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.     

Testing the mechanisms by which source-sink dynamics alter competitive outcomes in a model system

Dispersal among sites can affect within-site competitive outcomes via source-sink dynamics. Source-sink dynamics are thought to affect competitive outcomes primarily via spatial subsidies: by redistributing individuals from sources to sinks, source-sink dynamics can alter competitive outcomes in both sources and sinks. However, dispersal also can affect competitive outcomes via demography modification, which occurs when dispersal alters the parameters governing species' per capita demographic rates. For instance, dispersal of exploitative competitors might cause extinction of some of the resources for which competition occurs, thereby altering the competition coefficients. I used protist microcosms as a model system to test whether spatial subsidies alone could explain the effects of source-sink dynamics on competitive outcomes. I examined the long-term outcome of exploitative competition among three bacterivorous ciliate protists in microcosms of high enrichment (sources) and low enrichment (sinks) in both the presence and the absence of dispersal. Dispersal altered competitive outcomes. Fitting mathematical models to the population dynamics revealed that spatial subsidies were insufficient to account for the effects of dispersal. Fitting alternative models strongly suggested that demography modification was an important determinant of competitive outcomes. These results provide the first evidence that dispersal does not simply redistribute competitors but can alter their per capita demographic rates.     

Spatial heterogeneity, source-sink dynamics, and the local coexistence of competing species

Patch occupancy theory predicts that a trade-off between competition and dispersal should lead to regional coexistence of competing species. Empirical investigations, however, find local coexistence of superior and inferior competitors, an outcome that cannot be explained within the patch occupancy framework because of the decoupling of local and spatial dynamics. We develop two-patch metapopulation models that explicitly consider the interaction between competition and dispersal. We show that a dispersal-competition trade-off can lead to local coexistence provided the inferior competitor is superior at colonizing empty patches as well as immigrating among occupied patches. Immigration from patches that the superior competitor cannot colonize rescues the inferior competitor from extinction in patches that both species colonize. Too much immigration, however, can be detrimental to coexistence. When competitive asymmetry between species is high, local coexistence is possible only if the dispersal rate of the inferior competitor occurs below a critical threshold. If competing species have comparable colonization abilities and the environment is otherwise spatially homogeneous, a superior ability to immigrate among occupied patches cannot prevent exclusion of the inferior competitor. If, however, biotic or abiotic factors create spatial heterogeneity in competitive rankings across the landscape, local coexistence can occur even in the absence of a dispersal-competition trade-off. In fact, coexistence requires that the dispersal rate of the overall inferior competitor not exceed a critical threshold. Explicit consideration of how dispersal modifies local competitive interactions shifts the focus from the patch occupancy approach with its emphasis on extinction-colonization dynamics to the realm of source-sink dynamics. The key to coexistence in this framework is spatial variance in fitness. Unlike in the patch occupancy framework, high rates of dispersal can undermine coexistence, and hence diversity, by reducing spatial variance in fitness.     

Mechanisms of coexistence in competitive metacommunities

Although there is a large body of theory on spatial competitive coexistence, very little of it involves comparative analyses of alternative mechanisms. We thus have limited knowledge of the conditions under which multiple spatial mechanisms can operate or of emergent properties arising from interactions between mechanisms. Here we present a mathematical framework that allows for comparative analysis of spatial coexistence mechanisms. The basis for comparison is mechanisms operating in spatially homogeneous competitive environments (e.g., life-history trade-offs) versus mechanisms operating in spatially heterogeneous competitive environments (e.g., source-sink dynamics). Our comparative approach leads to several new insights about spatial coexistence. First, we show that spatial variation in the expression of a life-history trade-off leads to a unique regional pattern that cannot be predicted by considering trade-offs or source-sink dynamics alone. This result represents an instance where spatial heterogeneity constrains rather than promotes coexistence, and it illustrates the kind of counterintuitive emergent properties that arise due to interactions between different classes of mechanisms. Second, we clarify the role of dispersal mortality in spatial coexistence. Previous studies have shown that coexistence can be constrained or facilitated by dispersal mortality. Our broader analysis distinguishes situations where dispersal mortality is not necessary for coexistence from those where such mortality is essential for coexistence because it preserves spatial variation in the strength of competition. These results form the basis for two important future directions: evolution of life-history traits in spatially heterogeneous environments and elucidation of the cause and effect relationship(s) between biodiversity and ecosystem functioning.     

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.     

Productivity, dispersal and the coexistence of intraguild predators and prey

A great deal is known about the influence of dispersal on species that interact via competition or predation, but very little is known about the influence of dispersal on species that interact via both competition and predation. Here, I investigate the influence of dispersal on the coexistence and abundance-productivity relationships of species that engage in intraguild predation (IGP: competing species that prey on each other). I report two key findings. First, dispersal enhances coexistence when a trade-off between resource competition and IGP is strong and/or when the Intraguild Prey has an overall advantage, and impedes coexistence when the trade-off is weak and/or when the Intraguild Predator has an overall advantage. Second, the Intraguild Prey's abundance-productivity relationship depends crucially on the dispersal rate of the Intraguild Predator, but the Intraguild Predator's abundance-productivity relationship is unaffected by its own dispersal rate or that of the Intraguild Prey. This difference arises because the two species engage in both a competitive interaction as well as an antagonistic (predator-prey) interaction. The Intraguild Prey, being the intermediate consumer, has to balance the conflicting demands of resource acquisition and predator avoidance, while the Intraguild Predator has to contend only with resource acquisition. Thus, the Intraguild Predator's abundance increases monotonically with resource productivity regardless of either species' dispersal rate, while the Intraguild Prey's abundance-productivity relationship can increase, decrease, or become hump-shaped with increasing productivity depending on the Intraguild Predator's dispersal rate. The important implication is that a species' trophic position determines the effectiveness of dispersal in sampling spatial environmental heterogeneity. The dispersal behavior of a top predator is likely to have a stronger effect on coexistence and spatial patterns of abundance than the dispersal behavior of an intermediate consumer.     

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.     

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.     

Negative density-dependent emigration of males in an increasing red deer population

In species with polygynous mating systems, females are regarded as food-limited, while males are limited by access to mates. When local density increases, forage availability declines, while mate access for males may increase due to an increasingly female-biased sex ratio. Density dependence in emigration rates may consequently differ between sexes. Here, we investigate emigration using mark-recovery data from 468 young red deer Cervus elaphus marked in Snillfjord, Norway over a 20-year period when the population size has increased sixfold. We demonstrate a strong negative density-dependent emigration rate in males, while female emigration rates were lower and independent of density. Emigrating males leaving the natal range settled in areas with lower density than expected by chance. Dispersing males moved 42 per cent longer at high density in 1997 (37 km) than at low density in 1977 (26 km), possibly caused by increasing saturation of deer in areas surrounding the marking sites. Our study highlights that pattern of density dependence in dispersal rates may differ markedly between sexes in highly polygynous species. Contrasting patterns reported in small-scale studies are suggestive that spatial scale of density variation may affect the pattern of temporal density dependence in emigration rates and distances.     

Patterns of dispersal and dynamics among habitat patches varying in quality

Both source-sink theory and extensions of optimal foraging theory ("balanced dispersal" theory) address dispersal and population dynamics in landscapes where habitat patches vary in quality. However, studying dispersal mechanisms empirically has proven difficult, and dispersal is rarely tied back to long-term spatial dynamics. We used a manipulable laboratory system consisting of bacteria and protozoa to investigate the ability of source-sink and optimal foraging theories to explain both dispersal and emergent spatial dynamics. Consistent with source-sink models and contrary to balanced dispersal models, there was a consistent net flux of protist individuals from high to low resource patches. However, unlike the simplest source-sink models, intermediate rates of dispersal led to highest abundances in low resource patches. Side experiments found strong density dependence in local population dynamics and differences in average protist body size in high and low resource patches. Parameterization and analysis of a two-patch model showed that high migration from high to low resource patches could have depressed population density in low resource patches, creating pseudosinks. The movement of individuals and biomass from sources to sinks (a form of ecosystem subsidy) resulted in the convergence of body size and population densities in sources and sinks. Our results indicate a need to carefully consider movement patterns and interaction with local dynamics in potential source-sink systems.     

The Dispersal System of a Butterfly: A Test of Source-Sink Theory Suggests the Intermediate-Scale Hypothesis

Theory predicts source-sink dynamics can occur in species with the ideal preemptive distribution but not with the ideal free distribution. Source-sink dynamics can also occur in species with passive dispersal, in which a fixed fraction of the population disperses each generation. However, in nature, dispersal often approximates random diffusion rather than ideal choices or fixed probabilities. Here, I ask which dispersal system occurred in a butterfly (Euphydryas editha) known to have source-sink dynamics. The study used 13 experimental sites, where vacant and occupied habitat patches were juxtaposed. I estimated movement during the flight season and tested hypotheses about the type of dispersal system. Ideal free and ideal preemptive models were rejected because per capita movement rates were density independent. Passive dispersal was rejected because per capita rates were related to patch area and habitat preference. The diffusion model best explained the data because it predicted both the area relationship and an odd feature of the habitat preference: immigration was not higher in preferred habitat; rather, emigration was lower. The diffusion model implied that source-sink dynamics were driven by diffusion from areas of high to low population density. Existing source-sink theory assumes fine-scale patchiness, in which animals have perfect knowledge and ease of mobility. The results from the butterfly suggest that source-sink dynamics arise at coarser spatial scales, where diffusion models apply.     

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.     

Evolution of density- and patch-size-dependent dispersal rates

Based on a marginal value approach, we derive a nonlinear expression for evolutionarily stable (ES) dispersal rates in a metapopulation with global dispersal. For the general case of density-dependent population growth, our analysis shows that individual dispersal rates should decrease with patch capacity and-beyond a certain threshold-increase with population density. We performed a number of spatially explicit, individual-based simulation experiments to test these predictions and to explore further the relevance of variation in the rate of population increase, density dependence, environmental fluctuations and dispersal mortality on the evolution of dispersal rates. They confirm the predictions of our analytical approach. In addition, they show that dispersal rates in metapopulations mostly depend on dispersal mortality and inter-patch variation in population density. The latter is dominantly driven by environmental fluctuations and the rate of population increase. These conclusions are not altered by the introduction of neighbourhood dispersal. With patch capacities in the order of 100 individuals, kin competition seems to be of negligible importance for ES dispersal rates except when overall dispersal rates are low.     

Quantifying and testing coexistence mechanisms arising from recruitment fluctuations

Temporal fluctuations in recruitment are involved in two distinct coexistence mechanisms, the storage effect and relative nonlinearity of competition, which may act simultaneously to stabilize species coexistence. It is shown that comparisons of recruitment variation between species at high versus low densities can test whether these mechanisms are responsible for stable coexistence. Moreover, under certain circumstances, these comparisons can measure the total coexistence stabilizing effect of the mechanism. These comparisons are clearest for the situation of an invader (a species perturbed to low density) in the presence of its competitors, termed residents. Then average invader-resident differences in the variances of log recruitment, potentially weighted by adult survival rates and species' sensitivities to competition, are proportional to the overall stabilizing effect of the storage effect and relative nonlinearity of competition. Less effective comparisons are available for species naturally at high and low densities or with substantial mean differences in average fitness. These developments lead also to a technique of partitioning the long-term low-density growth rate of a species into community average measures of stabilizing mechanisms, deviations from these measures, and other factors. The community average measure is argued as most appropriate for understanding the ability of a coexistence mechanism to stabilize coexistence. Individual species' deviations from the community average indicate the ways in a which a coexistence mechanism may affect average fitness differences between species either enhancing or diminishing the ability of a given set of species to coexist, depending on other factors. This approach provides a general new tool for analyzing species coexistence.     

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     

Coexistence of competitors in metacommunities due to spatial variation in resource growth rates; does R * predict the outcome of competition?

Simple mathematical models are used to investigate the coexistence of two consumers using a single limiting resource that is distributed over distinct patches, and that has unequal growth rates in the different patches. Relatively low movement rates or high demographic rates of an inefficient resource exploiter allow it to coexist at a stable equilibrium with a more efficient species whose ratio of movement to demographic rates is lower. The range of conditions allowing coexistence depends on the between‐patch heterogeneity in resource growth rates, but this range can be quite broad. The between‐patch movement of the more efficient consumer turns patches with high resource growth rates into sources, while low‐growth‐rate patches effectively become sinks. A less efficient species can coexist with or even exclude the more efficient species from the global environment if it is better able to bias its spatial distribution towards the source patches. This can be accomplished with density independent dispersal if the less efficient species has a lower ratio of per capita between‐patch movement rate to demographic rates. Conditions that maximize the range of efficiencies allowing coexistence of two species are: a relatively high level of heterogeneity in resource growth conditions; high dispersal (or low demographic rates) of the superior competitor; and low dispersal (or high demographic rates) of the inferior competitor. Global exclusion of the more efficient competitor requires that the inferior competitor have sufficient movement to also produce a source‐sink environment.     

Coupling of two competitive systems via density dependent migration

Coupling of two Lotka–Volterra type competition systems with density-dependent migration was surveyed. We assumed that species x and y are each exclusively superior in subhabitat 1 and subhabitat 2, respectively, and that population densities that exert intra-and interspecific competitive effects also impose pressures for migration of individuals from a subhabitat. If the two species are, respectively, abundant in the subhabitats in which either species is competitively superior, and the migration has a mixing effect, then, it would be intuitively expected that, as potential migration rates increase, the two species are mixed well and coexist in the whole habitat. An analysis of this competitive situation using our model under the assumption of linear diffusion predicted that, even though weak mixing maintains coexistence in the whole habitat, strong mixing collapses coexistence and leads to the exclusion of one species. The assumption that migrations occur due to self- and cross-population pressures provides different predictions: (i) weak dominance and strong mixing destabilize the coexistence state and lead to a monopolizing equilibrium of either species (bi-stability of monopolizing equiliblia); (ii) conspicuous weakness of the inferior species makes the mixing equilibrium stable, regardless of the potential migration rate; and (iii) tri-stability exists in between situations (i) and (ii). In the third case, the attainable state is the mixing equilibrium or either of the monopolizing equilibria, depending on the initial state. Migration mechanisms with self- and cross-population pressures tends to mediate spatial segregation and makes coexistence possible, even with strong mixing.     

Balanced dispersal between spatially varying local populations: an alternative to the source-sink model

Analysis of long-term monitoring data on breeding collared flycatchers (Ficedula albicollis Temm.) has revealed equal numbers of immigrations and emigrations between neighboring populations of different sizes. Dispersal patterns were close to patterns simulated under a conditional dispersal and with populations near saturation level. Local growth rates of the 11 sites were computed and did not support the idea that the observed balanced exchanges could be the result of a source-sink system. This is the first empirical evidence for a system of discrete habitat patches with component populations that exist as simultaneous sources and sinks to their neighbors. Dispersal propensities were inversely related to population sizes, which showed little variation in time. These results are consistent with recent modeling of dispersal as an evolutionarily stable strategy, and they demonstrate that dispersal can be an active phenomenon requiring neither the dominance hierarchies nor the temporal instability generally invoked by ecological and population genetic models. We note a parallel to the concept of Ideal Free Distributions and discuss implications for the evolution of dispersal mechanisms in fragmented populations.