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.     

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.     

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 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     

Canonical functions for dispersal-induced synchrony

Two processes are universally recognized for inducing spatial synchrony in abundance: dispersal and correlated environmental stochasticity. In the present study we seek the expected relationship between synchrony and distance in populations that are synchronized by density-independent dispersal. In the absence of dispersal, synchrony among populations with simple dynamics has been shown to echo the correlation in the environment. We ask what functional form we may expect between synchrony and distance when dispersal is the synchronizing agent. We formulate a continuous-space, continuous-time model that explicitly represents the time evolution of the spatial covariance as a function of spatial distance. Solving this model gives us two simple canonical functions for dispersal-induced covariance in spatially extended populations. If dispersal is rare relative to birth and death, then covariances between nearby points will follow the dispersal distance distribution. At long distances, however, the covariance tails off according to exponential or Bessel functions (depending on whether the population moves in one or two dimensions). If dispersal is common, then the covariances will follow the mixture distribution that is approximately Gaussian around the origin and with an exponential or Bessel tail. The latter mixture results regardless of the original dispersal distance distribution. There are hence two canonical functions for dispersal-induced synchrony     

Density-dependent dispersal and spatial population dynamics

The synchronization of the dynamics of spatially subdivided populations is of both fundamental and applied interest in population biology. Based on theoretical studies, dispersal movements have been inferred to be one of the most general causes of population synchrony, yet no empirical study has mapped distance-dependent estimates of movement rates on the actual pattern of synchrony in species that are known to exhibit population synchrony. Northern vole and lemming species are particularly well-known for their spatially synchronized population dynamics. Here, we use results from an experimental study to demonstrate that tundra vole dispersal movements did not act to synchronize population dynamics in fragmented habitats. In contrast to the constant dispersal rate assumed in earlier theoretical studies, the tundra vole, and many other species, exhibit negative density-dependent dispersal. Simulations of a simple mathematical model, parametrized on the basis of our experimental data, verify the empirical results, namely that the observed negative density-dependent dispersal did not have a significant synchronizing effect.     

Non-additive and non-stationary properties in the spatial distribution of a large marine fish population

Density-independent and density-dependent variables both affect the spatial distributions of species. However, their effects are often separately addressed using different analytical techniques. We apply a spatially explicit regression framework that incorporates localized, interactive and threshold effects of both density-independent (water temperature) and density-dependent (population abundance) variables, to study the spatial distribution of a well-monitored flatfish population in the eastern Bering Sea. Results indicate that when population biomass was beyond a threshold a further increase in biomass-promoted habitat expansion in a non-additive fashion with water temperature. In contrast, during years of low population size, habitat occupancy was affected positively only by water temperature. These results reveal the spatial signature of intraspecific abundance distribution relationships as well as the non-additive and non-stationary responses of species spatial dynamics. Furthermore, these results underscore the importance of implementing analytical techniques that can simultaneously account for density-dependent and density-independent sources of variability when studying geographical distribution patterns.     

Testing the interaction between environmental variation and dispersal strategy on population dynamics using a soil mite experimental system

Dispersal can play an important role in both the local and regional dynamics of populations. Empirical studies have shown that the proportion of individuals dispersing is often density dependent, which may have implications for the effect of dispersal on populations. In this study, we manipulate the dispersal strategy of adults within two-patch laboratory populations of soil mites and compare the consequences of fixed (density-independent) and density-dependent dispersal in environments of constant and temporally varying resource availability. Effects of dispersal on population dynamics were dependent on the presence of environmental variation. Both dispersal strategies tended to spatially homogenize the population abundance of adults in a variable environment. However, the effect of environmental variation on mean adult abundance was greater with density-dependent dispersal than with fixed dispersal. Adult dispersal did not affect juvenile or egg abundance. This study demonstrates the potential significance of density-dependent dispersal for population dynamics, but emphasizes the role of the environmental context.     

The effects of density-dependent offspring mortality on the synchrony of reproduction

Mortality rates often depend on the size of a population. Using ideal free theory to model the optimal timing of reproduction in model populations, I considered how the specific relationship between density-dependent offspring mortality and population size affects the optimal temporal distribution of reproduction. The results suggest that the specific form of the relationship between density-dependent mortality and the number of offspring produced determines the degree to which reproduction within a population is synchronous. Specifically, reproductive synchrony decreases as density-dependent mortality becomes increasingly inversely related to the number of offspring produced and is highest when density-dependent mortality is directly density-dependent. These findings support the suggestion that predation pressure selects for greater reproductive synchrony in species where mortality is directly density-dependent, but does not affect the timing of reproduction in species with density-independent rates of mortality. This revised version was published online in July 2006 with corrections to the Cover Date.     

Population synchrony and stability in environmentally forced metacommunities

A general prediction from simple metapopulation models is that spatially synchronized forcing can spatially synchronize population dynamics and destabilize metapopulations. In contrast, spatially asynchronous forcing is predicted to decrease population synchrony and promote temporal stability and population persistence, especially in the presence of dispersal. Only recently have studies begun to experimentally address these predictions. Moreover, few studies have experimentally examined how such processes operate in the context of competition communities. Stabilizing processes may continue to operate when placed within a metacommunity context with multiple competing consumers but only at low to intermediate levels of dispersal. High dispersal rates can reverse these predictions and lead to destabilization. We tested this under controlled conditions using an experimental aquatic system composed of three competing species of zooplankton. Metacommunities experienced different levels of dispersal and environmental forcing in the form of spatially synchronous or asynchronous pH perturbations. We found support that dispersal can have contrasting effects on population stability depending on the degree to which population dynamics were synchronized in space. Dispersal under synchronous forcing or no forcing had either neutral of positive effects on spatial population synchrony of all three zooplankton species. In these treatments, dispersal reduced population stability at the local and metapopulation levels for two of three species. In contrast, asynchronously varying environments reduced population synchrony relative to unforced systems, regardless of dispersal level. In these treatments, dispersal enhanced temporal stability and persistence of populations not by reducing population synchrony but by enhancing population minima and spatial averaging of abundances. High dispersal rates under asynchronous forcing reduced the abundance of one species, consistent with increasing regional competition and general metacommunity theory. However, no effects on its stability or persistence were observed. Our work highlights the context‐dependent effects of dispersal on population dynamics in varying environments.     

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.     

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.     

Nonlinear Effect of Dispersal Rate on Spatial Synchrony of Predator-Prey Cycles

Spatially-separated populations often exhibit positively correlated fluctuations in abundance and other population variables, a phenomenon known as spatial synchrony. Generation and maintenance of synchrony requires forces that rapidly restore synchrony in the face of desynchronizing forces such as demographic and environmental stochasticity. One such force is dispersal, which couples local populations together, thereby synchronizing them. Theory predicts that average spatial synchrony can be a nonlinear function of dispersal rate, but the form of the dispersal rate-synchrony relationship has never been quantified for any system. Theory also predicts that in the presence of demographic and environmental stochasticity, realized levels of synchrony can exhibit high variability around the average, so that ecologically-identical metapopulations might exhibit very different levels of synchrony. We quantified the dispersal rate-synchrony relationship using a model system of protist predator-prey cycles in pairs of laboratory microcosms linked by different rates of dispersal. Paired predator-prey cycles initially were anti-synchronous, and were subject to demographic stochasticity and spatially-uncorrelated temperature fluctuations, challenging the ability of dispersal to rapidly synchronize them. Mean synchrony of prey cycles was a nonlinear, saturating function of dispersal rate. Even extremely low rates of dispersal (<0.4% per prey generation) were capable of rapidly bringing initially anti-synchronous cycles into synchrony. Consistent with theory, ecologically-identical replicates exhibited very different levels of prey synchrony, especially at low to intermediate dispersal rates. Our results suggest that even the very low rates of dispersal observed in many natural systems are sufficient to generate and maintain synchrony of cyclic population dynamics, at least when environments are not too spatially heterogeneous.     

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.     

The Moran effect revisited: spatial population synchrony under global warming

The world is spatially autocorrelated. Both abiotic and biotic properties are more similar among neighboring than distant locations, and their temporal co-fluctuations also decrease with distance. P. A. P. Moran realized the ecological importance of such ‘spatial synchrony’ when he predicted that isolated populations subject to identical log-linear density-dependent processes should have the same correlation in fluctuations of abundance as the correlation in environmental noise. The contribution from correlated weather to synchrony of populations has later been coined the ‘Moran effect’. Here, we investigate the potential role of the Moran effect in large-scale ecological outcomes of global warming. Although difficult to disentangle from dispersal and species interaction effects, there is compelling evidence from across taxa and ecosystems that spatial environmental synchrony causes population synchrony. Given this, and the accelerating number of studies reporting climate change effects on local population dynamics, surprisingly little attention has been paid to the implications of global warming for spatial population synchrony. However, a handful of studies of insects, birds, plants, mammals and marine plankton indicate decadal-scale changes in population synchrony due to trends in environmental synchrony. We combine a literature review with modeling to outline potential pathways for how global warming, through changes in the mean, variability and spatial autocorrelation of weather, can impact population synchrony over time. This is particularly likely under a ‘generalized Moran effect’, i.e. when relaxing Moran's strict assumption of identical log-linear density-dependence, which is highly unrealistic in the wild. Furthermore, climate change can influence spatial population synchrony indirectly, through its effects on dispersal and species interactions. Because changes in population synchrony may cascade through food-webs, we argue that the (generalized) Moran effect is key to understanding and predicting impacts of global warming on large-scale ecological dynamics, with implications for extinctions, conservation and management.     

Searching for mechanisms of synchrony in spatially structured gamebird populations

1.  Time series data on five species of gamebird from the Dolomitic Alps were used to examine the relative importance of dispersal and common stochastic events in causing synchrony between spatially structured populations.
2.  Cross-correlation analysis of detrended time series was used to describe the spatial pattern of fluctuations in abundance, while standardized time series were used to describe both fluctuations and the trend in abundance. There were large variations in synchrony both within and between species and only weak negative relationships with distance.
3.  Species in neighbouring habitats were more likely to be in synchrony than species separated by several habitats. Species with similar density-dependent structure were more likely to be in synchrony.
4.  In order to estimate the relative importance of dispersal and environmental stochasticity, we modelled the spatial dynamics of each species using two different approaches. First, we used estimating functions and bootstrapping of time series data to calculate the relative importance of dispersal and stochastic effects for each species. Second, we estimated the intensity of environmental stochasticity from climatic records during the breeding season and then modelled the dispersal rate and dispersal distance for each species. The two models exhibited similar results for rock ptarmigan, black grouse, hazel grouse and rock partridge, while contrasting patterns were observed for capercaillie.
5.  The results suggest that environmental stochasticity plays the dominant role in synchronizing the fluctuations of these galliform species, although there will also be some dispersal between populations.     

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.     

Relative roles of density-dependent and density-independent factors in population dynamics of British deer

It has become increasingly clear that both density-dependent and density-independent factors may influence the dynamics of mammalian populations; it remains more difficult, however, to determine which factors may play the more significant role in influencing population number in any particular case. In this paper we review published and unpublished data in an analysis of the various factors affecting population size and trend in three European species of deer: Red Deer ( Cervus elaphus ), Fallow Deer ( Dama damd ) and Roe Deer ( Capreolus capreolus). We select these species deliberately because they span a range of body size and reproductive strategy - it seems that different demographic parameters might thus play different roles in the dynamics of the three-which may also be differentially sensitive to the effects of density-dependent and density-independent factors. For each species we examine the available evidence to determine the relative roles and effects of density-dependent feedback mechanisms and density-independent factors such as climate on recruitment and mortality.
Despite differences in bionomic strategy between Red Deer (as essentially a K -strategist) and the more r-selected Roe, few differences emerge between the three species in the relative roles of density-dependent and density-independent factors - or of the stage at the life cycle at which each factor may act. Overall, however, it is clear that variation in density-independent factors, such as climate, appears primarily to affect levels of mortality within a population, while effects of density are particularly marked in relation to changes in recruitment.