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.     

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.     

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.     

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.     

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.     

Spatial synchrony through density-independent versus density-dependent dispersal

Many theoretical studies support the notion that strong dispersal fosters spatial synchrony. Nonetheless, the effect of conditional vs. unconditional dispersal has remained a matter of controversy. We scrutinize recent findings on a desynchronizing effect of negative density-dependent dispersal based on spatially explicit simulation models. Keeping net emigration rates equivalent, we compared density-independent and density-dependent dispersal for different types of intraspecific density regulation, ranging from under-compensation to over-compensation. In general, density-independent dispersal possessed a slightly higher synchronizing potential but this effect was very small and sensitive compared to the influence of the type of local density regulation. Notably, consistent outcomes for the comparison of conditional dispersal strategies strongly relied on the control of equivalent emigration rates. We conclude that the strength of dispersal is more important for spatial synchrony than its density dependence. Most important is the mode of intraspecific density regulation.     

Spatial synchrony through density-independent versus density-dependent dispersal

Many theoretical studies support the notion that strong dispersal fosters spatial synchrony. Nonetheless, the effect of conditional vs. unconditional dispersal has remained a matter of controversy. We scrutinize recent findings on a desynchronizing effect of negative density-dependent dispersal based on spatially explicit simulation models. Keeping net emigration rates equivalent, we compared density-independent and density-dependent dispersal for different types of intraspecific density regulation, ranging from under-compensation to over-compensation. In general, density-independent dispersal possessed a slightly higher synchronizing potential but this effect was very small and sensitive compared to the influence of the type of local density regulation. Notably, consistent outcomes for the comparison of conditional dispersal strategies strongly relied on the control of equivalent emigration rates. We conclude that the strength of dispersal is more important for spatial synchrony than its density dependence. Most important is the mode of intraspecific density regulation.     

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.     

Structured models of metapopulation dynamics

I develop models of metapopulation dynamics that describe changes in the numbers of individuals within patches. These models are analogous to structured population models, with patches playing the role of individuals. Single species models which do not include the effect of immigration on local population dynamics of occupied patches typically lead to a unique equilibrium. The models can be used to study the distributions of numbers of individuals among patches, showing that both metapopulations with local outbreaks and metapopulations without outbreaks can occur in systems with no underlying environmental variability. Distributions of local population sizes (in occupied patches) can vary independently of the total population size, so both patterns of distributions of local population sizes are compatible with either rare or common species. Models which include the effect of immigration on local population dynamics can lead to two positive equilibria, one stable and one unstable, the latter representing a threshold between regional extinction and persistence.     

Effects of demographic parameters on metapopulation size and persistence: an analytical stochastic model

An analytical stochastic metapopulation model is developed. It describes how individuals will be distributed among patches as a function of density-dependent birth, death and emigration rates, and the probability of successful dispersal. The model includes demographic stochasticity, but not catastrophes, environmental stochasticity or variation in patch size and suitability. All patches are equally likely to be colonized by migrants. The model predicts: (a) mean and variance of the number of individuals per patch; (b) probability distribution of individuals per patch; (c) mean number of individuals in transit; and (d) turn-over rate and expected persistence time of a single patch. The model shows that (a) dispersal rates must be intermediate in order to ensure metapopulation persistence; (b) the mean number of individuals per patch is often well below the carrying capacity; (c) long transit times and/or high mortality during dispersal reduce the mean number of individuals per patch; (d) density-dependent emigration responses will usually increase metapopulation size and persistence compared with density-independent dispersal; (e) an increase in the per capita net growth rate can both increase and decrease metapopulation size and persistence depending on whether dispersal rates are high or low; (f) density-independent birth, death, and emigration rates lead to a spatial pattern described by the negative binomial distribution.     

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.     

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.     

Density-Dependent Natal Dispersal Patterns in a Leopard Population Recovering from Over-Harvest

Natal dispersal enables population connectivity, gene flow and metapopulation dynamics. In polygynous mammals, dispersal is typically male-biased. Classically, the ‘mate competition’, ‘resource competition’ and ‘resident fitness’ hypotheses predict density-dependent dispersal patterns, while the ‘inbreeding avoidance’ hypothesis posits density-independent dispersal. In a leopard (Panthera pardus) population recovering from over-harvest, we investigated the effect of sex, population density and prey biomass, on age of natal dispersal, distance dispersed, probability of emigration and dispersal success. Over an 11-year period, we tracked 35 subadult leopards using VHF and GPS telemetry. Subadult leopards initiated dispersal at 13.6 ± 0.4 months. Age at commencement of dispersal was positively density-dependent. Although males (11.0 ± 2.5 km) generally dispersed further than females (2.7 ± 0.4 km), some males exhibited opportunistic philopatry when the population was below capacity. All 13 females were philopatric, while 12 of 22 males emigrated. Male dispersal distance and emigration probability followed a quadratic relationship with population density, whereas female dispersal distance was inversely density-dependent. Eight of 12 known-fate females and 5 of 12 known-fate male leopards were successful in settling. Dispersal success did not vary with population density, prey biomass, and for males, neither between dispersal strategies (philopatry vs. emigration). Females formed matrilineal kin clusters, supporting the resident fitness hypothesis. Conversely, mate competition appeared the main driver for male leopard dispersal. We demonstrate that dispersal patterns changed over time, i.e. as the leopard population density increased. We conclude that conservation interventions that facilitated local demographic recovery in the study area also restored dispersal patterns disrupted by unsustainable harvesting, and that this indirectly improved connectivity among leopard populations over a larger landscape.     

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.     

Effects of connectivity and recurrent local disturbances on community structure and population density in experimental metacommunities

Metacommunity theory poses that the occurrence and abundance of species is a product of local factors, including disturbance, and regional factors, like dispersal among patches. While metacommunity ideas have been broadly tested there is relatively little work on metacommunities subject to disturbance. We focused on how localized disturbance and dispersal interact to determine species composition in metacommunities. Experiments conducted in simple two-patch habitats containing eight protozoa and rotifer species tested how dispersal altered community composition in both communities that were disturbed and communities that connected to refuge communities not subject to disturbance. While disturbance lowered population densities, in disturbed patches connected to undisturbed patches this was ameliorated by immigration. Furthermore, species with high dispersal abilities or growth rates showed the fastest post-disturbance recovery in presence of immigration. Connectivity helped to counteract the negative effect of disturbances on local populations, allowing mass-effect-driven dispersal of individuals from undisturbed to disturbed patches. In undisturbed patches, however, local population sizes were not significantly reduced by emigration. The absence of a cost of dispersal for undisturbed source populations is consistent with a lack of complex demography in our system, such as age- or sex-specific emigration. Our approach provides an improved way to separate components of population growth from organisms' movement in post-disturbance recovery of (meta)communities. Further studies are required in a variety of ecosystems to investigate the transient dynamics resulting from disturbance and dispersal.     

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.     

Spatial variation and density-dependent dispersal in competitive coexistence

It is well known that dispersal from localities favourable to a species' growth and reproduction (sources) can prevent competitive exclusion in unfavourable localities (sinks). What is perhaps less well known is that too much emigration can undermine the viability of sources and cause regional competitive exclusion. Here, I investigate two biological mechanisms that reduce the cost of dispersal to source communities. The first involves increasing the spatial variation in the strength of competition such that sources can withstand high rates of emigration; the second involves reducing emigration from sources via density-dependent dispersal. I compare how different forms of spatial variation and modes of dispersal influence source viability, and hence source-sink coexistence, under dominance and pre-emptive competition. A key finding is that, while spatial variation substantially reduces dispersal costs under both types of competition, density-dependent dispersal does so only under dominance competition. For instance, when spatial variation in the strength of competition is high, coexistence is possible (regardless of the type of competition) even when sources experience high emigration rates; when spatial variation is low, coexistence is restricted even under low emigration rates. Under dominance competition, density-dependent dispersal has a strong effect on coexistence. For instance, when the emigration rate increases with density at an accelerating rate (Type III density-dependent dispersal), coexistence is possible even when spatial variation is quite low; when the emigration rate increases with density at a decelerating rate (Type II density-dependent dispersal), coexistence is restricted even when spatial variation is quite high. Under pre-emptive competition, density-dependent dispersal has only a marginal effect on coexistence. Thus, the diversity-reducing effects of high dispersal rates persist under pre-emptive competition even when dispersal is density dependent, but can be significantly mitigated under dominance competition if density-dependent dispersal is Type III rather than Type II. These results lead to testable predictions about source-sink coexistence under different regimes of competition, spatial variation and dispersal. They identify situations in which density-independent dispersal provides a reasonable approximation to species' dispersal patterns, and those under which consideration of density-dependent dispersal is crucial to predicting long-term coexistence.     

Female-biased density-dependent dispersal of a tephritid fly in a fragmented habitat and its implications for population regulation

The aim of this study was to quantify the rate of dispersal as a response to density in the specialist tephritid fly Paroxyna plantaginis (the main seed predator on its patchily distributed host plant, Tripolium vulgare, Asteraceae). Marked flies were released at three different fly densities in artificial host patches. The individual histories of recaptures were recorded as well as migration between patches and invasion by unmarked flies. The loss of marked flies relative to initial density was analysed using maximum likelihood estimation. Females generally had the highest loss rate. When comparing a density-independent model with a density-dependent model of the loss rate, the density-dependent model won four times out of six for the females but not a single time for the males. A stronger immigration rate of females relative to males supported the suggested female-biased dispersal. This indicates a sit-and-wait strategy for the territorial males and a pre-emptive competition strategy for egg-laying substrates for the females. These results may be of general importance for non-frugivorous tephritid systems with unpredictable and almost ephemeral accessibility to host plants and with a dynamics characterised by a high turnover rate and high attack levels. The study presents a method for measuring the propensity of individuals to leave an area as a response to local density. It is further an example of the consequences individual behavioural responses may have on the population dynamics of a patchy population.     

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.     

Evolution of dispersal in metapopulations with local density dependence and demographic stochasticity

In this paper, we predict the outcome of dispersal evolution in metapopulations based on the following assumptions: (i) population dynamics within patches are density-regulated by realistic growth functions; (ii) demographic stochasticity resulting from finite population sizes within patches is accounted for; and (iii) the transition of individuals between patches is explicitly modelled by a disperser pool. We show, first, that evolutionarily stable dispersal rates do not necessarily increase with rates for the local extinction of populations due to external disturbances in habitable patches. Second, we describe how demographic stochasticity affects the evolution of dispersal rates: evolutionarily stable dispersal rates remain high even when disturbance-related rates of local extinction are low, and a variety of qualitatively different responses of adapted dispersal rates to varied levels of disturbance become possible. This paper shows, for the first time, that evolution of dispersal rates may give rise to monotonically increasing or decreasing responses, as well as to intermediate maxima or minima.