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.     

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.     

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.     

The effect of travel loss on evolutionarily stable distributions of populations in space

A key assumption of the ideal free distribution (IFD) is that there are no costs in moving between habitat patches. However, because many populations exhibit more or less continuous population movement between patches and traveling cost is a frequent factor, it is important to determine the effects of costs on expected population movement patterns and spatial distributions. We consider a food chain (tritrophic or bitrophic) in which one species moves between patches, with energy cost or mortality risk in movement. In the two-patch case, assuming forced movement in one direction, an evolutionarily stable strategy requires bidirectional movement, even if costs during movement are high. In the N-patch case, assuming that at least one patch is linked bidirectionally to all other patches, optimal movement rates can lead to source-sink dynamics where patches with negative growth rates are maintained by other patches with positive growth rates. As well, dispersal between patches is not balanced (even in the two-patch case), leading to a deviation from the IFD. Our results indicate that cost-associated forced movement can have important consequences for spatial metapopulation dynamics. Relevance to marine reserve design and the study of stream communities subject to drift is discussed.     

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.     

Scale-dependent foraging and patch choice in fractal environments

Many spatially complex environments are fractal, and consumers in these environments face scale-dependent trade-offs between encountering high densities of small resource patches versus low densities of large resource patches. I address the effects of these trade-offs on foraging by incorporating scale-dependent encounter of resources in fractal landscapes into classical optimal foraging theory. This model is then used to predict optimal scales of perception (foraging scale) and patch choice in response to spatial features of landscapes. The model predicts that, for a given density of resources, landscapes with greater extent and fractal dimension and that contain patchy (low fractal dimension) resources favour large foraging scales and specialization on a small proportion of resource patches. Fragmented (low fractal dimension) landscapes of small extent with dispersed (high fractal dimension) resources favour smaller foraging scales and generalists that use a large proportion of available resource patches. These predictions synthesize the results of other spatially explicit consumer–resource models into a simple framework and agree reasonably well with results of several empirical studies. This study thus places optimal foraging theory in a spatial context and suggests evolutionary mechanisms of consumers' responses to important spatial phenomena (e.g. habitat fragmentation, resource aggregation). This revised version was published online in July 2006 with corrections to the Cover Date.     

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.     

The impact of directed versus random movement on population dynamics and biodiversity patterns

An improved understanding of dispersal behavior is needed to predict how populations and communities respond to habitat fragmentation. Most spatial dynamic theory concentrates on random dispersal, in which movement rates depend neither on the state of an individual nor its environment and movement directions are unbiased. We examine the neglected dispersal component of directed movement in which dispersal is a conditional and directional response of individuals to varying environmental conditions. Specifically, we assume that individuals bias their movements along local gradients in fitness. Random movers, unable to track heterogeneous environmental conditions, face source-sink dynamics, which can result in deterministic extinction or increase their vulnerability to stochastic extinction. Directed movers track environmental conditions closely. In fluctuating environments, random movers "spread their bets" across patches, while directed movers invest offspring in habitats currently enjoying propitious conditions. The autocorrelation in the environment determines each strategy's success. Random movers permeate entire landscapes, but directed movers are more geographically constrained. Local information constraints limit the ranges of directed movers and introduce a role for historical contingency in determining their ultimate distribution. These geographic differences have implications for biodiversity. Random movement maintains biodiversity through local coexistence, but directed movement favors a spatial partitioning of species.     

物种对资源竞争的动力机制及数值模拟

建立了集合种群物种在两个斑块中对资源竞争的数学模型,并进行了数值模拟实验,结果表明：（1）通过R^＊来预测竞争物种的结局,存在几种可能性：一是具有低R^＊值的物种竞争取代高R^＊值的物种;二是具有不同R^＊值的物种,甚至是具有相同R^＊值的物种也存在共存的可能性;三是具有高R^＊值的物种也可以竞争排斥低R^＊值的物种,结论存在不确定性。（2）竞争物种的随机迁移形成了源一汇结构,对物种竞争共存具有促进作用,但弱的资源利用者（较高的R^＊）的迁移率不宜过高。（3）在种群统计率相同的条件下,资源增长率差异越大,越不利于消费者物种的共存;若种群统计率不相同,在资源增长率相同的情况下,物种共存又是不可能的,在自然界中,物种共存需要资源增长率的差异。（4）不同类型的资源增长对竞争物种的稳定性的影响是不同的。     

The effects of habitat fragmentation on persistence of source-sink metapopulations in systems with predators and prey or apparent competitors.

We consider systems with one predator and one prey, or a common predator and two prey species (apparent competitors) in source and sink habitats. In both models, the predator species is vulnerable to extinction, if productivity in the source is insufficient to rescue demographically deficient sink populations. Conversely, in the model with two prey species, if the source is too rich, one of the prey species may be driven extinct by apparent competition, since the predator can maintain a large population because of the alternative prey. Increasing the rate of predator movement from the source population has opposite effects on prey and predator persistence. High emigration rate exposes the predator population to danger of extinction, reducing the number of individuals that breed and produce offspring in the source habitat. This may promote coexistence of prey by relaxing predation pressure and apparent competition between the two prey species. The number of sinks and spatial arrangement of patches, or connectivity between patches, also influence persistence of the species. More sinks favor the prey and fewer sinks are advantageous to the predator. A linear pattern with the source at one end is profitable for the predator, and a centrifugal pattern in which the source is surrounded by sinks is advantageous to the prey. When the dispersal rate is low, effects of the spatial structure may exceed those of the number of sinks. In brief, productivity in patches and patterns of connectivity between patches differentially influence persistence of populations in different trophic levels.     

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

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

The role of local populations within a landscape context: defining and classifying sources and sinks

The interaction of local populations has been the focus of an increasing number of studies in the past 30 years. The study of source-sink dynamics has especially generated much interest. Many of the criteria used to distinguish sources and sinks incorporate the process of apparent survival (i.e., the combined probability of true survival and site fidelity) but not emigration. These criteria implicitly treat emigration as mortality, thus biasing the classification of sources and sinks in a manner that could lead to flawed habitat management. Some of the same criteria require rather restrictive assumptions about population equilibrium that, when violated, can also generate misleading inference. Here, we expand on a criterion (denoted "contribution" or Cr) that incorporates successful emigration in differentiating sources and sinks and that makes no restrictive assumptions about dispersal or equilibrium processes in populations of interest. The metric Cr is rooted in the theory of matrix population models, yet it also contains clearly specified parameters that have been estimated in previous empirical research. We suggest that estimates of emigration are important for delineating sources and sinks and, more generally, for evaluating how local populations interact to generate overall system dynamics. This suggestion has direct implications for issues such as species conservation and habitat management.     

From random walks to informed movement

The analysis of animal movement is a large and continuously growing field of research. Detailed knowledge about movement strategies is of crucial importance for understanding eco‐evolutionary dynamics at all scales – from individuals to (meta‐)populations. This and the availability of detailed movement and dispersal data motivated Nathan and colleagues to published their much appreciated call to base movement ecology on a more thorough mechanistic basis. So far, most movement models are based on random walks. However, even if a random walk might describe real movement patterns acceptably well, there is no reason to assume that animals move randomly. Therefore, mechanistic models of foraging strategies should be based on information use and memory in order to increase our understanding of the processes that lead to animal movement decisions. We present a mechanistic movement model of an animal with a limited perceptual range and basic information storage capacities. This ‘spatially informed forager’ constructs an internal map of its environment by using perception, memory and learned or evolutionarily acquired assumptions about landscape attributes. We analyse resulting movement patterns and search efficiencies and compare them to area restricted search strategies (ARS) and biased correlated random walks (BCRW) of omniscient individuals. We show that, in spite of their limited perceptual range, spatially informed individuals boost their foraging success and may perform much better than the best ARS. The construction of an internal map and the use of spatial information results in the emergence of a highly correlated walk between patches and a rather systematic search within resource clusters. Furthermore, the resulting movement patterns may include foray search behaviour. Our work highlights the strength of mechanistic modelling approaches and sets the stage for the development of more sophisticated models of memory use for movement decisions and dispersal.     

Source-sink dynamics within a plant population: the impact of substrate and herbivory on palm demography

Site factors have frequently been shown to affect survival, growth, and reproduction in plant populations. The source-sink concept proposed by Pulliam is one way of integrating this spatial demographic variation into population models. Source-sink models describe a population where propagules from “source” habitats sustain less productive “sink” areas. We adapted this concept to model the population dynamics of the understory palm Chamaedorea radicalis on two substrates, rock outcrops and forest floor. In our model, sources and sinks correspond to fine-scale demographic structure within the population, rather than spatially discrete subpopulations as described in the Pulliam model. We constructed a stage-structured population matrix model that integrates the site-specific demography of individuals across two habitats types that are linked by migration. We then parameterized this model with field data from C. radicalis. To address whether observed differences in palm demography between rock outcrops and the forest floor were due to natural variation between microsites or due to differences in browsing intensity from free range livestock, we parameterized separate models based on the substrate-specific demography of protected, non-browsed palms and of palms exposed to burro browse. Results showed that herbivory reduced survival and fecundity on the forest floor, which in the absence of seed migration resulted in a projected decline of forest floor palms (sinks). However with seed dispersal, palms persisted and total population growth (both substrates) was projected to be positive, indicating that seed dispersal from non-browsed palms on rock outcrops (sources) was sufficient to sustain C. radicalis on the forest floor.     

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.     

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.     

How can maladaptive habitat choice generate source‐sink population dynamics?

Several theoretical models have been proposed to describe population dynamics in a spatially heterogeneous environment. The source-sink model is among the most popular. Diffendorfer recently summarized its assumptions and predictions. Given the model reviewed, he argued that source-sink population dynamics arises if dispersal is somehow constrained. I offer an additional mechanism by suggesting that source-sink population dynamics can be generated by anthropogenic changes in landscapes that occur so quickly that organisms no longer make optimal habitat selection decisions. Individuals select the same habitats as their ancestors but these decisions no longer provide high fitness because of human-induced changes in habitat quality, such as increased rates of predation and/or parasitism. Provided that some of the habitats selected are turned by human-induced changes into sink habitats, source-sink population dynamics can emerge.     

Hierarchical patch dynamics and animal movement pattern

In hierarchical patch systems, small-scale patches of high density are nested within large-scale patches of low density. The organization of multiple-scale hierarchical systems makes non-random strategies for dispersal and movement particularly important. Here, we apply a new method based on first-passage time on the pathway of a foraging seabird, the Antarctic petrel (Thalassoica antarctica), to quantify its foraging pattern and the spatial dynamics of its foraging areas. Our results suggest that Antarctic petrels used a nested search strategy to track a highly dynamic hierarchical patch system where small-scale patches were congregated within patches at larger scales. The birds searched for large-scale patches by traveling fast and over long distances. Once within a large-scale patch, the birds concentrated their search to find smaller scale patches. By comparing the pathway of different birds we were able to quantify the spatial scale and turnover of their foraging areas. On the largest scale we found foraging areas with a characteristic scale of about 400 km. Nested within these areas we found foraging areas with a characteristic scale of about 100 km. The large-scale areas disappeared or moved within a time frame of weeks while the nested small-scale areas disappeared or moved within days. Antarctic krill (Euphausia superba) is the dominant food item of Antarctic petrels and we suggest that our findings reflect the spatial dynamics of krill in the area.Electronic Supplementary Material Supplementary material is available to authorised users in the online version of this article at .     

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.     

Impacts of dispersal on rapid adaptation and dynamic stability of Daphnia in fluctuating environments

Prior ecological research has shown that spatial processes can enhance the temporal stability of populations in fluctuating environments. Less explored is the effect of dispersal on rapid adaptation and its concomitant impact on population dynamics. For asexually reproducing populations, theory predicts that dispersal in fluctuating environments can facilitate asynchrony among clones and enhance stability by reducing temporal variability of total population abundance. This effect is predicted when clones exhibit heritable variation in environmental optima and when fluctuations occur asynchronously among patches. We tested this in the field using artificial ponds and metapopulations composed of a diverse assemblage of Daphnia pulex clones. We directly manipulated dispersal presence/absence and environmental fluctuations in the form of nutrient pulses. Consistent with predictions, dispersal enhanced temporal asynchrony among clones in the presence of nutrient pulses; this in turn stabilized population dynamics. This effect only emerged when patches experienced spatially asynchronous nutrient pulses (dispersal had no effect when patches were synchronously pulsed). Clonal asynchrony was driven by strong positive selection for a single clone that exhibited a performance advantage under conditions of low resource availability. Our work highlights the importance of dispersal as a driver of eco-evolutionary dynamics and population stability in variable environments.