The evolution of dispersal – the importance of information about population density and habitat characteristics

The evolution of mobility patterns and dispersal strategies depend on different population, habitat and life history characteristics. The ability to perceive and make use of information about the surrounding environment for dispersal decisions will also differ between organisms. To investigate the evolutionary consequences of such differences, we have used a simulation model with nearest-neighbour dispersal in a metapopulation to study how variation in the ability to obtain and make use of information about habitat quality and conspecific density affects the evolution of dispersal strategies. We found a rather strong influence of variation in information on the overall rate of dispersal in a metapopulation. The highest emigration rate evolved in organisms with no information about either density or habitat quality and the lowest rate was found in organisms with information about both the natal and the neighbouring patches. For organisms that can make use of information about conspecific density, positively density-dependent dispersal evolved in the majority of cases, with the strongest density dependence occurring when an individual only has information about density in the natal patch. However, we also identified situations, involving strong local population fluctuations and frequent local extinctions, where negatively density-dependent dispersal evolved.     

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     

The ability of individuals to assess population density influences the evolution of emigration propensity and dispersal distance

We analyze the simultaneous evolution of emigration and settlement decisions for actively dispersing species differing in their ability to assess population density. Using an individual-based model we simulate dispersal as a multi-step (patch to patch) movement in a world consisting of habitat patches surrounded by a hostile matrix. Each such step is associated with the same mortality risk. Our simulations show that individuals following an informed strategy, where emigration (and settlement) probability depends on local population density, evolve a lower (natal) emigration propensity but disperse over significantly larger distances - i.e. postpone settlement longer - than individuals performing density-independent emigration. This holds especially when variation in environmental conditions is spatially correlated. Both effects can be traced to the informed individuals' ability to better exploit existing heterogeneity in reproductive chances. Yet, already moderate distance-dependent dispersal costs prevent the evolution of multi-step (long-distance) dispersal, irrespective of the dispersal strategy.     

Finite metapopulation models with density-dependent migration and stochastic local dynamics

The effects of small density-dependent migration on the dynamics of a metapopulation are studied in a model with stochastic local dynamics. We use a diffusion approximation to study how changes in the migration rate and habitat occupancy affect the rates of local colonization and extinction. If the emigration rate increases or if the immigration rate decreases with local population size, a positive expected rate of change in habitat occupancy is found for a greater range of habitat occupancies than when the migration is density-independent. In contrast, the reverse patterns of density dependence in respective emigration and immigration reduce the range of habitat occupancies where the metapopulation will be viable. This occurs because density-dependent migration strongly influences both the establishment and rescue effects in the local dynamics of metapopulations.     

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.     

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.     

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

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

Spatial connectedness imposes local‐ and metapopulation‐level selection on life history through feedbacks on demography

Dispersal evolution impacts the fluxes of individuals and hence, connectivity in metapopulations. Connectivity is therefore decoupled from the structural connectedness of the patches within the spatial network. Because of demographic feedbacks, local selection also drives the evolution of other life history traits. We investigated how different levels of connectedness affect trait evolution in experimental metapopulations of the two‐spotted spider mite. We separated local‐ and metapopulation‐level selection and linked trait divergence to population dynamics. With lower connectedness, an increased starvation resistance and delayed dispersal evolved. Reproductive performance evolved locally by transgenerational plasticity or epigenetic processes. Costs of dispersal, but also changes in local densities and temporal fluctuations herein are found to be putative drivers. In addition to dispersal, demographic traits are able to evolve in response to metapopulation connectedness at both the local and metapopulation level by genetic and/or non‐genetic inheritance. These trait changes impact the persistence of spatially structured populations.     

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.     

The evolution of density-dependent dispersal in a noisy spatial population model

It is well-known that dispersal is advantageous in many different ecological situations, e.g. to survive local catastrophes where populations live in spatially and temporally heterogeneous habitats. However, the key question, what kind of dispersal strategy is optimal in a particular situation, has remained unanswered. We studied the evolution of density-dependent dispersal in a coupled map lattice model, where the population dynamics are perturbed by external environmental noise. We used a very flexible dispersal function to enable evolution to select from practically all possible types of monotonous density-dependent dispersal functions. We treated the parameters of the dispersal function as continuously changing phenotypic traits. The evolutionary stable dispersal strategies were investigated by numerical simulations. We pointed out that irrespective of the cost of dispersal and the strength of environmental noise, this strategy leads to a very weak dispersal below a threshold density, and dispersal rate increases in an accelerating manner above this threshold. Decreasing the cost of dispersal increases the skewness of the population density distribution, while increasing the environmental noise causes more pronounced bimodality in this distribution. In case of positive temporal autocorrelation of the environmental noise, there is no dispersal below the threshold, and only low dispersal below it, on the other hand with negative autocorrelation practically all individual disperses above the threshold. We found our results to be in good concordance with empirical observations.     

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.     

Metapopulation viability analysis of the bog fritillary butterfly using RAMAS/GIS

Many species living in man-shaped landscapes are restricted to small natural habitat patches and form metapopulations; predicting their future is a central issue in applied ecology. We examined the viability of the bog fritillary butterfly Proclossiana eunomia Esper, a specialist glacial relict species, in a highly fragmented landscape (<1% of suitable habitat in 10 km²), by way of population viability analysis. We used comprehensive data from a long-term study in which a patchy population was monitored during ten consecutive years to parameterise a spatially structured metapopulation model using commercially available platform RAMAS/GIS 3.0. Population growth rate was density-dependent and modulated by various climatic variables acting on different developmental stages of the butterfly. Density dependence was probably related to larval parasitism by a specific parasitoid. Population size was negatively affected by an increase in the mean temperature. Dispersal was modelled as the observed proportion of movements between patches, taking into account the probability of emigration out of a given patch. Our model provided results close to the picture of the system drawn from the field data and was considered as useful in making predictions about the metapopulation. Demographic parameters proved to have a far higher impact on metapopulation persistence than dispersal or correlation of local dynamics. Scenarios simulating both global warming and management of habitat patches by rustic herbivore grazing indicated a decrease in the viability of the metapopulation. Our results prompted the regional nature conservation agency to modify the planned management regime. We urge conservation biologists to use structured population models including local population dynamics for viability analysis targeted to such threatened metapopulations in highly fragmented landscapes.     

局域种群的Allee效应和集合种群的同步性

从包含Allee效应的局域种群出发,建立了耦合映像格子模型,即集合种群模型.通过分析和计算机模拟表明:(1)当局域种群受到Allee效应强度较大时,集合种群同步灭绝;(2)而当Allee效应强度相对较弱时,通过稳定局域种群动态(减少混沌)使得集合种群发生同步波动,而这种同步波动能够增加集合种群的灭绝风险;(3)斑块间的连接程度对集合种群同步波动的发生有很大的影响,适当的破碎化有利于集合种群的续存.全局迁移和Allee效应结合起来增加了集合种群同步波动的可能,从而增加集合种群的灭绝风险.这些结果对理解同步性的机理、利用同步机理来制定物种保护策略和害虫防治都有重要的意义.     

Potential metapopulation structure and the effects of habitat quality on population size of the endangered False Ringlet butterfly

The False Ringlet (Coenonympha oedippus) is a European butterfly species, endangered due to the severe loss and fragmentation of its habitat. In Hungary, two remaining populations of the butterfly occur in lowland Purple Moorgrass meadows. We studied a metapopulation occupying twelve habitat patches in Central Hungary. Our aim was to reveal what measures of habitat quality affect population size and density of this metapopulation, estimate dispersal parameters and describe phenology of subpopulations. Local population sizes and dispersal parameters were estimated from an extensive mark–release–recapture dataset, while habitat quality was characterized by groundwater level, cover of grass tussocks, bush cover, height of vegetation and grass litter at each habitat patch. The estimated size of the metapopulation was more than 3,000 individuals. We estimated a low dispersal capacity, especially for females, indicating a very low probability of (re)colonization. Butterfly abundance and density in local populations increased with higher grass litter, lower groundwater level and larger area covered by tussocks. We suppose that these environmental factors affect butterfly abundance by determining the microclimatic conditions for both larvae and adult butterflies. Our results suggest that the long-term preservation of the studied metapopulation needs the maintenance of high quality habitat patches by appropriate mowing regime and water regulation. Management also should facilitate dispersal to strengthen metapopulation structure with creating stepping-stones or gradually increase habitat quality in present matrix.     

Stabilization through spatial pattern formation in metapopulations with long-range dispersal

Many studies of metapopulation models assume that spatially extended populations occupy a network of identical habitat patches, each coupled to its nearest neighbouring patches by density-independent dispersal. Much previous work has focused on the temporal stability of spatially homogeneous equilibrium states of the metapopulation, and one of the main predictions of such models is that the stability of equilibrium states in the local patches in the absence of migration determines the stability of spatially homogeneous equilibrium states of the whole metapopulation when migration is added. Here, we present classes of examples in which deviations from the usual assumptions lead to different predictions. In particular, heterogeneity in local habitat quality in combination with long-range dispersal can induce a stable equilibrium for the metapopulation dynamics, even when within-patch processes would produce very complex behaviour in each patch in the absence of migration. Thus, when spatially homogeneous equilibria become unstable, the system can often shift to a different, spatially inhomogeneous steady state. This new global equilibrium is characterized by a standing spatial wave of population abundances. Such standing spatial waves can also be observed in metapopulations consisting of identical habitat patches, i.e. without heterogeneity in patch quality, provided that dispersal is density dependent. Spatial pattern formation after destabilization of spatially homogeneous equilibrium states is well known in reaction–diffusion systems and has been observed in various ecological models. However, these models typically require the presence of at least two species, e.g. a predator and a prey. Our results imply that stabilization through spatial pattern formation can also occur in single-species models. However, the opposite effect of destabilization can also occur: if dispersal is short range, and if there is heterogeneity in patch quality, then the metapopulation dynamics can be chaotic despite the patches having stable equilibrium dynamics when isolated. We conclude that more general metapopulation models than those commonly studied are necessary to fully understand how spatial structure can affect spatial and temporal variation in population abundance.     

Evolutionary suicide and evolution of dispersal in structured metapopulations

 We study the evolution of dispersal in a structured metapopulation model. The metapopulation consists of a large (infinite) number of local populations living in patches of habitable environment. Dispersal between patches is modelled by a disperser pool and individuals in transit between patches are exposed to a risk of mortality. Occasionally, local catastrophes eradicate a local population: all individuals in the affected patch die, yet the patch remains habitable. We prove that, in the absence of catastrophes, the strategy not to migrate is evolutionarily stable. Under a given set of environmental conditions, a metapopulation may be viable and yet selection may favor dispersal rates that drive the metapopulation to extinction. This phenomenon is known as evolutionary suicide. We show that in our model evolutionary suicide can occur for catastrophe rates that increase with decreasing local population size. Evolutionary suicide can also happen for constant catastrophe rates, if local growth within patches shows an Allee effect. We study the evolutionary bifurcation towards evolutionary suicide and show that a discontinuous transition to extinction is a necessary condition for evolutionary suicide to occur. In other words, if population size smoothly approaches zero at a boundary of viability in parameter space, this boundary is evolutionarily repelling and no suicide can occur. Received: 10 November 2000 / Revised version: 13 February 2002 / Published online: 17 July 2002     

Metapopulation persistence in dynamic landscapes: the role of dispersal distance

Species associated with transient habitats need efficient dispersal strategies to ensure their regional survival. Using a spatially explicit metapopulation model, we studied the effect of the dispersal range on the persistence of a metapopulation as a function of the local population and landscape dynamics (including habitat patch destruction and subsequent regeneration). Our results show that the impact of the dispersal range depends on both the local population and patch growth. This is due to interactions between dispersal and the dynamics of patches and populations via the number of potential dispersers. In general, long-range dispersal had a positive effect on persistence in a dynamic landscape compared to short-range dispersal. Long-range dispersal increases the number of couplings between the patches and thus the colonisation of regenerated patches. However, long-range dispersal lost its advantage for long-term persistence when the number of potential dispersers was low due to small population growth rates and/or small patch growth rates. Its advantage also disappeared with complex local population dynamics and in a landscape with clumped patch distribution.     

EVOLUTION OF DISPERSAL RATES IN METAPOPULATION MODELS: BRANCHING AND CYCLIC DYNAMICS IN PHENOTYPE SPACE

We study the evolution of dispersal rates in a two patch metapopulation model. The local dynamics in each patch are given by difference equations, which, together with the rate of dispersal between the patches, determine the ecological dynamics of the metapopulation. We assume that phenotypes are given by their dispersal rate. The evolutionary dynamics in phenotype space are determined by invasion exponents, which describe whether a mutant can invade a given resident population. If the resident metapopulation is at a stable equilibrium, then selection on dispersal rates is neutral if the population sizes in the two patches are the same, while selection drives dispersal rates to zero if the local abundances are different. With non-equilibrium metapopulation dynamics, non-zero dispersal rates can be maintained by selection. In this case, and if the patches are ecologically identical, dispersal rates always evolve to values which induce synchronized metapopulation dynamics. If the patches are ecologically different, evolutionary branching into two coexisting dispersal phenotypes can be observed. Such branching can happen repeatedly, leading to polymorphisms with more than two phenotypes. If there is a cost to dispersal, evolutionary cycling in phenotype space can occur due to the dependence of selection pressures on the ecological attractor of the resident population, or because phenotypic branching alternates with the extinction of one of the branches. Our results extend those of Holt and McPeek (1996), and suggest that phenotypic branching is an important evolutionary process. This process may be relevant for sympatric speciation.     

On fitness in structured metapopulations

In this paper we derive a general expression measuring fitness in general structured metapopulation models. We apply the theory to a model structured by local population size and in which local dynamics is explicitly modelled. In particular, we calculate the evolutionarily stable dispersal strategy for individuals that can assess the local population density in the case where only dispersal is subject to evolutionary control but all other model ingredients are assumed fixed. We show that there exists a threshold size such that at ESS everyone should stay as long as the population size is below the threshold and everyone should disperse immediately as the population size reaches the threshold. Received: 13 August 1999 / Revised version: 2 May 2001 / Published online: 12 October 2001