Evolution of migration rate in a spatially realistic metapopulation model

We use an individual-based, spatially realistic metapopulation model to study the evolution of migration rate. We first explore the consequences of habitat change in hypothetical patch networks on a regular lattice. If the primary consequence of habitat change is an increase in local extinction risk as a result of decreased local population sizes, migration rate increases. A nonmonotonic response, with migration rate decreasing at high extinction rate, was obtained only by assuming very frequent catastrophes. If the quality of the matrix habitat deteriorates, leading to increased mortality during migration, the evolutionary response is more complex. As long as habitat patch occupancy does not decrease markedly with increased migration mortality, reduced migration rate evolves. However, once mortality becomes so high that empty patches remain uncolonized for a long time, evolution tends to increase migration rate, which may lead to an "evolutionary rescue" in a fragmented landscape. Kin competition has a quantitative effect on the evolution of migration rate in our model, but these patterns in the evolution of migration rate appear to be primarily caused by spatiotemporal variation in fitness and mortality during migration. We apply the model to real habitat patch networks occupied by two checkerspot butterfly (Melitaea) species, for which sufficient data are available to estimate rigorously most of the model parameters. The model-predicted migration rate is not significantly different from the empirically observed one. Regional variation in patch areas and connectivities leads to regional variation in the optimal migration rate, predictions that can be tested empirically.     

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.     

Evolution of reproductive effort in a metapopulation with local extinctions and ecological succession

Abstract Using a metapopulation model, we study how local extinctions, limited population life span, and local demographic disequilibrium affect the evolution of the reproductive effort in a species with overlapping generations but no senescence. We show that in a metapopulation with saturation of all sites and an infinite deme maximal life span (no succession), local extinctions simply constitute an additional source of extrinsic mortality. When either the hypothesis of an infinite deme maximal life span or the saturation hypothesis is relaxed, nontrivial predictions arise. in particular, we find interactions between the evolutionarily stable reproductive effort strategy and the demographic dynamics in the metapopulation. We predict that larger reproductive effort may be selected for in habitats of poorer productivity, contrary to what would be predicted in a single population. Also, we predict that higher dispersal rates should favor selection for lower reproductive efforts. However, metapopulation parameters that favor high dispersal rates also favor larger reproductive efforts. Conflicting selection pressures in the metapopulation also allow maintaining evolutionarily stable polymorphism between a low and high reproductive effort for particular trade-offs between survival and fecundity.     

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.     

Evolution of migration in a periodically changing environment

The ability to migrate can evolve in response to various forces. In particular, when selection is heterogeneous in space but constant in time, local adaptation induces a fitness cost on immigrants and selects against migration. The evolutionary outcome, however, is less clear when selection also varies temporally. Here, we present a two-locus model analyzing the effects of spatial and temporal variability in selection on the evolution of migration. The first locus is under temporally varying selection (various periodic functions are considered, but a general nonparametric framework is used), and the second locus is a modifier controlling migration ability. First, we study the dynamics of local adaptation and derive the migration rate that maximizes local adaptation as a function of the speed and geometry of the fluctuations in the environment. Second, we derive an analytical expression for the evolutionarily stable migration rate. When there is no cost of migration, we show that higher migration rates are favored when selection changes fast. When migration is costly, however, the evolutionarily stable migration rate is maximal for an intermediate speed of the variation of selection. This model may help in understanding the evolution of migration in a broad range of scenarios and, in particular, in host-parasite systems, where selection is thought to vary quickly in both space and time.     

Evolution of bird migration in a biogeographical context

We infer from the literature that migratory habits of birds evolved in various phylogenetic lineages and biogeographical contexts, either after gradual range expansion into seasonal habitats, or due to environmental changes within established breeding ranges. Shifts of breeding ranges are the results of interactions between colonization due to dispersal and extinction due to deteriorating conditions. Range expansions provide a platform for the evolution of migration from the newly colonized areas towards seasonally favourable non‐breeding areas. A comparison of palaeoclimatic changes with concurrent evolution and distribution of passerine birds suggests that at least some of the basic genera of the Passerida radiated on the northern continents when quasi‐tropical or subtropical climates prevailed. The Passerida may be a special case, but they suggest that ‘tropical origin’ does not necessarily imply a ‘southern origin’ of migratory species. Climate deterioration required adaptations either towards on‐site survival under harsh conditions or towards escape movements allowing improved non‐breeding survival in less seasonal climates or with reversed seasonality. Taxon‐specific life‐history traits and environmental conditions favoured either sedentary or migratory lines of adaptation. Repeated climate variation induced range shifts and concurrent increases or decreases in the expression of migratory behaviour. Two examples of waders suggest that the principle of range shift, followed by the development of migratory habits, is also applicable for other taxonomic groups.     

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.     

Gene genealogies in a metapopulation

A simple genealogical process is found for samples from a metapopulation, which is a population that is subdivided into a large number of demes, each of which is subject to extinction and recolonization and receives migrants from other demes. As in the migration-only models studied previously, the genealogy of any sample includes two phases: a brief sample-size adjustment followed by a coalescent process that dominates the history. This result will hold for metapopulations that are composed of a large number of demes. It is robust to the details of population structure, as long as the number of possible source demes of migrants and colonists for each deme is large. Analytic predictions about levels of genetic variation are possible, and results for average numbers of pairwise differences within and between demes are given. Further analysis of the expected number of segregating sites in a sample from a single deme illustrates some previously known differences between migration and extinction/recolonization. The ancestral process is also amenable to computer simulation. Simulation results show that migration and extinction/recolonization have very different effects on the site-frequency distribution in a sample from a single deme. Migration can cause a U-shaped site-frequency distribution, which is qualitatively similar to the pattern reported recently for positive selection. Extinction and recolonization, in contrast, can produce a mode in the site-frequency distribution at intermediate frequencies, even in a sample from a single deme.     

Synchronism in a metapopulation model

We consider a spatially explicit metapopulation model with interaction among the two nearest neighbors to relate, with a simple mathematical expression, chaos in the local, uncoupled, populations, the degree of interaction among patches, size of the metapopulation, and the stability of the synchronized attractor. Since synchronism is strongly correlated with extinction, our results can provide useful information on factors leading to population extinction.     

Chaotic dynamics may determine the effect of inter-patch migration on metapopulation survival

A simple, strategic model of a system of habitat fragments connected by conservation corridors is presented. The intrinsic dynamics of the population on each fragment are stochastic. In addition, at each generation there is a probability of a catastrophic event occurring which affects all the habitat fragments by greatly reducing the size of the population on each. Global extinction is considered to occur when all the populations simultaneously fall below a threshold value. If the intrinsic dynamics on each fragment are simple cycles or a stable equilibrium, then the addition of conservation corridors does not reduce the frequency of global extinction. This is because migration between fragments induces their populations to have values which are similar to each other. However, if the intrinsic population dynamics are chaotic then the probability of global extinction is greatly reduced by the introduction of conservation corridors. Although local extinction is likely, the chaos acts to oppose the synchronising effect of migration. Often a subset of the populations survive a catastrophe and can recolonize the other patches.     

Cultural niche construction in a metapopulation

Cultural niche construction is the process by which certain evolving cultural traits form a cultural niche that affects the evolution of other genetic and cultural traits [Laland, K., et al., 2001. Cultural niche construction and human evolution. J. Evol. Biol. 14, 22-33; Ihara, Y., Feldman, M., 2004. Cultural niche construction and the evolution of small family size. Theor. Popul. Biol. 65, 105-111]. In this study we focus on cultural niche construction in a metapopulation (a population of populations), where the frequency of one cultural trait (e.g. the level of education) determines the transmission rate of a second trait (e.g. the adoption of fertility reduction preferences) within and between populations. We formulate the Metapopulation Cultural Niche Construction (MPCNC) model by defining the cultural niche induced by the first trait as the construction of a social interaction network on which the second trait may percolate. Analysis of the model reveals dynamics that are markedly different from those observed in a single population, allowing, for example, different (or even opposing) dynamics in each population. In particular, this model can account for the puzzling phenomenon reported in previous studies [Bongaarts, J., Watkins, S., 1996. Social interactions and contemporary fertility transitions. Popul. Dev. Rev. 22 (4), 639-682] that the onset of the demographic transition in different countries occurred at ever lower levels of development.     

Neutral additive genetic variance in a metapopulation

For neutral, additive quantitative characters, the amount of additive genetic variance within and among populations is predictable from Wright's FST, the effective population size and the mutational variance. The structure of quantitative genetic variance in a subdivided metapopulation can be predicted from results from coalescent theory, thereby allowing single-locus results to predict quantitative genetic processes. The expected total amount of additive genetic variance in a metapopulation of diploid individual is given by 2Ne sigma m2 (1 + FST), where FST is Wright's among-population fixation index, Ne is the eigenvalue effective size of the metapopulation, and sigma m2 is the mutational variance. The expected additive genetic variance within populations is given by 2Ne sigma e2(1-FST), and the variance among demes is given by 4FSTNe sigma m2. These results are general with respect to the types of population structure involved. Furthermore, the dimensionless measure of the quantitative genetic variance among populations, QST, is shown to be generally equal to FST for the neutral additive model. Thus, for all population structures, a value of QST greater than FST for neutral loci is evidence for spatially divergent evolution by natural selection.     

Dispersal-related life-history trade-offs in a butterfly metapopulation

1. Recent studies on butterflies have documented apparent evolutionary changes in dispersal rate in response to climate change and habitat change. These studies often assume a trade-off between dispersal rate (or flight capacity) and reproduction, which is the rule in wing-dimorphic species but might not occur equally in wing-monomorphic species such as butterflies. 2. To investigate the relationship between dispersal rate and fecundity in the Glanville fritillary butterfly Melitaea cinxia we recorded lifetime individual movements, matings, ovipositions, and maximal life span in a large (32 x 26 m) population cage in the field. Experimental material was obtained from 20 newly established and 20 old local populations within a large metapopulation in the Aland Islands in Finland. 3. Females of the Glanville fritillary from newly established populations are known to be more dispersive in the field, and in the cage they showed significantly greater mobility, mated earlier, and laid more egg clutches than females from old populations. The dispersive females from new populations exhibited no reduced lifetime fecundity in the cage, but they had a shorter maximal life span than old-population females. 4. These results challenge the dispersal-fecundity trade-off for nonmigratory butterflies but instead suggest a physiological trade-off between high metabolic performance and reduced maximal life span. High metabolic performance may explain high rates of dispersal and oviposition in early life. 5. In fragmented landscapes, an ecological trade-off exists between being more dispersive and hence spending more time in the landscape matrix vs. having more time for reproduction in the habitat. We estimate with a dispersal model parameterized for the Glanville fritillary that the lifetime egg production is 4% smaller on average in the more dispersive butterflies in a representative landscape, with much variation depending on landscape structure in the neighbourhood of the natal patch, from--26 to 45% in the landscape analysed in this paper.     

Effects of dispersal in a tri-trophic metapopulation model

The aim of this paper is to understand how dispersal in a patchy environment influences the stability properties of tri-trophic metapopulations. Differential equation models for tri-trophic metapopulations are formulated and analysed. The patchy nature of the metapopulations is incorporated through dispersal phases. Two variants are studied: one with a dispersal phase for the top and one with a dispersal phase for the middle level. A complete characterisation of stable and unstable equilibria is given and the possibility of invasion in these food chains is studied. A dispersal phase for the middle level can destabilize the bottom level-middle level interaction, because of the delay that dispersal causes in the reaction to the resource. When the middle level is not efficiently controlled by the top level, the unstable bottom level-middle level pair can destabilize the entire food chain. Dispersal for the top level can destabilize in the same way. A characterisation of the long term behaviour of the models is given. Bistability with a stable three species equilibrium and a stable limit cycle is one of the possibilities.     

Optimal harvesting strategies for a metapopulation

We consider optimal strategies for harvesting a population that is composed of two local populations. The local populations are connected by the dispersal of juveniles, e.g. larvae, and together form a metapopulation. We model the metapopulation dynamics using coupled difference equations. Dynamic programming is used to determine policies for exploitation that are economically optimal. The metapopulation harvesting theory is applied to a hypothetical fishery and optimal strategies are compared to harvesting strategies that assume the metapopulation is composed either of single unconnected populations or of one well-mixed population. Local populations that have high per capita larval production should be more conservatively harvested than would be predicted using conventional theory. Recognizing the metapopulation structure of a stock and using the appropriate theory can significantly improve economic gains.     

Strong inbreeding depression in a Daphnia metapopulation

The deleterious effects of inbreeding have long been known, and inbreeding can increase the risk of extinction for local populations in metapopulations. However, other consequences of inbreeding in metapopulations are still not well understood. Here we show the presence of strong inbreeding depression in a rockpool metapopulation of the planktonic freshwater crustacean Daphnia magna, which reproduces by cyclical parthenogenesis. We conducted three experiments in real and artificial rockpools to quantify components of inbreeding depression in the presence and the absence of competition between clonal lines of selfed and outcrossed genotypes. In replicated asexual populations, we recorded strong selection against clones produced by selfing in competition with clones produced by outcrossing. In contrast, inbreeding depression was much weaker in single-clone populations, that is, in the absence of competition between inbred and outbred clones. The finding of a competitive advantage of the outbred genotypes in this metapopulation suggests that if rockpool populations are inbred, hybrid offspring resulting from crosses between immigrants and local genotypes might have a strong selective advantage. This would increase the effective gene flow in the metapopulation. However, the finding of low inbreeding depression in the monoclonal populations suggests that inbred and outbred genotypes might have about equal chances of establishing new populations.     

Dynamics of speciation and diversification in a metapopulation

We develop a simple framework for modeling speciation and diversification as a continuous process of accumulation of genetic (or morphological) differences accompanied by species and subpopulation extinction and/or range expansion. This framework can be used to approach a number of questions such as species-area distribution, species-range size distribution, the rate of ecological turnover, asymmetries of range division between sister species, waiting time until speciation and extinction, the relationship between the geographic range size and the probability of speciation, the relationships between subpopulation-level parameters and metapopulation-level parameters, and the effects of taxonomic level on these rates, distributions, and parameters. We illustrate some of these applications using numerical simulations. We develop approximations describing the dependence of the number of different taxonomic units, their average range size, and the rate of their turnover on the system size, the rate of fixation of genetic (or morphological) changes in local demes, and the rate of local extinction and colonization.