing the habitat selection in the matrix. The model adequately reproduced field estimates of population-level parameters (e.g., interpatch connectivity, maximum and final dispersal distances), and its performance was clearly improved when including the effect of matrix heterogeneity on movement properties. To assume there is a homogeneous matrix results in large errors in the estimate of interpatch connectivity, especially for close patches separated by open habitat or corridors of dispersal habitat, showing how important it is to consider matrix heterogeneity when it is present. Movement properties affect the interaction of dispersing individuals with the landscape and can be used as a mechanistic representation of dispersal at the metapopulation level. This is so when the effect of matrix heterogeneity on movement properties is evaluated under biologically meaningful spatial and temporal scales.     

A multivariate analysis of fine-scale species density in the plant communities of a saltwater lagoon – the importance of disturbance intensity

Several factors might influence an organism's tendency or willingness to leave a given patch. One such factor is conspecific density, which may affect the per capita emigration rate. Some previous field studies on butterflies have reported positively density-dependent dispersal (emigration increases with population density) whereas the opposite, negatively density-dependent dispersal, has been found in other species. We investigated the effect of conspecific density on both the tendency to cross a patch boundary and within-patch mobility in Melitaea cinxia , by experimentally manipulating density in large outdoor cages divided into two habitat patches, separated by a barrier of unsuitable habitat. In contrast to previous results for M. cinxia , we found that the butterflies moved away from a patch at higher rates in high conspecific density (positively density-dependent emigration). The within-patch mobility, measured as the distance travelled per time unit, was however unaffected by butterfly density. A possible explanation for the seeming discrepancy with previous results could be that we used higher butterfly densities. For species with fluctuating population dynamics, such as M. cinxia , dispersal activity both at low and at high local density will be important for population phenomena such as fluctuations in distributional range over good and bad years.     

Floater dynamics can explain positive patterns of density-dependent fecundity in animal populations

After some 70 years of debate on density-dependent regulation of animal populations, there is still poor understanding of where spatial and temporal density dependence occurs. Clearly defining the portion of the population that shapes density-dependent patterns may help to solve some of the ambiguities that encircle density dependence and its patterns. In fact, individuals of the same species and population can show different dynamics and behaviors depending on their locations (e.g., breeding vs. dispersal areas). Considering this form of intrapopulation heterogeneity may improve our understanding of density dependence and population dynamics in general. We present the results of individual-based simulations on a metapopulation of the Spanish imperial eagle Aquila adalberti. Our results suggest that high rates of floater mortality within settlement areas can determine a shift in the classical relationship (from negative to positive) between the fecundity (i.e., fledglings per pair) and density (i.e., number of pairs) of the breeding population. Finally, we proved that different initial conditions affecting the breeder portion of the population can lead to the same values of fecundity. Our results can represent a starting point for new and more complex approaches studying the regulation of animal populations, where the forgotten and invisible component--the floater--is taken into account.     

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.     

Subsocial spiders in space and time: A fine scale approach to the dynamics of dispersal

Less than 0.2% of all spider species live in close associations with conspecifics. Among these, subsocial spiders show characteristics of both solitary spiders (e.g., individuals disperse for breeding) and social spiders (e.g., prolonged cooperative behaviours at least prior to independent reproduction). Dispersing individuals build small webs, usually with one inhabitant, whereas colonies are large webs with plant debris and harbouring multiple females. We studied the spatiotemporal dynamics of dispersal in the subsocial spider Anelosimus baeza. We followed the occupancy of all colonies and dispersal webs over the breeding season by mapping the number and sex of spiders with respect to their location in three dimensions. We studied the settlement patterns of new webs and fluctuation in web occupancy through movement between occupied and abandoned webs of colonies and dispersal webs. The occupancy of webs was highly dynamic with changes occurring at small time scales. The similarity in the patterns of web occupancy by females among dispersal webs was partially explained by their spatial and their temporal proximity. Our results suggest that dispersal webs may be used by spiders as a temporary refuge by both sexes during the breeding season. Patterns described here suggest new approaches to dispersal studies in group living spiders.     

The magnitude of local adaptation under genotype‐dependent dispersal

Dispersal moves individuals from patches where their immediate ancestors were successful to sites where their genotypes are untested. As a result, dispersal generally reduces fitness, a phenomenon known as “migration load.” The strength of migration load depends on the pattern of dispersal and can be dramatically lessened or reversed when individuals move preferentially toward patches conferring higher fitness. Evolutionary ecologists have long modeled nonrandom dispersal, focusing primarily on its effects on population density over space, the maintenance of genetic variation, and reproductive isolation. Here, we build upon previous work by calculating how the extent of local adaptation and the migration load are affected when individuals differ in their dispersal rate in a genotype‐dependent manner that alters their match to their environment. Examining a one‐locus, two‐patch model, we show that local adaptation occurs through a combination of natural selection and adaptive dispersal. For a substantial portion of parameter space, adaptive dispersal can be the predominant force generating local adaptation. Furthermore, genetic load may be largely averted with adaptive dispersal whenever individuals move before selective deaths occur. Thus, to understand the mechanisms driving local adaptation, biologists must account for the extent and nature of nonrandom, genotype‐dependent dispersal, and the potential for adaptation via spatial sorting of genotypes.     

Do all inter-patch movements represent dispersal? A mixed kernel study of butterfly mobility in fragmented landscapes

1. In times of ongoing habitat fragmentation, the persistence of many species is determined by their dispersal abilities. Consequently, understanding the rules underlying movement between habitat patches is a key issue in conservation ecology. 2. We have analysed mark-release-recapture (MRR) data on inter-patches movements of the Dusky Large Blue butterfly Maculinea nausithous in a fragmented landscape in northern Bavaria, Germany. The aim of the analysis was to quantify distance dependence of dispersal as well as to evaluate the effect of target patch area on immigration probability. For statistical evaluation, we apply a 'reduced version' of the virtual migration model (VM), only fitting parameters for dispersal distance and immigration. In contrast to other analyses, we fit a mixed dispersal kernel to the MRR data. 3. A large fraction of recaptures happened in other habitat patches than those where individuals were initially caught. Further, we found significant evidence for the presence of a mixed dispersal kernel. The results indicate that individuals follow different strategies in their movements. Most movements are performed over small distances, nonetheless involving travelling between nearby habitat patches (median distance c. 480 m). A small fraction (c. 0·025) of the population has a tendency to move over larger distances (median distance c. 3800 m). Further, immigration was positively affected by patch area (I～A(ζ) ), with the scaling parameter ζ = 0·5. 4. Our findings should help to resolve the long-lasting dispute over the suitability of the negative exponential function vs. inverse-power one for modelling dispersal. Previous studies on various organisms found that the former typically gives better overall fit to empirical distance distributions, but that the latter better represents long-distance movement probabilities. As long-distance movements are more important for landscape-level effects and thus, e.g. for conservation-oriented analyses like PVAs, fitting inverse-power kernels has often been preferred. 5. We conclude that the above discrepancy may simply stem from the fact that recorded inter-patch movements are an outcome of two different processes: daily routine movements and genuine dispersal. Consequently, applying mixed dispersal kernels to disentangle the two processes is recommended.     

The ideal free distribution as an evolutionarily stable strategy

We examine the evolutionary stability of strategies for dispersal in heterogeneous patchy environments or for switching between discrete states (e.g. defended and undefended) in the context of models for population dynamics or species interactions in either continuous or discrete time. There have been a number of theoretical studies that support the view that in spatially heterogeneous but temporally constant environments there will be selection against unconditional, i.e. random, dispersal, but there may be selection for certain types of dispersal that are conditional in the sense that dispersal rates depend on environmental factors. A particular type of dispersal strategy that has been shown to be evolutionarily stable in some settings is balanced dispersal, in which the equilibrium densities of organisms on each patch are the same whether there is dispersal or not. Balanced dispersal leads to a population distribution that is ideal free in the sense that at equilibrium all individuals have the same fitness and there is no net movement of individuals between patches or states. We find that under rather general assumptions about the underlying population dynamics or species interactions, only such ideal free strategies can be evolutionarily stable. Under somewhat more restrictive assumptions (but still in considerable generality), we show that ideal free strategies are indeed evolutionarily stable. Our main mathematical approach is invasibility analysis using methods from the theory of ordinary differential equations and nonnegative matrices. Our analysis unifies and extends previous results on the evolutionary stability of dispersal or state-switching strategies.