Evolutionary stability of ideal free nonlocal dispersal

We study the evolutionary stability of nonlocal dispersal strategies that can produce ideal free population distributions, that is, distributions where all individuals have equal fitness and there is no net movement of individuals at equilibrium. We find that the property of producing ideal free distributions is necessary and often sufficient for evolutionary stability. Our results extend those already developed for discrete diffusion models on finite patch networks to the case of nonlocal dispersal models based on integrodifferential equations. The analysis is based on the use of comparison methods and the construction of sub- and supersolutions.     

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.     

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.     

Evolution of positive and negative density-dependent dispersal

Understanding the evolution of density-dependent dispersal strategies has been a major challenge for evolutionary ecologists. Some existing models suggest that selection should favour positive and others negative density-dependence in dispersal. Here, we develop a general model that shows how and why selection may shift from positive to negative density-dependence in response to key ecological factors, in particular the temporal stability of the environment. We find that in temporally stable environments, particularly with low dispersal costs and large group sizes, habitat heterogeneity selects for negative density-dependent dispersal, whereas in temporally variable environments, particularly with high dispersal costs and small group sizes, habitat heterogeneity selects for positive density-dependent dispersal. This shift reflects the changing balance between the greater competition for breeding opportunities in more productive patches, versus the greater long-term value of offspring that establish themselves there, the latter being very sensitive to the temporal stability of the environment. In general, dispersal of individuals out of low-density patches is much more sensitive to habitat heterogeneity than is dispersal out of high-density patches.     

Density-dependent migration and synchronism in metapopulations

A spatially explicit metapopulation model with density-dependent dispersal is proposed in order to study the stability of synchronous dynamics. A stability criterion is obtained based on the computation of the transversal Liapunov number of attractors on the synchronous invariant manifold. We examine in detail a special case of density-dependent dispersal rule where migration does not occur if the patch density is below a certain critical density, while the fraction of individuals that migrate to other patches is kept constant if the patch density is above the threshold level. Comparisons with density-independent migration models indicate that this simple density-dependent dispersal mechanism reduces the stability of synchronous dynamics. We were able to quantify exactly this loss of stability through the frequency that synchronous trajectories are above the critical density.     

Research progress in avian dispersal behavior

Dispersal, defined as a linear spreading move-ment of individuals away from others of the population is a fundamental characteristic of organisms in nature. Dispersal is a central concept in ecological, behavioral and evolutionary studies, driven by different forces such as avoidance of inbreeding depression, density-dependent competition and the need to change breeding locations. By effective dispersal, organisms can enlarge their geo-graphic range and adjust the dynamic, sex ratio and gen-etic compositions of a population. Birds are one of the groups that are studied intensively by human beings. Due to their diurnal habits, diverse life history strategies and complex movement, birds are also ideal models for the study of dispersal behaviors. Certain topics of avian dispersal including sex-biased, asymmetric dispersal caused by differences in body conditions, dispersal pro-cesses, habitat selection and long distance dispersal are discussed here. Bird-ringing or marking, radio-telemetry and genetic markers are useful tools widely applied in dispersal studies. There are three major challenges regard-ing theoretical study and methodology research of dis-persal: (1) improvement in research methodology is needed, (2) more in-depth theoretical research is neces-sary, and (3) application of theoretical research into the conservation efforts for threatened birds and the manage-ment of their habitats should be carried out immediately.     

Research progress in avian dispersal behavior

Dispersal, defined as a linear spreading movement of individuals away from others of the population is a fundamental characteristic of organisms in nature. Dispersal is a central concept in ecological, behavioral and evolutionary studies, driven by different forces such as avoidance of inbreeding depression, density-dependent competition and the need to change breeding locations. By effective dispersal, organisms can enlarge their geographic range and adjust the dynamic, sex ratio and genetic compositions of a population. Birds are one of the groups that are studied intensively by human beings. Due to their diurnal habits, diverse life history strategies and complex movement, birds are also ideal models for the study of dispersal behaviors. Certain topics of avian dispersal including sex-biased, asymmetric dispersal caused by differences in body conditions, dispersal processes, habitat selection and long distance dispersal are discussed here. Bird-ringing or marking, radio-telemetry and genetic markers are useful tools widely applied in dispersal studies. There are three major challenges regarding theoretical study and methodology research of dispersal: (1) improvement in research methodology is needed, (2) more in-depth theoretical research is necessary, and (3) application of theoretical research into the conservation efforts for threatened birds and the management of their habitats should be carried out immediately. __________ Translated from Acta Ecologica Sinica, 2008, 28(4): 1354–1365 [译自: 生态学报]     

Evolutionary Convergence to Ideal Free Dispersal Strategies and Coexistence

We study a two species competition model in which the species have the same population dynamics but different dispersal strategies and show how these dispersal strategies evolve. We introduce a general dispersal strategy which can result in the ideal free distributions of both competing species at equilibrium and generalize the result of Averill et al. (2011). We further investigate the convergent stability of this ideal free dispersal strategy by varying random dispersal rates, advection rates, or both of these two parameters simultaneously. For monotone resource functions, our analysis reveals that among two similar dispersal strategies, selection generally prefers the strategy which is closer to the ideal free dispersal strategy. For nonmonotone resource functions, our findings suggest that there may exist some dispersal strategies which are not ideal free, but could be locally evolutionarily stable and/or convergent stable, and allow for the coexistence of more than one species.     

Towards a mechanistic understanding of dispersal evolution in plants: conservation implications

Aim A species’ dispersal characteristics will play a key role in determining its likely fate during a period of environmental change. However, these characteristics are not constant within a species – instead, there is often both considerable interpopulation and interindividual variability. Also changes in selection pressures can result in the evolution of dispersal characteristics, with knock‐on consequences for a species’ population dynamics. Our aim here is to make our theoretical understanding of dispersal evolution more conservation‐relevant by moving beyond the rather abstract, phenomenological models that have dominated the literature towards a more mechanism‐based approach. Methods We introduce a continuous‐space, individual‐based model for wind‐dispersed plants where release height is determined by an individual’s ‘genotype’. A mechanistic wind dispersal model is used to simulate seed dispersal. Selection acts on variation in release height that is generated through mutation. Results We confirm that, when habitat is fragmented, both evolutionary rescue and evolutionary suicide remain possible outcomes when a mechanistic dispersal model is used. We also demonstrate the potential for what we term evolutionary entrapment. A population that under some conditions can evolve to be sufficiently dispersive that it expands rapidly across a fragmented landscape can, under different conditions, become trapped by a combination of limited dispersal and a large gap between patches. Conclusions While developing evolutionary models to be used as conservation tools is undoubtedly a challenge, we believe that, with a concerted collaborative effort linking the knowledge and methods of ecologists, evolutionary biologists and geneticists, it is an achievable aim.     

The evolution of dispersal in a two-patch system: some consequences of differences between migrants and residents

We investigate how age-structure and differences in certain demographic traits between residents and immigrants of a single species act to determine the evolutionarily stable dispersal strategy in a two-patch environment that is heterogeneous in space but constant in time. These two factors have been neglected in previous models of the evolution of dispersal, which generally consider organisms with very simple life-cycles and assume that, whatever their origin, individuals in a given habitat have the same bio-demographic characteristics. However, there is increasing empirical evidence that dispersing individuals have different demographic properties from phylopatric ones. We develop a matrix model in which recruitment depends on local population densities. We assume that dispersal entails a proportional cost to immigrant fecundity, which can be compensated by differences in survival rates between immigrants and residents. The evolutionarily stable strategies (ESS) for dispersal are identified using a combination of analytical expressions and numerical simulations. Our results show that philopatry is selected (1) when dispersal rates do not vary in space, (2) when the metapopulation is a source-sink system and (3) when dispersal rates vary in space (asymmetric dispersal) and immigrants do not compensate for their reduced fecundity. We observe that non-zero asymmetric dispersal rates may be evolutionarily stable when (1) immigrants and residents are demographically alike and (2) immigrants compensate totally for their reduced fecundity through an increase in adult survival. Under these conditions, we find that the ESS occurs when the fitnesses at equilibrium in the two habitats, measured in our model by the realized reproductive rates, are each equal to unity. A comparison with previous studies suggests a unifying rule for the evolution of dispersal: the dispersal rates which permit the spatial homogenization of fitnesses are ESSs. This condition provides new insight into the evolutionary stability of source-sink systems. It also supports the hypothesis that immigrants have adapted demographic strategies, rather than the hypothesis that dispersal is costly and immigrants are at a disavantage compared with residents.     

Dynamical facilitation of the ideal free distribution in nonideal populations

The ideal free distribution (IFD) requires that individuals can accurately perceive density‐dependent habitat quality, while failure to discern quality differences below a given perception threshold results in distributions approaching spatial uniformity. Here, we investigate the role of population growth in restoring a nonideal population to the IFD. We place a simple model of discrete patch choice under limits to the resolution by which patch quality is perceived and include population growth driven by that underlying quality. Our model follows the population's distribution through both breeding and dispersal seasons when perception limits differ in their likely influence. We demonstrate that populations of perception limited movers can approximate an IFD provided sufficient population growth; however, the emergent IFD would be temporally inconstant and correspond to reproductive events. The time to emergence of the IFD during breeding is shorter under exponential growth than under logistic growth. The IFD during early colonization of a community persists longer when more patches are available to individuals. As the population matures and dispersal becomes increasingly random, there is an oscillation in the observance of IFD, with peaks most closely approximating the IFD occurring immediately after reproductive events, and higher reproductive rates producing distributions closer to the IFD.     

Dispersal and alternative breeding site fidelity strategies in an amphibian

Dispersal (i.e. movement from a natal or breeding site to another breeding site) is a central process in ecology and evolution as it affects the eco‐evolutionary dynamics of spatially structured populations. Dispersal evolution is regulated by the balance between costs and benefits, which is influenced by the individual phenotype (i.e. phenotype‐dependent dispersal) and environmental factors (i.e. condition‐dependent dispersal). Even though these processes have been extensively studied in species with simple life cycles, our knowledge about these mechanisms in organisms displaying complex life cycles remains fragmentary. In fact, little is specifically known about how the interplay between individual and environmental factors may lead to alternative dispersal strategies that, in turn, lead to the coexistence of contrasted site fidelity phenotypes. In this paper, we examined breeding dispersal in a pond‐breeding amphibian, the great crested newt Triturus cristatus, within usual walking distances for a newt. We took advantage of recent developments in multi‐event capture–recapture models and used capture–recapture data (946 newts marked) collected in a spatially structured population occupying a large pond network (73 ponds). We showed a high rate of breeding site infidelity (i.e. pond use) and the coexistence of two dispersal phenotypes, namely, a highly pond faithful phenotype and a dispersing phenotype. Individuals that were site faithful at time t – 1 were therefore more likely to remain site faithful at time t. Our results also demonstrated that the probability that individuals belong to one or the other dispersal phenotypes depended on environmental and individual factors. In particular, we highlighted the existence of a dispersal syndrome implying a covariation pattern among dispersal behavior, body size, and survival. Our work opens new research prospects in the evolution of dispersal in organisms displaying complex life cycles and raises interesting questions about the evolutionary pathways that contribute to the diversification of movement strategies in the wild.     

Dispersal capacity explains the evolution of lifespan variability

The evolutionary explanation for lifespan variation is still based on the antagonistic pleiotropy hypothesis, which has been challenged by several studies. Alternative models assume the existence of genes that favor aging and group benefits at the expense of reductions in individual lifespans. Here we propose a new model without making such assumptions. It considers that limited dispersal can generate, through reduced gene flow, spatial segregation of individual organisms according to lifespan. Individuals from subpopulations with shorter lifespan could thus resist collapse in a growing population better than individuals from subpopulations with longer lifespan, hence reducing lifespan variability within species. As species that disperse less may form more homogeneous subpopulations regarding lifespan, this may lead to a greater capacity to maximize lifespan that generates viable subpopulations, therefore creating negative associations between dispersal capacity and lifespan across species. We tested our model with individual‐based simulations and a comparative study using empirical data of maximum lifespan and natal dispersal distance in 26 species of birds, controlling for the effects of genetic variability, body size, and phylogeny. Simulations resulted in maximum lifespans arising from lowest dispersal probabilities, and comparative analyses resulted in a negative association between lifespan and natal dispersal distance, thus consistent with our model. Our findings therefore suggest that the evolution of lifespan variability is the result of the ecological process of dispersal.     

A modeling exercise to show why population models should incorporate distinct life histories of dispersers

Dispersal is an important form of movement influencing population dynamics, species distribution and gene flow between populations. In population models, dispersal is often included in a simplified manner by removing a random proportion of the population. Many ecologists now argue that models should be formulated at the level of individuals instead of the population level. To fully understand the effects of dispersal on natural systems, it is therefore necessary to incorporate individual-level differences in dispersal behavior in population models. Here, we parameterized an integral projection model, which allows for studying how individual life histories determine population-level processes, using bulb mites, Rhizoglyphus robini, to assess to what extent dispersal expression (frequency of individuals in the dispersal stage) and dispersal probability affect the proportion of successful dispersers and natal population growth rate. We find that allowing for life-history differences between resident phenotypes and disperser phenotypes shows that multiple combinations of dispersal probability and dispersal expression can produce the same proportion of leaving individuals. Additionally, a given proportion of successful dispersing individuals result in different natal population growth rates. The results highlight that dispersal life histories, and the frequency with which disperser phenotypes occur in the natal population, significantly affect population-level processes. Thus, biological realism of dispersal population models can be increased by incorporating the typically observed life-history differences between resident phenotypes and disperser phenotypes, and we here present a methodology to do so.     

Optimal life‐history schedule in a metapopulation with juvenile dispersal

Previous models have predicted that when mortality increases with age, older individuals should invest more of their resources in reproduction and produce less dispersive offspring, as both their future reproductive value and their prospect of competing with their own sib decline. Those models assumed stable population sizes. We here study for the first time the evolution of age‐specific reproductive effort and of age‐specific offspring dispersal rate in a metapopulation with extinction‐recolonization dynamics and juvenile dispersal. Our model explores the evolutionary consequences of disequilibrium in the age structure of individuals in local populations, generated by disturbances. Life‐history decisions are then shaped both by changes with age in individual performances, and by changes in ecological conditions, as young and old individuals do not live on average in the same environments. Lower juvenile dispersal favours the evolution of higher reproductive effort in young adults in a metapopulation with extinction‐recolonization compared with a well‐mixed population. Contrary to previous predictions for stable structured populations, we find that offspring dispersal should generally increase with maternal age. This is because young individuals, who are overrepresented in recently colonized populations, should allocate more to reproduction and less to dispersal as a strategy to exploit abundant recruitment opportunities in such populations.     

A field test of simple dispersal models as predictors of movement in a cohort of lake-dwelling brook charr

1. Dispersal can be a major determinant of the distribution and abundance of animals, as well as a key mechanism linking behaviour to population dynamics, but progress in understanding dispersal has been hampered by the lack of a general framework for modelling dispersal. 2. This study tested the capacity of simple models to summarize and predict the lake-wide dispersal of an emerging cohort of young-of-the-year brook charr Salvelinus fontinalis, over 12 surveys conducted during a 2-month period. 3. The models are based on two types of dispersal kernel, the normal distribution from a simple diffusion process, and a Laplace distribution depicting exponential decay of the frequency of dispersers away from the point of origin. In all, four models were assessed: one-group diffusion (D1S) and exponential (E1S) models assuming homogeneous dispersal behaviour within the cohort, and two-group diffusion (D2S) and exponential (E2S) models accounting for intrapopulation differences in dispersal between sedentary and mobile individuals. 4. A rigorous cross-validation, based on calibrating the models to the distributions from the first two surveys only and then validating them on the remaining 10 distributions, was used to compare model predictions with observed values for five properties of the dispersal distributions: counts in individual shoreline sections; mean lateral displacement, variance and kurtosis of displacements; and the percentage of long-distance dispersers. 5. Substantial intrapopulation heterogeneity in dispersal behaviour was apparent: 83% of all individuals were estimated to be sedentary and the remainder mobile. Remarkably, the two-group exponential model E2S - calibrated to data from only two surveys conducted 3.5 and 8.5 days after the beginning of emergence - predicted reasonably well all properties of the spatial distribution of the cohort until the end of the study, 7 weeks later. 6. Standardized measures of mobility derived from simple models may lead to better understanding of population dynamics and improved management. Specifically, the ability to accurately predict long-distance dispersal may be critical to assessing population persistence and cohort strength whenever key habitats, such as refugia or productive areas supporting a large proportion of the cohort, are sparsely distributed or distant from the point of origin.     

Modeling Distribution of Dispersal Distances in Male White-Tailed Deer

Abstract: Dispersal distances and their distribution pattern are important to understanding such phenomena as disease spread and gene flow, but oftentimes dispersal characteristics are modeled as a fixed trait for a given species. We found that dispersal distributions differ for spring and autumn dispersals of yearling male white-tailed deer (Odocoileus virginianus) but that combined data can be adequately modeled based on a log-normal distribution. We modeled distribution of dispersal distances from 3 distinct populations in Pennsylvania and Maryland, USA, based on the relationship between percent forest cover and mean dispersal distance and the relationship between mean and variance of dispersal distances. Our results suggest distributions of distances for dispersing yearling male white-tailed deer can be modeled by simply measuring a readily obtained landscape metric, percent forest cover, which could be used to create generalized spatially explicit disease or gene flow models.     

On the evolution of dispersal via heterogeneity in spatial connectivity

Dispersal has long been recognized as a mechanism that shapes many observed ecological and evolutionary processes. Thus, understanding the factors that promote its evolution remains a major goal in evolutionary ecology. Landscape connectivity may mediate the trade-off between the forces in favour of dispersal propensity (e.g. kin-competition, local extinction probability) and those against it (e.g. energetic or survival costs of dispersal). It remains, however, an open question how differing degrees of landscape connectivity may select for different dispersal strategies. We implemented an individual-based model to study the evolution of dispersal on landscapes that differed in the variance of connectivity across patches ranging from networks with all patches equally connected to highly heterogeneous networks. The parthenogenetic individuals dispersed based on a flexible logistic function of local abundance. Our results suggest, all else being equal, that landscapes differing in their connectivity patterns will select for different dispersal strategies and that these strategies confer a long-term fitness advantage to individuals at the regional scale. The strength of the selection will, however, vary across network types, being stronger on heterogeneous landscapes compared with the ones where all patches have equal connectivity. Our findings highlight how landscape connectivity can determine the evolution of dispersal strategies, which in turn affects how we think about important ecological dynamics such as metapopulation persistence and range expansion.     

The ideal free pike: 50 years of fitness-maximizing dispersal in Windermere

The ideal free distribution (IFD) theory is one of the most influential theories in evolutionary ecology. It predicts how animals ought to distribute themselves within a heterogeneous habitat in order to maximize lifetime fitness. We test the population level consequence of the IFD theory using 40-year worth data on pike (Esox lucius) living in a natural lake divided into two basins. We do so by employing empirically derived density-dependent survival, dispersal and fecundity functions in the estimation of basin-specific density-dependent fitness surfaces. The intersection of the fitness surfaces for the two basins is used for deriving expected spatial distributions of pike. Comparing the derived expected spatial distributions with 50 years data of the actual spatial distribution demonstrated that pike is ideal free distributed within the lake. In general, there was a net migration from the less productive north basin to the more productive south basin. However, a pike density-manipulation experiment imposing shifting pike density gradients between the two basins managed to switch the net migration direction and hence clearly demonstrated that the Windermere pike choose their habitat in an ideal free manner. Demonstration of ideal free habitat selection on an operational field scale like this has never been undertaken before.     

Microsatellite-based parentage analysis reveals non-ideal free distribution in a parasitoid population

Habitat selection by dispersers is the focus of much theoretical models, most of which are based on the assumption of negative density dependence. The archetype of these models is the ideal free distribution, characterized by an evolutionary stable state where more competitors aggregate in better habitats, so that the fitness benefit of resource abundance is equally offset by the cost of competition in all habitats. In this study, we used parentage analysis on microsatellite genotypes to test the ideal free distribution in a natural population of aphid parasitoids. Parentage analysis was conducted on parasitoids emerging from aphid colonies. We inferred the number of foundress females which had reproduced in each colony, as well as the number of offspring for each foundress. As predicted by the ideal free distribution, the number of offspring per foundress per colony did not depend on the number of hosts per colony. However, contrary to ideal free distribution predictions, it was affected by the number of foundresses per colony. In surprising contrast with the basic assumption of negative density dependence, individual fitness increased with the number of foundresses. Moreover, parentage analysis revealed a very low number of offspring per foundress per colony (mean = 1.8). This observed distribution questions the validity of classical models of habitat choice based on competition. Indeed, our results provide a new illustration reinforcing a growing body of theory and data on positive density dependence. Our results also suggest that the avoidance of hyperparasitism and predation, although generally neglected, may shape the distribution of parasitoids in the field.