Density-dependent Dispersal Research Articles

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.

Density-dependent population dynamics and dispersal in heterogeneous metapopulations

1. Metapopulation microcosms were constructed to test the effect of four different types of habitat heterogeneity on the dynamics and dispersal in spatially extended systems; homogeneity, spatial heterogeneity, temporal heterogeneity and spatio-temporal heterogeneity. Resources were distributed across discrete habitat patches in bruchid beetle (Callosobruchus maculatus) metapopulations, and long-term time series were recorded. 2. Mathematical models were fitted to the long-term time series from the experimental systems using a maximum likelihood approach. Models were composed of separate birth, death, emigration and immigration terms all of which incorporated stochasticity drawn from different probability distributions. Models with density-dependent and density-independent birth, death and emigration terms were investigated and, in each case, the model that best described the empirical data was identified. 3. At the local scale, population sizes differed between patches depending on the type of heterogeneity. Larger populations were associated with higher resource availabilities. As a result of this, the variation between local population sizes was greatest when there was spatial heterogeneity in which mean resource abundance varied from patch to patch. Variation in population sizes within patches was largest when there was temporal heterogeneity. 4. Density-dependent processes leading to the regulation of local population dynamics in our experimental systems were strongest in homogeneity or temporal heterogeneity treatments. Associated with this, we found that these systems were best described using mathematical models with density dependence acting on mortality. In contrast, spatial and spatio-temporal time series were adequately described using density-independent population processes. 5. Experimental metapopulations showed varying degrees of density-dependent dispersal. Local net dispersal each week was primarily driven by the local population size and secondarily affected by neighbourhood population density. Mathematical population models illustrated the importance of explicit description of density-dependent dispersal in all systems except the homogeneous metapopulations.

Olfactory plasticity is regulated by pheromonal signaling in Caenorhabditis elegans.

Population density-dependent dispersal is a well-characterized strategy of animal behavior in which dispersal rate increases when population density is higher. Caenorhabditis elegans shows positive chemotaxis to a set of odorants, but the chemotaxis switches from attraction to dispersal after prolonged exposure to the odorants. We show here that this plasticity of olfactory behavior is dependent on population density and that this regulation is mediated by pheromonal signaling. We show that a peptide, suppressor of NEP-2 (SNET-1), negatively regulates olfactory plasticity and that its expression is down-regulated by the pheromone. NEP-2, a homolog of the extracellular peptidase neprilysin, antagonizes SNET-1, and this function is essential for olfactory plasticity. These results suggest that population density information is transmitted through the external pheromone and endogenous peptide signaling to modulate chemotactic behavior.

Metapopulation dynamics of the bog fritillary butterfly: experimental changes in habitat quality induced negative density-dependent dispersal

Habitat quality and habitat geometry are two crucial factors driving metapopulation dynamics. However, their intricacy has prevented so far a reliable test of their relative impact on local population dynamics and persistence. Here we report on a long-term study in which we manipulated habitat quality within a butterfly metapopulation, whereas habitat geometry was kept constant. The treatment consisted in lowering the quality of certain habitat patches while others were kept untreated, using the same spatial design over years. The effect of the treatment on metapopulation dynamics was assessed by comparing residence probability and dispersal rates within the same habitat network on 11 and 6 independent butterfly generations before and after treatment, respectively. Results showed that the experimental decrease in habitat quality generated significantly higher emigration rates from treated patches. This increase was associated with a significant decrease in dispersal rates out of untreated patches, and a significant higher residence probability in these patches. The direct relation between lower habitat quality and higher dispersal propensity in treated patches was expected. However, the lower dispersal from untreated patches after treatment was opposite to the expectation of positive density dependent dispersal generally observed in butterflies. Such negative density-dependent dispersal would allow a rapid fine-tuning of dispersal rates to changes in habitat quality, particularly when the spatial autocorrelation of the environmental is low. Accordingly,dispersal would promote an ideal free distribution of individuals in the landscape according to their fitness expectation.

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.

Modeling density dependence in heterogeneous landscapes: Dispersal as a case study

Population models often pose density-dependent rates as relations between current population size on a habitat patch, n, and some threshold size defined by limiting resources, r. In fourteen recent modeling studies incorporating density-dependent dispersal, formulations of the density-dependent rate (or probability) fall into two distinct groups, expressing the rate as a function of n– r or n/ r. These two depictions of the same process differ fundamentally: they can cause strikingly different dynamics in otherwise identical systems and they have different scaling properties in heterogeneous landscapes. Here I consider the implications of the two formulations under two broad ecological scenarios: scramble competition for an equally divided resource (e.g. food) and contest competition for an unequally divided resource (e.g. nest sites). In both cases, simple arguments show that the n/ r form is preferable when density dependence is driven by individual access to resources. Other circumstances may require different formulations, but modelers must ensure that these have appropriate scaling and non-equilibrium behavior.

Automated observation and analysis of earthworm surface behaviour under experimental habitat quality and availability conditions

Abstract Currently, the driving factors of active earthworm dispersal across the soil surface are not sufficiently understood, and distances traversed by individual earthworms have rarely been quantified. Research progress has been hampered by the lack of adequate observation methods as well as fast, objective and quantitative measurements of nocturnal earthworm behaviour. In this work, we report on the potential of a new, automated method using infrared-sensitive webcams and computer image analysis. Nightly surface activities of Lumbricus terrestris L. were monitored quantitatively while manipulating levels of disturbance, burrow availability and congener presence in standard observation units. The automated observation system proved to be simple and inexpensive to build, provided reliable quantitative measures of locomotive behaviour without animal disturbance, and considerably reduced human workload and bias. Waterlogging of the burrow zone stimulated surface activities around and away from the home burrow as compared to habitat disturbance by pesticide application and vibration. However, dispersing earthworms never settled in prefabricated burrows. Surface activity of individuals subjected to waterlogged conditions was influenced by the availability of alternative habitat. Minimal habitat disturbance (vibration) and the presence of conspecific individuals resulted in an increased amount of burrow-anchored, possibly sexually oriented, behaviour, but reciprocal burrow visits and mating were not observed. Pesticide application did not result in dispersal, increased foraging activities or sexual attraction attempts during this short-term study. The presence, extent and mechanisms of the remote assessment of important cues in the surroundings of the home burrow by L. terrestris need further research. Infrared monitoring opens new research avenues of earthworm surface behaviour studies (e.g. density-dependent dispersal, habitat selection, (re)colonization, invasion).

Turing bifurcation in a reaction–diffusion system with density-dependent dispersal

Motivated by the recent finding [N. Kumar, G.M. Viswanathan, V.M. Kenkre, Physica A 388 (2009) 3687] that the dynamics of particles undergoing density-dependent nonlinear diffusion shows sub-diffusive behaviour, we study the Turing bifurcation in a two-variable system with this kind of dispersal. We perform a linear stability analysis of the uniform steady state to find the conditions for the Turing bifurcation and compare it with the standard Turing condition in a reaction–diffusion system, where dispersal is described by simple Fickian diffusion. While activator–inhibitor kinetics are a necessary condition for the Turing instability as in standard two-variable systems, the instability can occur even if the diffusion constant of the inhibitor is equal to or smaller than that of the activator. We apply these results to two model systems, the Brusselator and the Gierer–Meinhardt model.

Information use and density-dependent emigration in an agrobiont spider

Density of conspecifics is considered as one of the main conditions affecting dispersal behavior and leading to a stabilization of population dynamics. Density-dependent dispersal can be induced by local competition at different phases during development and/or by density-related sources of social information. Here, we assessed the importance of population density on emigration rates and the degree to which the presence of silk threads at dispersal takeoff locations affects immediate dispersal decision making in the spider Erigone atra. By quantifying behaviors in wind tunnels under standardized laboratory conditions, silk-assisted long- and short-distance dispersal is quantified before the actual onset of the dispersal event. Increased densities during juvenile development only affected short-distance dispersal behavior. In females, short-distance dispersal increased with the female density experienced during development, whereas responses in males increased under combined high male/low female-experienced densities. Elevated densities at the onset of dispersal led to a general increase of predispersal behaviors. The presence of silk threads at takeoff platforms similarly induced an increase of dispersal displays, with specifically an increase in long-distance dispersal in both sexes. Our results demonstrate that the spider E. atra uses information related to density during development, most probably to avoid competition by performing short-distance dispersal. In contrast, density-related cues at the time of dispersal (i.e., increased densities and the presence of silk threads) increase general dispersal activities and long-distance ballooning events. Short- and long-distance dispersal strategies are consequently guided by differential density-related information use. Key words: araneae, density, dispersal, information, silk. [Behav Ecol]

No evidence of juvenile body mass affecting dispersal in male red deer

Dispersal is an important mechanism in population dynamics with a sparse empirical basis. Environmental causes of dispersal may work directly or indirectly. In a population with documented negative density-dependent male dispersal, we investigated if the effect of density on dispersal was indirectly mediated through body mass. We analysed the probability of dispersal in 170 juvenile red deer males in Snillfjord municipality, Norway, during a 20-year period of rapid population growth (1977–1997). Body mass and dispersal propensity were not related. Thus, changes in population density act directly on dispersal and are not affected by body mass. Body mass-dependent dispersal occurs in species with strong antagonistic interactions and a high cost of dispersal. Our result suggests that the cost of dispersal in male red deer is low in terms of energy expenditure and survival. We conclude that the effect of body mass on dispersal is likely to vary with mating system and cost of dispersal.

Effect of non‐random dispersal strategies on spatial coexistence mechanisms

1. Random dispersal leads to spatial coexistence via two mechanisms (emigration-mediated and source-sink), both of which involve the movement of organisms from areas of higher to lower fitness. What is not known is whether such coexistence would occur if organisms dispersed non-randomly, using cues such as density and habitat quality to gauge fitness differences between habitats. Here, I conduct a comparative analysis of random and non-random dispersal strategies in a foodweb with a basal resource, top predator, and two intermediate consumers that exhibit a trade-off between competitive ability and predator susceptibility. 2. I find a striking contrast between density- and habitat-dependent dispersal in their effects on spatial coexistence. Dispersal in response to competitor and predator density facilitates coexistence while dispersal in response to habitat quality (resource productivity and predator pressure) inhibits it. Moreover, density-dependent dispersal changes species' distribution patterns from interspecific segregation to interspecific aggregation, while habitat-dependent dispersal preserves the interspecific segregation observed in the absence of dispersal. Under density-dependent dispersal, widespread spatial coexistence results in an overall decline in the abundance of the inferior competitor that is less susceptible to predation and an overall increase in the abundance of the superior competitor that is more susceptible to predation. Under habitat-dependent dispersal, restricted spatial coexistence results in species' abundances being essentially unchanged from those observed in the absence of dispersal. 3. A key outcome is that when the superior competitor moves in the direction of increasing fitness but the inferior competitor does not, spatial coexistence is possible in both resource-poor and resource-rich habitats. However, when the inferior competitor moves in the direction of increasing fitness but the superior competitor does not, spatial coexistence is precluded in resource-poor habitats and greatly reduced in resource-rich habitats. This suggests that species-specific differences may play an important role in driving spatial coexistence patterns. 4. The comparative framework yields predictions that can be tested with experiments that manipulate the relative mobilities of interacting species, or observational data on relative abundances and distribution patterns.

Information processing in models for density-dependent emigration: A comparison

Density-dependent emigration has been recognized as a fitness enhancing strategy. Yet, especially in the modelling literature there is no consensus about how density-dependent emigration should quantitatively be incorporated into metapopulation models. In this paper we compare the performance of five different dispersal strategies (defined by the functional link between density and emigration probability). Four of these strategies are based on published functional relationships between local population density and emigration probability, one assumes density-independent dispersal. We use individual-based simulations of time-discrete metapopulation dynamics and conduct evolution experiments for a broad range of values for dispersal mortality and environmental stochasticity. For each set of these conditions we analyze the evolution of emigration rates in ‘monoculture experiments’ (with only one type of dispersal strategy used by all individuals in the metapopulation) as well as in selection experiments that allow a pair-wise comparison of the performance of each functional type. We find that a single-parameter ‘asymptotic threshold’ strategy – derived from the marginal value theorem – with a decelerating increase of emigration rate with increasing population density, out-competes any other strategy, i.e. density-independent emigration, a ‘linear threshold’ strategy and a flexible three-parameter strategy. Only when environmental conditions select for extremely high emigration probabilities (close to one), strategies may perform approximately equally. A simple threshold strategy derived for the case of continuous population growth performs even worse than the density-independent strategy. As the functional type of the dispersal function implemented in metapopulation models may severely affect predictions concerning the survival of populations, range expansion, or community changes we clearly recommend to carefully select adequate functions to model density-dependent dispersal.

Habitat quality, conspecific density, and habitat pre-use affect the dispersal behaviour of two earthworm species, Aporrectodea icterica and Dendrobaena veneta, in a mesocosm experiment

Dispersal capacity is a life-history trait that may have profound consequences for earthworm populations: it influences population dynamics, species persistence and distribution and community structure. It also determines the level of gene flow between populations and affects processes such as local adaptation, speciation and the evolution of life-history traits. It may play a great role in soil functioning by determining the spatial distribution of ecosystem engineers such as earthworms. Dispersal is an evolutionary outcome of the behaviour in response to the ecological constraints of the species. Hence different dispersal behaviour is expected from the different ecological types of earthworms. Nevertheless the dispersal behaviour of earthworms has been little documented. In this work we test a series of basic mechanisms that are fundamental and complementary to understand earthworms dispersal behaviour. We focus on the dispersal triggered by environmental conditions, a fundamental process usually termed “conditional dependent dispersal”. We show experimentally in mesocosms that in one week: 1) earthworm dispersal can be triggered by low habitat quality, either through soil quality or the presence/absence of litter. 2) Earthworms can be subject to positive density dependent dispersal, that is the rate of dispersal increases when density increases; and 3) earthworm dispersal can be reduced by the pre-use of the soil by conspecific individuals that are no longer present. Our results suggest that earthworms may be more mobile than expected from previous estimations, and that they present high capacities of habitat selection. In the light of our findings we elaborate a behavioural scenario of earthworm foraging, and propose several priority working directions.

Evolution of cross-diffusion and self-diffusion

This article is concerned with the evolution of certain types of density-dependent dispersal strategy in the context of two competing species with identical population dynamics and same random dispersal rates. Such density-dependent movement, often referred to as cross-diffusion and self-diffusion, assumes that the movement rate of each species depends on the density of both species and that the transition probability from one place to its neighbourhood depends solely on the arrival spot (independent of the departure spot). Our results suggest that for a one-dimensional homogeneous habitat, if the gradients of two cross- and self-diffusion coefficients have the same direction, the species with the smaller gradient will win, i.e. the dispersal strategy with the smaller gradient of cross- and self-diffusion coefficient will evolve. In particular, it suggests that the species with constant cross- and self-diffusion coefficients may have competitive advantage over species with non-constant cross- and self-diffusion coefficients. However, if the two gradients have opposite directions, neither of the two dispersal strategies wins as these two species can coexist.

Evolution of density-dependent dispersal in a structured metapopulation

We study the evolution of density-dependent dispersal in a structured metapopulation subject to local catastrophes that eradicate local populations. To this end we use the theory of structured metapopulation dynamics and the theory of adaptive dynamics. The set of evolutionarily possible dispersal functions (i.e., emigration rates as a function of the local population density) is derived mechanistically from an underlying resource–consumer model. The local resource dynamics is of a flow-culture type and consumers leave a local population with a constant probability per unit of time κ when searching for resources but not when handling resources (i.e., eating and digesting). The time an individual spends searching (as opposed to handling) depends on the local resource density, which in turn depends on the local consumer density, and so the average per capita emigration rate depends on the local consumer density as well. The derived emigration rates are sigmoid functions of local consumer population density. The parameters of the local resource–consumer dynamics are subject to evolution. In particular, we find that there exists a unique evolutionarily stable and attracting dispersal rate κ ∗ for searching consumers. The κ ∗ increases with local resource productivity and decreases with resource decay rate. The κ ∗ also increases with the survival probability during dispersal, but as a function of the catastrophe rate it reaches a maximum before dropping off to zero again.

Human Dispersals: Mathematical Models and the Archaeological Record

The theoretical literature on human population dispersal processes at the large time and space scale is reviewed, including references to and discussions of relevant empirical data. The basic Fisher-KPP reaction-diffusion system is summarized for the single population situation, and developments relating to the Allee effect, density-dependent dispersal, time delay, advection, spatial and temporal heterogeneity, and anomalous and stratified diffusion are reviewed. Two- and three-population competitive reaction-diffusion systems of Lotka-Volterra type are also reviewed, as are dynamic approaches to carrying capacity that incorporate predator-prey instabilities, ecosystem engineering, and gene-culture coevolution.

Human Dispersals: Mathematical Models and the Archaeological Record

The theoretical literature on human population dispersal processes at the large time and space scale is reviewed, including references to and discussions of relevant empirical data. The basic Fisher-KPP reaction-diffusion system is summarized for the single population situation, and developments relating to the Allee effect, density-dependent dispersal, time delay, advection, spatial and temporal heterogeneity, and anomalous and stratified diffusion are reviewed. Two- and three-population competitive reaction-diffusion systems of Lotka-Volterra type are also reviewed, as are dynamic approaches to carrying capacity that incorporate predator-prey instabilities, ecosystem engineering, and gene-culture coevolution.

Accelerating invasion rates result from the evolution of density-dependent dispersal

Evolutionary processes play an important role in shaping the dynamics of range expansions, and selection on dispersal propensity has been demonstrated to accelerate rates of advance. Previous theory has considered only the evolution of unconditional dispersal rates, but dispersal is often more complex. For example, many species emigrate in response to crowding. Here, we use an individual-based model to investigate the evolution of density dependent dispersal into empty habitat, such as during an invasion. The landscape is represented as a lattice and dispersal between populations follows a stepping-stone pattern. Individuals carry three ‘genes’ that determine their dispersal strategy when experiencing different population densities. For a stationary range we obtain results consistent with previous theoretical studies: few individuals emigrate from patches that are below equilibrium density. However, during the range expansion of a previously stationary population, we observe evolution towards dispersal strategies where considerable emigration occurs well below equilibrium density. This is true even for moderate costs to dispersal, and always results in accelerating rates of range expansion. Importantly, the evolution we observe at an expanding front depends upon fitness integrated over several generations and cannot be predicted by a consideration of lifetime reproductive success alone. We argue that a better understanding of the role of density dependent dispersal, and its evolution, in driving population dynamics is required especially within the context of range expansions.

Synchronism in population networks with non linear coupling

A quite general spatially explicit metapopulation model featuring density-dependent dispersal is proposed. A study of the stability of synchronized attractors is done based on an explicit calculation of the transverse Lyapunov number of these attractors. An analytic expression for the transverse Lyapunov number depending on the Lyapunov number of the synchronous trajectory, the eigenvalues of the network configuration matrix and the function modelling the density-dependent dispersal (the number of migrants as a function of the local density) is presented. Numerical simulations are also performed upon selecting biologically relevant features, such as local dynamics, network topology and density-dependent dispersal mechanism.

Simultaneous positive and negative density‐dependent dispersal in a colonial bird species

Contradictory patterns of density-dependent animal dispersal can potentially be reconciled by integrating the conspecific attraction hypothesis with the traditional competition hypothesis. We propose a hypothesis that predicts a U-shaped relationship between density and both natal and breeding dispersal distance. Using 10 years of observations on a breeding colony of the Blue-footed Booby (Sula nebouxii), the hypothesis was confirmed by documenting simultaneous positive and negative density-dependent dispersal distances in natal and breeding dispersal of males and breeding dispersal of females within the colony. Point-pattern analyses demonstrated that the breeding sites of Blue-footed Boobies were highly aggregated in all years within a large study area, and aggregation presumably resulted in heterogeneity in patch density throughout the colony. As predicted, at moderate to high densities, dispersal distances showed positive density dependence, with individuals moving to lower density patches. In contrast, at low to moderate densities, dispersal distances showed negative density dependence, with individuals moving to higher density patches. In both sexes of the 1994 cohort, the higher the mean density in patches used by an individual over the long term (up to age 11 years), the fewer fledglings it produced. A positive effect of density on long-term reproductive success was not detected, possibly because birds that failed during pair formation or incubation were not sampled. Density of conspecifics may be an important influence on habitat selection of breeders, and dispersal may tend to carry individuals to patches where pair formation opportunities are better and negative effects of competition on reproductive success are reduced.