The evolution of dispersal

A non-local model for dispersal with continuous time and space is carefully justified and discussed. The necessary mathematical background is developed and we point out some interesting and challenging problems. While the basic model is not new, a spread parameter (effectively the width of the dispersal kernel) has been introduced along with a conventional rate paramter, and we compare their competitive advantages and disadvantages in a spatially heterogeneous environment. We show that, as in the case of reaction-diffusion models, for fixed spread slower rates of diffusion are always optimal. However, fixing the dispersal rate and varying the spread while assuming a constant cost of dispersal leads to more complicated results. For example, in a fairly general setting given two phenotypes with different, but small spread, the smaller spread is selected while in the case of large spread the larger spread is selected. S. Martinez was partially supported by Fondecyt 1020126 and Fondecyt Lineas Complementarias 8000010. K. Mischaikow was supported in part by NSF Grant DMS 0107396. Key words or phases:Non-local dispersal – Integral kernel – Evolution of dispersal     

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 color of noise and the evolution of dispersal

The process of dispersal is vital for the long-term persistence of all species and hence is a ubiquitous characteristic of living organisms. A present challenge is to increase our understanding of the factors that govern the dispersal rate of individuals. Here I extend previous work by incorporating both spatial and temporal heterogeneity in terms of patch quality into a spatially explicit lattice model. The spatial heterogeneity is modeled as a two-dimensional fractal landscape, while temporal heterogeneity is included by using one-dimensional noise. It was found that the color of both the spatial and temporal variability influences the rate of dispersal selected as reddening of the temporal noise leads to a reduction in dispersal, while reddening of spatial variability results in an increase in the dispersal rate. These results demonstrate that the color of environmental noise should be considered in future studies looking at the evolution of life history characteristics.     

Joint evolution of dispersal and inbreeding load

Inbreeding avoidance is often invoked to explain observed patterns of dispersal, and theoretical models indeed point to a possibly important role. However, while inbreeding load is usually assumed constant in these models, it is actually bound to vary dynamically under the combined influences of mutation, drift, and selection and thus to evolve jointly with dispersal. Here we report the results of individual-based stochastic simulations allowing such a joint evolution. We show that strongly deleterious mutations should play no significant role, owing to the low genomic mutation rate for such mutations. Mildly deleterious mutations, by contrast, may create enough heterosis to affect the evolution of dispersal as an inbreeding-avoidance mechanism, but only provided that they are also strongly recessive. If slightly recessive, they will spread among demes and accumulate at the metapopulation level, thus contributing to mutational load, but not to heterosis. The resulting loss of viability may then combine with demographic stochasticity to promote population fluctuations, which foster indirect incentives for dispersal. Our simulations suggest that, under biologically realistic parameter values, deleterious mutations have a limited impact on the evolution of dispersal, which on average exceeds by only one-third the values expected from kin-competition avoidance.     

Speciation and the evolution of dispersal along environmental gradients

We analyze the joint evolution of an ecological character and of dispersal distance in asexual and sexual populations inhabiting an environmental gradient. Several interesting phenomena resulting from the evolutionary interplay of these characters are revealed. First, asexual and sexual populations exhibit two analogous evolutionary regimes, in which either speciation in the ecological character occurs in conjunction with evolution of short-range dispersal, or dispersal distance remains high and speciation does not occur. Second, transitions between these two regimes qualitatively differ between asexual and sexual populations, with the former showing speciation with long-range dispersal and the latter showing no speciation with short-range dispersal. Third, a phenotypic gradient following the environmental gradient occurs only in the last case, i.e., for non-speciating sexual populations evolving towards short-range dispersal. Fourth, the transition between the evolutionary regimes of long-range dispersal with no speciation and short-range dispersal with speciation is typically abrupt, mediated by a positive feedback between incipient speciation and the evolution of short-range dispersal. Fifth, even though the model of sexual evolution analyzed here does not permit assortative mating preferences, speciation occurs for a surprisingly wide range of conditions. This illustrates that dispersal evolution is a powerful alternative to preference evolution in enabling spatially distributed sexual populations to respond to frequency-dependent disruptive selection.     

Centres of dispersal and evolution in the neotropical region

For the first time, centres of dispersal in the sense of De Lattin (1957) have been analysed for South and Central America. According to the results of this analysis, at least 40 centres have to be considered, the situation of which has been influenced by quaternary climatic fluctuations and vegetation fluctuations. The latest rate of differentiation of the faunal elements, which have to be associated with the centres (subspecific level) can be understood for a temporary indicator of the last function of the centres in the sense of centres of preservation of faunas and floras during regressive phases. The isolation of the montane forest centres occured before that of most of the lowland forest centres of the central and northern part of South America. During a postglacial arid phase, there has been a gene flow, via open migration roads, between numerous Amazonian Hylea‐Campo populations and populations of the costal savanna of Guiana, Venezuela and the Campo Cerrados. At the same time, these migration roads played the role of barriers of dispersal to the forest fauna and were reconquered by the forest at the end of the aridity phase. At the present time, transition zones of subspecificly differentiated forest populations can be found within the range of these old migration roads. Although the Campo Cerrado has been acting as a barrier of dispersal to forest species since the beginning of the postglacial arid phase, it had obviously been passed through by Amazonian and Serra‐do‐Mar faunal elements prior to that time. The location of the centres of dispersal and the differentiation of their faunal elements support the assumption that the great richness in species of neotropic biomes may be attributed to a large extent to quaternary biochore shifts and the resulting constant isolation of populations. Independent of this, however, numerous faunal elements indicate that this latest phase of differentiation is, in many cases, based on much older ones.     

Multigene families and the evolution of complexity

Summary Higher organisms are complex, and their developmental processes are controlled by the sequential expression of genes that often form multigene families. Facts are surveyed on how functional diversity of genes is related to duplication of genes or segments of genes, by emphasizing that diversity is often enhanced by alternate splicing and proteolytic cleavage involving duplicated genes or gene segments. Analyses of a population genetics model for the origin of gene families suggest that positive Darwinian selection is needed for acquiring gene families with desirable functions. Based on these considerations, examples that show acceleration of amino acid substitution relative to synonymous change during evolutionary processes are surveyed. Some of such examples strongly suggest that positive selection has worked. In other cases it is difficult to judge whether or not acceleration is caused by positive Darwinian selection. As a general pattern, acceleration of amino acid substitution is often found to be related to gene duplication. It is thought that complexity and diversity of gene function have been advantageous in the long evolutionary course of higher organisms.     

The combined effects of amino acid substitutions and indels on the evolution of structure within protein families

Background

In the process of protein evolution, sequence variations within protein families can cause changes in protein structures and functions. However, structures tend to be more conserved than sequences and functions. This leads to an intriguing question: what is the evolutionary mechanism by which sequence variations produce structural changes? To investigate this question, we focused on the most common types of sequence variations: amino acid substitutions and insertions/deletions (indels). Here their combined effects on protein structure evolution within protein families are studied.

Results

Sequence-structure correlation analysis on 75 homologous structure families (from SCOP) that contain 20 or more non-redundant structures shows that in most of these families there is, statistically, a bilinear correlation between the amount of substitutions and indels versus the degree of structure variations. Bilinear regression of percent sequence non-identity (PNI) and standardized number of gaps (SNG) versus RMSD was performed. The coefficients from the regression analysis could be used to estimate the structure changes caused by each unit of substitution (structural substitution sensitivity, SSS) and by each unit of indel (structural indel sensitivity, SIDS). An analysis on 52 families with high bilinear fitting multiple correlation coefficients and statistically significant regression coefficients showed that SSS is mainly constrained by disulfide bonds, which almost have no effects on SIDS.

Conclusions

Structural changes in homologous protein families could be rationally explained by a bilinear model combining amino acid substitutions and indels. These results may further improve our understanding of the evolutionary mechanisms of protein structures.     

On the evolution of multigene families

Multigene families are classified into three groups: small families as exemplified by hemoglobin genes of mammals; middlesize multigene families, by genes of mammalian histocompatibility antigens; and large multigene families, by variable region genes of immunoglobulins. Facts and theories on these evolving multigene families are reviewed, with special reference to the population genetics of their concerted evolution. It is shown that multigene families are evolving under continued occurrence of unequal (but homologous) crossing-over and gene conversion, and that mechanisms for maintaining genetic variability are totally different from the conventional models of population genetics. Thus, in view of widespread occurrence of multigene families in genomes of higher organisms, the evolutionary theory based mainly on change of gene frequency at each locus would appear to need considerable revision.     

Mutation surfing and the evolution of dispersal during range expansions

A growing body of empirical evidence demonstrates that at an expanding front, there can be strong selection for greater dispersal propensity, whereas recent theory indicates that mutations occurring towards the front of a spatially expanding population can sometimes ‘surf’ to high frequency and spatial extent. Here, we consider the potential interplay between these two processes: what role may mutation surfing play in determining the course of dispersal evolution and how might dispersal evolution itself influence mutation surfing? Using an individual‐based coupled‐map lattice model, we first run simulations to determine the fate of dispersal mutants that occur at an expanding front. Our results highlight that mutants that have a slightly higher dispersal propensity than the wild type always have a higher survival probability than those mutants with a dispersal propensity lower than, or very similar to, the wild type. However, it is not always the case that mutants with very high dispersal propensity have the greatest survival probability. When dispersal mortality is high, mutants of intermediate dispersal survive most often. Interestingly, the rate of dispersal that ultimately evolves at an expanding front is often substantially higher than that which confers a novel mutant with the greatest probability of survival. Second, we run a model in which we allow dispersal to evolve over the course of a range expansion and ask how the fate of a neutral or nonneutral mutant depends upon when and where during the expansion it arises. These simulations highlight that the success of a neutral mutant depends upon the dispersal genotypes that it is associated with. An important consequence of this is that novel mutants that arise at the front of an expansion, and survive, typically end up being associated with more dispersive genotypes than the wild type. These results offer some new insights into causes and the consequences of dispersal evolution during range expansions, and the methodology we have employed can be readily extended to explore the evolutionary dynamics of other life history characteristics.     

Conditional dispersal, clines, and the evolution of dispersiveness

Conditional dispersal, in which an individual’s decision over whether to disperse is a response to environmental conditions, features prominently in studies of dispersal evolution. Using models of clines, I examine how one widely discussed cost of dispersal, namely, that dispersal impedes local adaptation, changes with conditional dispersal and what this implies for dispersal evolution. I examine the consequences for dispersal evolution of the responsiveness of dispersal to the environment, the accuracy of any proximal cues that individuals rely upon to assess habitat quality, and whether dispersal responds to fitness itself or only to some fitness components (juvenile survivorship). All of the conditional dispersal behaviors that I consider weaken the indirect cost of dispersal inhibiting local adaptation. However, if individuals rely on imprecise cues to assess habitat quality and base dispersal decisions on juvenile survivorship, then conditional dispersal can incur additional costs by exacerbating overcrowding. Conditional dispersal initially leads to steeper clines in traits under direct selection, but when dispersiveness can itself evolve, conditional dispersal allows sigmoidal clines to persist long after those obtained with unconditional movement would become stepped. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Habitat persistence,habitat availability and the evolution of dispersal

Many organisms live in ephemeral habitats, making dispersal a vital element of life history. Here, we investigate how dispersal rate evolves in response to habitat persistence, mean habitat availability and landscape pattern. We show that dispersal rate is generally lowered by reduced habitat availability and by longer habitat persistence. However, for habitats that persist for an average of ten times the length of a generation, we show a clear non-monotonic relationship between habitat availability and dispersal rate. Some patterns of available habitat result in populations with dispersal polymorphisms. We explain these observations as a metapopulation effect, with the rate of evolution a function of both within-population and between-population selection pressures. Individuals in corridors evolve much lower dispersal rates than those in the mainland populations, especially within long, narrow corridors. We consider the implications of the results for conservation.     

Recruitment trade-offs and the evolution of dispersal mechanisms in plants

In this study we place seed size vs. seed number trade-offs in the context of plant dispersal ability. The objective was to suggest explanations for the evolution of different seed dispersal mechanisms, in particular fleshy fruits, wind dispersal and the maintenance of unassisted dispersal. We suggest that selection for improved dispersal may act either by increasing the intercept of a dispersal curve (log seed number vs. distance) or by flattening the slope of the curve. 'Improved dispersal' is defined as a marginal increase in the number of recruits sited at some (arbitrary) distance away from the parent plant. Increasing the intercept of the dispersal curve, i.e. producing more seeds, is associated with a reduction in seed size, which in turn affects the recruitment ability, provided that this ability is related to seed size. If recruitment is related to seed size there will be a recruitment cost of evolving increased seed production. On the other hand, a flattening of the slope by evolving dispersal attributes is likely to be associated with a fecundity cost. An exception is wind dispersal where smaller (and hence more numerous) seeds may lead to more efficient dispersal. We derive two main predictions: If recruitment is strongly related to seed size, selection for improved dispersal acts on the slope of the dispersal curve, i.e. by favouring evolution of dispersal attributes on seeds or fruits. If, on the other hand, recruitment is only weakly related to seed size (or not related, or negatively related), selection for improved dispersal favours increased seed production. Despite its simplicity, the model suggests explanations for (i) why so many plant species lack special seed dispersal attributes, (ii) differences in dispersal spectra among plant communities, and (iii) adaptive radiation in seed size and dispersal attributes during angiosperm evolution. This revised version was published online in July 2006 with corrections to the Cover Date.     

Sex differences in dispersal and the evolution of helping and harming

In this article, we explore the impact of sex-biased dispersal on local relatedness and on selection for helping and harming behavior among males and females. We show that in a patch-structured population, when there is a marked sex bias in dispersal, selection will almost always favor harming behavior among individuals of the sex more prone to dispersal. This result holds regardless of the effects of mating skew or overlapping generations. Selection may well also favor helping behavior among individuals of the philopatric sex, particularly if there is generational overlap, but this is less likely to occur if individuals of the philopatric sex compete more intensely for fewer breeding opportunities. In this last case, if generational overlap is low and mating skew pronounced, the result may be selection for harming behavior among both males and females. In general, the rate of dispersal and the level of relatedness among individuals of one sex do not reliably predict their level of helping or harming behavior; selection on either males or females depends on the dispersal of both sexes.     

The evolution of dispersal under demographic stochasticity

Temporal and spatial variations of the environment are important factors favoring the evolution of dispersal. With few exceptions, these variations have been considered to be exclusively fluctuations of habitat quality. However, since the presence of conspecifics forms part of an individual's environment, demographic stochasticity may be a component of this variability as well, in particular when local populations are small. To study this effect, we analyzed the evolution of juvenile dispersal in a metapopulation model in which habitat quality is constant in space and time but occupancy fluctuates because of demographic stochasticity. Our analysis extends previous studies in that it includes competition of resources and competition for space. Also, juvenile dispersal is not given by a fixed probability but is made conditional on the presence of free territories in a patch, whereas individuals born in full patches will always disperse. Using a combination of analytical and numerical approaches, we show that demographic stochasticity in itself may provide enough variability to favor dispersal even from patches that are not fully occupied. However, there is no simple relationship between the evolution of dispersal and various indicators of demographic stochasticity. Selected dispersal depends on all aspects of the life-history profile, including kin selection.     

Sex ratio evolution when fitness and dispersal vary

In a heterogeneous environment, when the fitness of males and females are differently influenced by habitat quality, habitat-dependent sex ratios may evolve to favor the production of the sex that benefits more (or loses less) from the local habitat. Similarly, sex-biased dispersal favors the evolution of habitat-dependent sex ratios. The present study documents the convergence stable sex ratios expected in the presence of sex-specific fitness gains when dispersal is partial, sex-biased or costly, using a simple model with patches of two qualities. Results show that partial dispersal reduces the sex ratio bias expected with sex-specific fitness gains. The direction of the sex ratio bias can be reversed by sex-biased dispersal or the existence of sex-specific dispersal costs, provided that fitness gains for the two sexes are not too different. The reversal of the sex ratio bias is more readily observed when sex-specific dispersal rates are opposite and extreme. Both dispersal and fitness gains, especially when they are sex-specific, should thus be considered when making predictions about sex ratio evolution in a heterogeneous environment.     

On several conjectures from evolution of dispersal

We address several conjectures raised in Cantrell et al. [Evolution of dispersal and ideal free distribution, Math. Biosci. Eng. 7 (2010), pp. 17-36 [ 9 ]] concerning the dynamics of a diffusion-advection-competition model for two competing species. A conditional dispersal strategy, which results in the ideal free distribution of a single population at equilibrium, was found in Cantrell et al. [ 9 ]. It was shown in [ 9 ] that this special dispersal strategy is a local evolutionarily stable strategy (ESS) when the random diffusion rates of the two species are equal, and here we show that it is a global ESS for arbitrary random diffusion rates. The conditions in [ 9 ] for the coexistence of two species are substantially improved. Finally, we show that this special dispersal strategy is not globally convergent stable for certain resource functions, in contrast with the result from [ 9 ], which roughly says that this dispersal strategy is globally convergent stable for any monotone resource function.     

On several conjectures from evolution of dispersal

We address several conjectures raised in Cantrell et al. [Evolution of dispersal and ideal free distribution, Math. Biosci. Eng. 7 (2010), pp. 17–36 [9 Cantrell, R. S., Cosner, C. and Lou, Y. 2010. Evolution of dispersal and ideal free distribution. Math. Biosci. Eng., 7: 17–36. [Crossref], [PubMed], [Web of Science ®] , [Google Scholar]]] concerning the dynamics of a diffusion–advection–competition model for two competing species. A conditional dispersal strategy, which results in the ideal free distribution of a single population at equilibrium, was found in Cantrell et al. [9 Cantrell, R. S., Cosner, C. and Lou, Y. 2010. Evolution of dispersal and ideal free distribution. Math. Biosci. Eng., 7: 17–36. [Crossref], [PubMed], [Web of Science ®] , [Google Scholar]]. It was shown in [9 Cantrell, R. S., Cosner, C. and Lou, Y. 2010. Evolution of dispersal and ideal free distribution. Math. Biosci. Eng., 7: 17–36. [Crossref], [PubMed], [Web of Science ®] , [Google Scholar]] that this special dispersal strategy is a local evolutionarily stable strategy (ESS) when the random diffusion rates of the two species are equal, and here we show that it is a global ESS for arbitrary random diffusion rates. The conditions in [9 Cantrell, R. S., Cosner, C. and Lou, Y. 2010. Evolution of dispersal and ideal free distribution. Math. Biosci. Eng., 7: 17–36. [Crossref], [PubMed], [Web of Science ®] , [Google Scholar]] for the coexistence of two species are substantially improved. Finally, we show that this special dispersal strategy is not globally convergent stable for certain resource functions, in contrast with the result from [9 Cantrell, R. S., Cosner, C. and Lou, Y. 2010. Evolution of dispersal and ideal free distribution. Math. Biosci. Eng., 7: 17–36. [Crossref], [PubMed], [Web of Science ®] , [Google Scholar]], which roughly says that this dispersal strategy is globally convergent stable for any monotone resource function.