Migration dynamics for the ideal free distribution

This article verifies that the ideal free distribution (IFD) is evolutionarily stable, provided the payoff in each patch decreases with an increasing number of individuals. General frequency-dependent models of migratory dynamics that differ in the degree of animal omniscience are then developed. These models do not exclude migration at the IFD where balanced dispersal emerges. It is shown that the population distribution converges to the IFD even when animals are nonideal (i.e., they do not know the quality of all patches). In particular, the IFD emerges when animals never migrate from patches with a higher payoff to patches with a lower payoff and when some animals always migrate to the best patch. It is shown that some random migration does not necessarily lead to undermatching, provided migration occurs at the IFD. The effect of population dynamics on the IFD (and vice versa) is analyzed. Without any migration, it is shown that population dynamics alone drive the population distribution to the IFD. If animal migration tends (for each fixed population size) to the IFD, then the combined migration-population dynamics evolve to the population IFD independent of the two timescales (i.e., behavioral vs. population).     

Ideal free distributions, evolutionary games, and population dynamics in multiple-species environments

In this article, we develop population game theory, a theory that combines the dynamics of animal behavior with population dynamics. In particular, we study interaction and distribution of two species in a two-patch environment assuming that individuals behave adaptively (i.e., they maximize Darwinian fitness). Either the two species are competing for resources or they are in a predator-prey relationship. Using some recent advances in evolutionary game theory, we extend the classical ideal free distribution (IFD) concept for single species to two interacting species. We study population dynamical consequences of two-species IFD by comparing two systems: one where individuals cannot migrate between habitats and one where migration is possible. For single species, predator-prey interactions, and competing species, we show that these two types of behavior lead to the same population equilibria and corresponding species spatial distributions, provided interspecific competition is patch independent. However, if differences between patches are such that competition is patch dependent, then our predictions strongly depend on whether animals can migrate or not. In particular, we show that when species are settled at their equilibrium population densities in both habitats in the environment where migration between habitats is blocked, then the corresponding species spatial distribution need not be an IFD. Thus, when species are given the opportunity to migrate, they will redistribute to reach an IFD (e.g., under which the two species can completely segregate), and this redistribution will also influence species population equilibrial densities. Alternatively, we also show that when two species are distributed according to the IFD, the corresponding population equilibrium can be unstable.     

The migration game in habitat network: the case of tuna

Long-distance migration is a widespread process evolved independently in several animal groups in terrestrial and marine ecosystems. Many factors contribute to the migration process and of primary importance are intra-specific competition and seasonality in the resource distribution. Adaptive migration in direction of increasing fitness should lead to the ideal free distribution (IFD) which is the evolutionary stable strategy of the habitat selection game. We introduce a migration game which focuses on migrating dynamics leading to the IFD for age-structured populations and in time varying habitats, where dispersal is costly. The model predicts migration dynamics between these habitats and the corresponding population distribution. When applied to Atlantic bluefin tunas, it predicts their migration routes and their seasonal distribution. The largest biomass is located in the spawning areas which have also the largest diversity in the age-structure. Distant feeding areas are occupied on a seasonal base and often by larger individuals, in agreement with empirical observations. Moreover, we show that only a selected number of migratory routes emerge as those effectively used by tunas.     

Dispersal,kin competition,and the ideal free distribution in a spatially heterogeneous population

In this paper, we reanalyze simple models of the evolution of dispersal in a heterogeneous landscape. Previous analyses concluded that without temporal variability, dispersal can evolve only if it is not costly and if it is conditional on the habitat. If both conditions hold, these models predict that selection on dispersal should lead to balanced dispersal between habitats (the number of immigrants equals the number of emigrants in each habitat). To evaluate the generality of these conclusions, we extended the analysis of these models to finite populations. This requires us to establish fitness measures for finite class-structured populations. These fitness measures allow us to take kin competition into account. Our analysis shows that even without temporal variability, conditional dispersal and the absence of a dispersal cost are not necessary conditions for dispersal to evolve. In the absence of a dispersal cost, we predict that selection on conditional dispersal will always lead to panmixia and not simply to balanced dispersal. When dispersal is costly, we show that the ideal free distribution (IFD) and balanced dispersal do not occur. Our results show that the deviations from IFD are of the order of the dispersal cost. We propose an approach to test our predictions.     

Dispersal among habitats varying in fitness: reciprocating migration through ideal habitat selection

Current evolutionary models of dispersal set the ends of a continuum where the number of individuals emigrating from a habitat either equals the number of individuals immigrating (balanced dispersal) or where emigrants flow from a source habitat to a corresponding sink. Theories of habitat selection suggest a more sophisticated conditional strategy where individuals disperse from habitats where they have the greatest impact on fitness to habitats where their per capita impact is lower. Asymmetries between periods of population growth and decline result in a reciprocating dispersal strategy where the direction of migration is reversed as populations wax and wane. Thus, for example, if net migration of individuals flows from high- to low-density habitats during periods of population growth, net migration will flow in the opposite direction during population decline. Stochastic simulations and analytical models of reciprocating dispersal demonstrate that fitness, carrying capacity, stochastic dynamics, and interference from dominants interact to determine whether dispersal is balanced between habitats, or whether one habitat or the other acts as a net donor of dispersing individuals. While the pattern of dispersal may vary, each is consistent with an underlying strategy of density-dependent habitat selection.     

The ideal free distribution: a review and synthesis of the game-theoretic perspective

The Ideal Free Distribution (IFD), introduced by Fretwell and Lucas in [Fretwell, D.S., Lucas, H.L., 1970. On territorial behavior and other factors influencing habitat distribution in birds. Acta Biotheoretica 19, 16-32] to predict how a single species will distribute itself among several patches, is often cited as an example of an evolutionarily stable strategy (ESS). By defining the strategies and payoffs for habitat selection, this article puts the IFD concept in a more general game-theoretic setting of the “habitat selection game”. Within this game-theoretic framework, the article focuses on recent progress in the following directions: (1) studying evolutionarily stable dispersal rates and corresponding dispersal dynamics; (2) extending the concept when population numbers are not fixed but undergo population dynamics; (3) generalizing the IFD to multiple species.For a single species, the article briefly reviews existing results. It also develops a new perspective for Parker’s matching principle, showing that this can be viewed as the IFD of the habitat selection game that models consumer behavior in several resource patches and analyzing complications involved when the model includes resource dynamics as well. For two species, the article first demonstrates that the connection between IFD and ESS is now more delicate by pointing out pitfalls that arise when applying several existing game-theoretic approaches to these habitat selection games. However, by providing a new detailed analysis of dispersal dynamics for predator-prey or competitive interactions in two habitats, it also pinpoints one approach that shows much promise in this general setting, the so-called “two-species ESS”. The consequences of this concept are shown to be related to recent studies of population dynamics combined with individual dispersal and are explored for more species or more patches.     

Male Migration in Barbary Macaques (Macaca sylvanus) at Affenberg Salem

We analyzed male migration during a 20-year period in the free-ranging Barbary macaque population of Affenberg Salem. Most natal migrations occurred around puberty, but only one third of all males left the natal group. Secondary group transfers were rare. All males immediately transferred to other bisexual groups. Migration rates were highest during periods with high adult female/male ratios within social groups. Immigrants highly preferred groups with fewer males of their own age than in the natal group, and many males immigrated into groups that had no male their own age. These groups originated from a skewed distribution of resident males during group fissions. A comparison of emigrants with their natal peers supports the inbreeding avoidance hypothesis as cause of emigration rather than the male competition avoidance hypothesis. Emigrants had no lower individual rank position and did not come from lower-ranking matrilines. Emigrants had more female maternal relatives, especially sisters. Males without female relatives almost never emigrated. Conversely, there is virtually no indication that emigrants were evicted from the natal group. Emigrants had no increased mortality. Paternity data revealed that the reproductive success of emigrants and natal males is similar, indicating that emigration had no reproductive cost. Many similarities between emigrants and natal males that separated from female maternal kin during group fissions suggest that inner migration during fissions is an alternative way to avoid maternal inbreeding. The mating system resulted in a genetic structure within social groups that largely diminished the chances for paternal inbreeding even without recognizing paternal kin.     

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.     

Effects of connectivity and recurrent local disturbances on community structure and population density in experimental metacommunities

Metacommunity theory poses that the occurrence and abundance of species is a product of local factors, including disturbance, and regional factors, like dispersal among patches. While metacommunity ideas have been broadly tested there is relatively little work on metacommunities subject to disturbance. We focused on how localized disturbance and dispersal interact to determine species composition in metacommunities. Experiments conducted in simple two-patch habitats containing eight protozoa and rotifer species tested how dispersal altered community composition in both communities that were disturbed and communities that connected to refuge communities not subject to disturbance. While disturbance lowered population densities, in disturbed patches connected to undisturbed patches this was ameliorated by immigration. Furthermore, species with high dispersal abilities or growth rates showed the fastest post-disturbance recovery in presence of immigration. Connectivity helped to counteract the negative effect of disturbances on local populations, allowing mass-effect-driven dispersal of individuals from undisturbed to disturbed patches. In undisturbed patches, however, local population sizes were not significantly reduced by emigration. The absence of a cost of dispersal for undisturbed source populations is consistent with a lack of complex demography in our system, such as age- or sex-specific emigration. Our approach provides an improved way to separate components of population growth from organisms' movement in post-disturbance recovery of (meta)communities. Further studies are required in a variety of ecosystems to investigate the transient dynamics resulting from disturbance and dispersal.     

Dispersal in a metapopulation of the bush cricket, Metrioptera bicolor (Orthoptera: Tettigoniidae)

1. I present a stochastic simulation model that describes individual movements of Metrioptera bicolor Philippi in a heterogeneous landscape, consisting of patches of suitable habitat surrounded by a matrix of unprofitable habitats. Although the model is parameterized with information about daily movement behaviour, it can generate spatially explicit predictions about inter-patch dispersal rates for much longer periods, e.g. one generation.
2. Long-term dispersal experiments were conducted to evaluate model predictions. Patch-specific emigration rates and the total distance moved by individuals could be predicted with satisfactory precision. Because of the stochastic nature of the model, it failed to predict which recipient patches emigrating individuals actually chose in a particular situation.
3. Spatially explicit simulations of the movement model were made for the whole natural distribution area of M. bicolor . The results suggest that emigration rates are negatively correlated with patch size. Local populations occurring on small patches may be more prone to extinction than those on large patches, by losing more emigrants than are compensated for by immigration.     

Scale‐dependent role of demography and dispersal on the distribution of populations in heterogeneous landscapes

Both dispersal and local demographic processes determine a population's distribution among habitats of varying quality, yet most theory, experiments, and field studies have focused on the former. We use a generic model to show how both processes contribute to a population's distribution, and how the relative importance of each mechanism depends on scale. In contrast to studies only considering habitat‐dependent dispersal, we show that predictions of ideal free distribution (IFD) theory are relevant even at landscape scales, where the assumptions of IFD theory are violated. This is because scales that inhibit one process, promote the other's ability to drive populations to the IFD. Furthermore, because multiple processes can generate IFDs, the pattern alone does not specify a causal mechanism. This is important because populations with IFDs generated by dispersal or demography respond much differently to shifts in resource distributions.     

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.     

Resource matching and population dynamics in a two-patch system

We study resource matching – the relationship between resource supply and forager numbers – under conditions of fluctuating population dynamics in a two-patch system. For the inter-patch dispersal we apply the patch-departure rule following the principle of the ideal free distribution: leave the current patch of residence if local conditions are worse than conditions elsewhere on average. We show that such a dispersal rule synchronises cyclic and chaotic local population dynamics, but unlike many other dispersal rules, leaves the underlying population dynamics untouched. We also show that the IFD dispersal rule is not very sensitive to biased information and navigation failures during the dispersal phase. Even under such circumstances we observe a quick process of populations becoming synchronised, even when the population dynamics are chaotic. We conclude that an IFD patch-departure rule represents an ESS dispersal behaviour towards which the dispersal patterns should evolve.     

Unnatural selection of salmon life histories in a modified riverscape

Altered river flows and fragmented habitats often simplify riverine communities and favor non‐native fishes, but their influence on life‐history expression and survival is less clear. Here, we quantified the expression and ultimate success of diverse salmon emigration behaviors in an anthropogenically altered California river system. We analyzed two decades of Chinook salmon monitoring data to explore the influence of regulated flows on juvenile emigration phenology, abundance, and recruitment. We then followed seven cohorts into adulthood using otolith (ear stone) chemical archives to identify patterns in time‐ and size‐selective mortality along the migratory corridor. Suppressed winter flow cues were associated with delayed emigration timing, particularly in warm, dry years, which was also when selection against late migrants was the most extreme. Lower, less variable flows were also associated with reduced juvenile and adult production, highlighting the importance of streamflow for cohort success in these southernmost populations. While most juveniles emigrated from the natal stream as fry or smolts, the survivors were dominated by the rare few that left at intermediate sizes and times, coinciding with managed flows released before extreme summer temperatures. The consistent selection against early (small) and late (large) migrants counters prevailing ecological theory that predicts different traits to be favored under varying environmental conditions. Yet, even with this weakened portfolio, maintaining a broad distribution in migration traits still increased adult production and reduced variance. In years exhibiting large fry pulses, even marginal increases in their survival would have significantly boosted recruitment. However, management actions favoring any single phenotype could have negative evolutionary and demographic consequences, potentially reducing adaptability and population stability. To recover fish populations and support viable fisheries in a warming and increasingly unpredictable climate, coordinating flow and habitat management within and among watersheds will be critical to balance trait optimization versus diversification.     

Area-dependent migration by ringlet butterflies generates a mixture of patchy population and metapopulation attributes

Interpretation of spatially structured population systems is critically dependent on levels of migration between habitat patches. If there is considerable movement, with each individual visiting several patches, there is one ”patchy population”; if there is intermediate movement, with most individuals staying within their natal patch, there is a metapopulation; and if (virtually) no movement occurs, then the populations are separate (Harrison 1991, 1994). These population types actually represent points along a continuum of much to no mobility in relation to patch structure. Therefore, interpretation of the effects of spatial structure on the dynamics of a population system must be accompanied by information on mobility. We use empirical data on movements by ringlet butterflies, Aphantopus hyperantus, to investigate two key issues that need to be resolved in spatially-structured population systems. First, do local habitat patches contain largely independent local populations (the unit of a metapopulation), or merely aggregations of adult butterflies (as in patchy populations)? Second, what are the effects of patch area on migration in and out of the patches, since patch area varies considerably within most real population systems, and because human landscape modification usually results in changes in habitat patch sizes? Mark-release-recapture (MRR) data from two spatially structured study systems showed that 63% and 79% of recaptures remained in the same patch, and thus it seems reasonable to call both systems metapopulations, with some capacity for separate local dynamics to take place in different local patches. Per capita immigration and emigration rates declined with increasing patch area, while the resident fraction increased. Actual numbers of emigrants either stayed the same or increased with area. The effect of patch area on movement of individuals in the system are exactly what we would have expected if A. hyperantus were responding to habitat geometry. Large patches acted as local populations (metapopulation units) and small patches simply as locations with aggregations (units of patchy populations), all within 0.5 km². Perhaps not unusually, our study system appears to contain a mixture of metapopulation and patchy-population attributes.     

Consequences of large-scale processes for the conservation of bird populations

1.  Detailed studies of population ecology are usually carried out in relatively restricted areas in which emigration and immigration play a role. We used a modelling approach to explore the population consequences of such dispersal and applied ideas from our simulations to the conservation of wild birds.
2.  Our spatial model incorporates empirically derived variation in breeding output between habitats, density dependence and dispersal. The outputs indicate that dispersal can have considerable consequences for population abundance and distribution. The abundance of a species within a patch can be markedly affected by the surrounding habitat matrix.
3.  Dispersal between habitats may result in lower population densities at the edge of good quality habitat blocks and could partially explain why some species are restricted to large habitat fragments.
4.  Habitat deterioration may not only lead to population declines within that habitat but also in adjacent habitats of good quality. This may confound studies attempting to diagnose population declines.
5.  Although mobile species have the advantages of colonizing sites within metapopulations, dispersal into poorer quality territories may markedly reduce total populations.
6.  There are two main approaches to conservation: one is to concentrate on establishing and maintaining protected areas, while the other involves conservation of the wider countryside. If dispersal is an important process then protecting only isolated areas may be insufficient to maintain the populations within them.     

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.     

Model assessments of the optimal design of nature reserves for maximizing species longevity

Using a computational model for the population growth and dispersal of a model species in a fluctuating environment, we test three nature reserve geometries (one large, many small, and a self-similar distribution of reserve sizes) to determine which geometry maximizes species longevity. The self-similar distribution is a close approximation to the distribution of managed areas in the conterminous United States. We consider models with and without migration from or between reserve fragments and both short- and long-range dispersal mechanisms. The optimal geometry depends on the type of dispersal and on the relative probability of survival in protected and non-protected areas. When no migration is allowed from or between reserve fragments of the three geometries, many small equally sized reserves are the optimal geometry. When migration is allowed, the optimal geometry is a single large reserve when the survivability in non-protected areas is low and a self-similar distribution when the survivability is high.     

Behavioural synchronization of large‐scale animal movements – disperse alone,but migrate together?

Dispersal and migration are superficially similar large‐scale movements, but which appear to differ in terms of inter‐individual behavioural synchronization. Seasonal migration is a striking example of coordinated behaviour, enabling animal populations to track spatio‐temporal variation in ecological conditions. By contrast, for dispersal, while social context may influence an individual's emigration and settlement decisions, transience is believed to be mostly a solitary behaviour. Here, we review differences in drivers that may explain why migration appears to be more synchronized than dispersal. We derive the prediction that the contrast in the importance of behavioural synchronization between dispersal and migration is linked to differences in the selection pressures that drive their respective evolution. Although documented examples of collective dispersal are rare, this behaviour may be more common than currently believed, with important consequences for eco‐evolutionary dynamics. Crucially, to date, there is little available theory for predicting when we should expect collective dispersal to evolve, and we also lack empirical data to test predictions across species. By reviewing the state of the art in research on migration and collective movements, we identify how we can harness these advances, both in terms of theory and data collection, to broaden our understanding of synchronized dispersal and its importance in the context of global change.     

Population structures and individual performances of <Emphasis Type="Italic">Trillium grandiflorum</Emphasis> in hedgerow and forest habitats

In agricultural landscapes, linear habitats, such as hedgerows at field margins increase structural connectivity among forest patches, potentially providing dispersal corridors for forest herbs. The spatial structure of linear habitats, however, also results in edge effects and perturbations that can influence the individual and population performance of forest plants. This study compares the stage structure and components of growth and reproduction of 14 Trillium grandiflorum populations in hedgerows and forests. Hedgerow Trillium tended to grow faster and, when mature, produced more flowers and more ovules per flowers than forest Trillium, a pattern possibly associated to differences in nutrients and light availability between the two habitats. Seed production and germination rate, however, did not differ between hedgerows and forests. At the population level, seedlings and juveniles were proportionally less abundant in hedgerows than in forests. Although well-established plants can thrive in hedgerows, reduced recruitment may eventually limit the capacity to establish new populations and therefore hamper migration along hedgerow-corridors. Considering the strategies by which plants persist in linear habitats becomes particularly relevant at a time when species are expected to be much in need of dispersal corridors because of climatic stress.