Evolution of dispersal in density regulated populations: A haploid model

The evolution of dispersal is explored in a density-dependent framework. Attention is restricted to haploid populations in which the genotypic fitnesses at a single diallelic locus are decreasing functions of the changing number of individuals in the population. It is shown that migration between two populations in which the genotypic response to density is reversed can maintain both alleles when the intermigration rates are constant or nondecreasing functions of the population densities. There is always a unique symmetric interior equilibrium with equal numbers but opposite gene frequencies in the two populations, provided the system is not degenerate. Numerical examples with exponential and hyperbolic fitnesses suggest that this is the only stable equilibrium state under constant positive migration rates (m) less than . Practically speaking, however, there is only convergence after a reasonable number of generations for relatively small migration rates ( ). A migration-modifying mutant at a second, neutral locus, can successfully enter two populations at a stable migration-selection balance if and only if it reduces the intermigration rates of its carriers at the original equilibrium population size. Moreover, migration modification will always result in a higher equilibrium population size, provided the system approaches another symmetric interior equilibrium. The new equilibrium migration rate will be lower than that at the original equilibrium, even when the modified migration rate is a nondecreasing function of the population sizes. Therefore, as in constant viability models, evolution will lead to reduced dispersal.     

TESTING MODELS OF MIGRATION AND ISOLATION AMONG POPULATIONS OF CHINOOK SALMON (ONCORHYNCHUS TSCHAWYTSCHA)

The chinook salmon (Oncorhynchus tschawytscha) is a behaviorally, morphologically, and ecologically variable species distributed over a large geographic range. Although previous genetic surveys have revealed considerable genetic differences among populations with different life history types and from different major river drainages, it is not clear to what degree these genetically distinct populations are connected by low levels of gene flow. The work described in this paper addresses this question by surveying DNA restriction site variation at six nuclear genes from nine populations encompassing most of the species's North American range, and then attempting to fit the patterns of variation observed at these genes to five different evolutionary models using computer simulations of the coalescent process. Two commonly used constant population size models, one hypothesizing no migration among populations and one hypothesizing equal rates of migration among populations, were found to be statistically inconsistent with the observed patterns of variation. The other three models, which involved either recent divergence among populations coupled with large changes in populations size, unequal migration rates among populations, or selection, were all found to be consistent with the observed patterns of variation. Assuming selective neutrality, these results suggest that either the populations have all descended from a common ancestral population within the last ~50,000 years and have all suffered large declines in effective population size since that time, or that they have a more ancient divergence time but are connected by low levels of gene flow. These conclusions rest on the assumption of selective neutrality. With the methods employed, it was not possible to simultaneously test hypotheses of both selective neutrality and population structure.     

Inferring landscape resistance to gene flow when genetic drift is spatially heterogeneous

In connectivity models, land cover types are assigned cost values characterizing their resistance to species movements. Landscape genetic methods infer these values from the relationship between genetic differentiation and cost distances. The spatial heterogeneity of population sizes, and consequently genetic drift, is rarely included in this inference although it influences genetic differentiation. Similarly, migration rates and population spatial distributions potentially influence this inference. Here, we assessed the reliability of cost value inference under several migration rates, population spatial patterns and degrees of population size heterogeneity. Additionally, we assessed whether considering intra-population variables, here using gravity models, improved the inference when drift is spatially heterogeneous. We simulated several gene flow intensities between populations with varying local sizes and spatial distributions. We then fit gravity models of genetic distances as a function of (i) the ‘true’ cost distances driving simulations or alternative cost distances, and (ii) intra-population variables (population sizes, patch areas). We determined the conditions making the identification of the ‘true’ costs possible and assessed the contribution of intra-population variables to this objective. Overall, the inference ranked cost scenarios reliably in terms of similarity with the ‘true’ scenario (cost distance Mantel correlations), but this ‘true’ scenario rarely provided the best model goodness of fit. Ranking inaccuracies and failures to identify the ‘true’ scenario were more pronounced when migration was very restricted (<4 dispersal events/generation), population sizes were most heterogeneous and some populations were spatially aggregated. In these situations, considering intra-population variables helps identify cost scenarios reliably, thereby improving cost value inference from genetic data.     

Density-dependent migration and human population structure in historical Massachusetts

Studies of population structure often focus on the effects of population size and migration rates on genetic variation. Few studies, however, have investigated the relationship between these two factors. The purpose of this paper is to determine the extent to which migration (and gene flow) is density-dependent (that is, affected by population size) for populations in historical Massachusetts. Data from 4,859 marriage records were analyzed from four populations in north-central Massachusetts during the time period 1741 to 1849. These data were placed into 29 samples defined in terms of population and time cohort. Within each cohort the overall exogamy rate was computed along with three estimates of gene flow based on marital migration: local migration (k), long-distance migration (m), and effective migration rate (me). Three samples show unusually low rates that reflect the history of settlement. Regression analyses were used with the remaining samples, and they show nonlinear density-dependent migration that is unrelated to temporal trends. Migration is highest in samples with small population sizes (less than 800) and large population sizes (greater than 1,600). Migration is lowest in medium-sized populations. Two processes are suggested to explain this curvilinear relationship of migration and population size. In small populations, the lack of suitable potential mates and/or availability of settled land leads to an increase in migration into the population. As population size increases, this migration decreases. After populations reach a certain size, migration increases again, most likely reflecting the economic pull of larger populations. These patterns could act to enhance, or counter, genetic drift, depending on the direction of density dependence.     

Influence of Gene Flow and Breeding Tactics on Gene Diversity within Populations

Expressions describing the accumulation of gene correlations within and among lineages and individuals of a population are derived. The model permits different migration rates by males and females and accounts for various breeding tactics within lineages. The resultant equations enable calculation of the probabilistic quantities for the fixation indices, rates of loss of genetic variation, accumulation of inbreeding, and coefficients of relationship for the population at any generation. All fixation indices were found to attain asymptotic values rapidly despite the consistent loss of genetic variation and accumulation of inbreeding within the population. The time required to attain asymptotic values, however, was prolonged when gene flow among lineages was relatively low (less than 20%). The degree of genetic differentiation among breeding groups, inbreeding coefficients, and gene correlations within lineages were found to be primarily functions of breeding tactics within groups rather than gene flow among groups. Thus, the asymptotic value of S. Wright's island model is not appropriate for describing genetic differences among groups within populations. An alternative solution is provided that under limited conditions will reduce to the original island model. The evolution of polygynous breeding tactics appears to be more favorable for promoting intragroup gene correlations than modification of migration rates. Inbreeding and variance effective sizes are derived for populations that are structured by different migration and breeding tactics. Processes that reduce the inbreeding effective population size result in a concomitant increase in variance effective population size.     

Inferring number of populations and changes in connectivity under the n-island model

Inferring the demographic history of species is one of the greatest challenges in populations genetics. This history is often represented as a history of size changes, ignoring population structure. Alternatively, when structure is assumed, it is defined a priori as a population tree and not inferred. Here we propose a framework based on the IICR (Inverse Instantaneous Coalescence Rate). The IICR can be estimated for a single diploid individual using the PSMC method of Li and Durbin (2011). For an isolated panmictic population, the IICR matches the population size history, and this is how the PSMC outputs are generally interpreted. However, it is increasingly acknowledged that the IICR is a function of the demographic model and sampling scheme with limited connection to population size changes. Our method fits observed IICR curves of diploid individuals with IICR curves obtained under piecewise stationary symmetrical island models. In our models we assume a fixed number of time periods during which gene flow is constant, but gene flow is allowed to change between time periods. We infer the number of islands, their sizes, the periods at which connectivity changes and the corresponding rates of connectivity. Validation with simulated data showed that the method can accurately recover most of the scenario parameters. Our application to a set of five human PSMCs yielded demographic histories that are in agreement with previous studies using similar methods and with recent research suggesting ancient human structure. They are in contrast with the view of human evolution consisting of one ancestral population branching into three large continental and panmictic populations with varying degrees of connectivity and no population structure within each continent.Subject terms: Population genetics, Biological models, Population genetics     

When does gene flow facilitate evolutionary rescue?

Experimental and theoretical studies have highlighted the impact of gene flow on the probability of evolutionary rescue in structured habitats. Mathematical modeling and simulations of evolutionary rescue in spatially or otherwise structured populations showed that intermediate migration rates can often maximize the probability of rescue in gradually or abruptly deteriorating habitats. These theoretical results corroborate the positive effect of gene flow on evolutionary rescue that has been identified in experimental yeast populations. The observations that gene flow can facilitate adaptation are in seeming conflict with traditional population genetics results that show that gene flow usually hampers (local) adaptation. Identifying conditions for when gene flow facilitates survival chances of populations rather than reducing them remains a key unresolved theoretical question. We here present a simple analytically tractable model for evolutionary rescue in a two-deme model with gene flow. Our main result is a simple condition for when migration facilitates evolutionary rescue, as opposed as no migration. We further investigate the roles of asymmetries in gene flow and/or carrying capacities, and the effects of density regulation and local growth rates on evolutionary rescue.     

Effective Sizes for Subdivided Populations

Many derivations of effective population sizes have been suggested in the literature; however, few account for the breeding structure and none can readily be expanded to subdivided populations. Breeding structures influence gene correlations through their effects on the number of breeding individuals of each sex, the mean number of progeny per female, and the variance in the number of progeny produced by males and females. Additionally, hierarchical structuring in a population is determined by the number of breeding groups and the migration rates of males and females among such groups. This study derives analytical solutions for effective sizes that can be applied to subdivided populations. Parameters that encapsulate breeding structure and subdivision are utilized to derive the traditional inbreeding and variance effective sizes. Also, it is shown that effective sizes can be determined for any hierarchical level of population structure for which gene correlations can accrue. Derivations of effective sizes for the accumulation of gene correlations within breeding groups (coancestral effective size) and among breeding groups (intergroup effective size) are given. The results converge to traditional, single population measures when similar assumptions are applied. In particular, inbreeding and intergroup effective sizes are shown to be special cases of the coancestral effective size, and intergroup and variance effective sizes will be equal if the population census remains constant. Instantaneous solutions for effective sizes, at any time after gene correlation begins to accrue, are given in terms of traditional F statistics or transition equations. All effective sizes are shown to converge upon a common asymptotic value when breeding tactics and migration rates are constant. The asymptotic effective size can be expressed in terms of the fixation indices and the number of breeding groups; however, the rate of approach to the asymptote is dependent upon dispersal rates. For accurate assessment of effective sizes, initial, instantaneous or asymptotic, the expressions must be applied at the lowest levels at which migration among breeding groups is nonrandom. Thus, the expressions may be applicable to lineages within socially structured populations, fragmented populations (if random exchange of genes prevails within each population), or combinations of intra- and interpopulation discontinuities of gene flow. Failure to recognize internal structures of populations may lead to considerable overestimates of inbreeding effective size, while usually underestimating variance effective size.     

Pervasive migration across rainforest and sandy coastal plain Aechmea nudicaulis (Bromeliaceae) populations despite contrasting environmental conditions

Understanding the colonization of extreme marginal habitats and the relative roles of space and environment in maintaining peripheral populations remains challenging. Here, we leverage a system of pairs of rainforest and sandy coastal plain communities that allow us to decouple spatial and environmental effects in the population structure and migration rates of the bromeliad Aechmea nudicaulis. Structure and gene flow between populations were estimated from Bayesian clustering and coalescent‐based migration models applied to chloroplast sequence and nuclear microsatellite data. Contrary to our initial expectation, the sharp environmental gradient between rainforest and sandy plains does not seem to have affected the colonization and migration dynamics in A. nudicaulis. Our analyses uncover pervasive gene flow between neighbouring habitats in both chloroplast and nuclear data despite the striking differences in environmental conditions. This result is consistent with a scenario of repeated colonization of the sandy coastal plains from forest populations through seed dispersal, as well as the maintenance of gene flow between habitats through pollination. We also recovered a broad north/south population structure that has been found in other Atlantic rainforest groups and possibly reflects older phylogeographic dynamics.     

Population structure and gene flow reversals in Atlantic salmon (Salmo salar) over contemporary and long-term temporal scales: effects of population size and life history

Metapopulation dynamics are increasingly invoked in management and conservation of endangered species. In this context, asymmetrical gene flow patterns can be density dependent, with migration occurring mainly from larger into smaller populations, which may depend on it for their persistence. Using genetic markers, such patterns have recently been documented for various organisms including salmonids, suggesting this may be a more general pattern. However, metapopulation theory does not restrict gene flow asymmetry to 'source-sink' structures, nor need these patterns be constant over longer evolutionary timescales. In anadromous salmonids, gene flow can be expected to be shaped by various selective pressures underlying homing and dispersal ('straying') behaviours. The relative importance of these selective forces will vary spatially and for populations of different census size. Furthermore, the consequences of life-history variation among populations for dispersal and hence gene flow remain poorly quantified. We examine population structure and connectivity in Atlantic salmon (Salmo salar L.) from Newfoundland and Labrador, a region where populations of this species are relatively pristine. Using genetic variation at 13 microsatellite loci from samples (N=1346) collected from a total of 20 rivers, we examine connectivity at several regional and temporal scales and test the hypothesis that the predominant direction of gene flow is from large into small populations. We reject this hypothesis and find that the directionality of migration is affected by the temporal scale over which gene flow is assessed. Whereas large populations tend to function as sources of dispersal over contemporary timescales, such patterns are often changed and even reversed over evolutionary, coalescent-derived timescales. These patterns of population structure furthermore vary between different regions and are compatible with demographic and life-history attributes. We find no evidence for sex-biased dispersal underlying gene flow asymmetry. Our findings caution against generalizations concerning the directionality of gene flow in Atlantic salmon and emphasize the need for detailed regional study, if such information is to be meaningfully applied in conservation and management of salmonids.     

Evolution of microbial genomes: sequence acquisition and loss

We present models describing the acquisition and deletion of novel sequences in populations of microorganisms. We infer that most novel sequences are neutral. Thus, sequence duplications and gene transfer between organisms sharing the same environment are rarely expected to generate adaptive functions. Two classes of models are considered: (1) a homogeneous population with constant size, and (2) an island model in which the population is subdivided into patches that are in contact through slow migration. Distributions of gene frequencies are derived in a Moran model with overlapping generations. We find that novel, neutral or near-neutral coding sequences in microorganisms will not be fixed globally because they offer large target sizes for mutations and because the populations are so large. At most, such genes may have a transient presence in only a small fraction of the population. Consequently, a microbial population is expected to have a very large diversity of transient neutral gene content. Only sequences that are under strong selection, globally or in individual patches, can be expected to persist. We suggest that genome size is maintained in microorganisms by a quasi-steady state mechanism in which random fluctuations in the effective acquisition and deletion rates result in genome sizes that vary from patch to patch. We assign the genomic identity of a global population to those genes that are required for the participation of patches in the genetic sweeps that maintain the genomic coherence of the population. In contrast, we stress the influence of sequence loss on the isolation and the divergence (speciation) of novel patches from a global population.     

Effects of migration on the genetic covariance matrix

In 1996, Schluter showed that the direction of morphological divergence of closely related species is biased toward the line of least genetic resistance, represented by g_max , the leading eigenvector of the matrix of genetic variance–covariance (the G -matrix). G is used to predict the direction of evolutionary change in natural populations. However, this usage requires that G is sufficiently constant over time to have enough predictive significance. Here, we explore the alternative explanation that G can evolve due to gene flow to conform to the direction of divergence between incipient species. We use computer simulations in a mainland–island migration model with stabilizing selection on two quantitative traits. We show that a high level of gene flow from a mainland population is required to significantly affect the orientation of the G -matrix in an island population. The changes caused by the introgression of the mainland alleles into the island population affect all aspects of the shape of G (size, eccentricity, and orientation) and lead to the alignment of g_max with the line of divergence between the two populations' phenotypic optima. Those changes decrease with increased correlation in mutational effects and with a correlated selection. Our results suggest that high migration rates, such as those often seen at the intraspecific level, will substantially affect the shape and orientation of G , whereas low migration (e.g., at the interspecific level) is unlikely to substantially affect the evolution of G .     

What shapes local density? The importance of migration rates and local growth for density‐patch size relationships in two Cionus weevils

1. The relative effect of migration and local growth on the spatio‐temporal density‐distribution of two co‐existing herbivorous weevils, Cionus scrophulariae L. and C. tuberculosus Scop., in 32 host plant Scrophularia nodosa L. patches of varying sizes was investigated. 2. Predictions of the temporal development of the slope in the density‐patch size relationships were derived from a basic population model with scale‐dependent migration rates. The model indicated that the slopes in the density‐patch size relationships during the early season should be reflected by the net scaling of immigration and emigration rates, whereas the slopes during the later season should increase as a result of local growth. 3. Emigration rates of the weevils were estimated in a field experiment, were the weevils coexisted in space and time. These results were then combined with a previous estimate of immigration rates in order to determine the net scaling of migration rates. 4. The emigration rate differed between species, caused by different movement rates in small patches, which could explain differences in the general slope of the density‐patch size relationships of the weevils in the natural figwort patches throughout the summer. The slopes in the relationships in the early season were largely predicted by the net scaling of migration rates. The slope also increased in the later season for C. tuberculosus, whereas the slope decreased for C. scrophulariae. 5. It was concluded that the understanding of both inter‐ and intra‐specific variations in density‐patch size relationships of insect herbivores can be improved using population models incorporating scale‐dependent migration and local growth.     

Population genetics and the evolution of geographic range limits in an annual plant

Abstract Theoretical models of species' geographic range limits have identified both demographic and evolutionary mechanisms that prevent range expansion. Stable range limits have been paradoxical for evolutionary biologists because they represent locations where populations chronically fail to respond to selection. Distinguishing among the proposed causes of species' range limits requires insight into both current and historical population dynamics. The tools of molecular population genetics provide a window into the stability of range limits, historical demography, and rates of gene flow. Here we evaluate alternative range limit models using a multilocus data set based on DNA sequences and microsatellites along with field demographic data from the annual plant Clarkia xantiana ssp. xantiana. Our data suggest that central and peripheral populations have very large historical and current effective population sizes and that there is little evidence for population size changes or bottlenecks associated with colonization in peripheral populations. Whereas range limit populations appear to have been stable, central populations exhibit a signature of population expansion and have contributed asymmetrically to the genetic diversity of peripheral populations via migration. Overall, our results discount strictly demographic models of range limits and more strongly support evolutionary genetic models of range limits, where adaptation is prevented by a lack of genetic variation or maladaptive gene flow.     

Long‐term ‘islands’ in the landscape: low gene flow,effective population size and genetic divergence in the shrub Hakea oldfieldii (Proteaceae)

The genetic structure of disjunct populations is determined by founding genetic properties, demographic processes, gene flow, drift and local selection. We aim to identify the genetic consequences of natural population disjunction at regional and local scales in Hakea oldfieldii using nuclear and plastid markers to investigate long‐term effective population sizes and gene flow, and patterns of diversity and divergence, among populations. Regional divergence was significant as shown by a consistent pattern in principal coordinates, neighbor‐joining and Bayesian analyses, but divergence at the local level was also significant with localized distribution of plastid haplotypes and populations clustering separately in Bayesian analyses. Historical, recent and first‐generation gene flow was low, suggesting that recent habitat fragmentation has not reduced gene migration significantly. Genetic bottlenecks were detected in three populations. Long‐term effective population size was significantly correlated with the number of alleles/locus and observed heterozygosity, but not with census population size, suggesting that the loss of diversity is associated with long‐term changes rather than recent fragmentation. Inbreeding coefficients were significant in only three populations, suggesting that the loss of diversity is linked to drift and bottlenecks associated with demographic processes (local extinction by fires) rather than inbreeding. Historical disjunction as a result of specific ecological requirements, contraction of habitats following drying during the Pleistocene, low gene flow and changes in population size are likely to have been important forces driving divergence through isolation by distance and drift. © 2015 The Linnean Society of London, Botanical Journal of the Linnean Society, 2015, 179 , 319–334.     

Extranuclear differentiation and gene flow in the finite island model

Use of sequence information from extranuclear genomes to examine deme structure in natural populations has been hampered by lack of clear linkage between sequence relatedness and rates of mutation and migration among demes. Here, we approach this problem in two complementary ways. First, we develop a model of extranuclear genomes in a population divided into a finite number of demes. Sex-dependent migration, neutral mutation, unequal genetic contribution of separate sexes and random genetic drift in each deme are incorporated for generality. From this model, we derive the relationship between gene identity probabilities (between and within demes) and migration rate, mutation rate and effective deme size. Second, we show how within- and between-deme identity probabilities may be calculated from restriction maps of mitochondrial (mt) DNA. These results, when coupled with our results on gene flow and genetic differentiation, allow estimation of relative interdeme gene flow when deme sizes are constant and genetic variants are selectively neutral. We illustrate use of our results by reanalyzing published data on mtDNA in mouse populations from around the world and show that their geographic differentiation is consistent with an island model of deme structure.     

Restricted distribution and limited gene flow in the model ciliate Tetrahymena thermophila

The biogeography of microbial eukaryotes has long been debated, but few phylogeographic data have been available to assess whether protists tend to have ubiquitous or endemic distributions. We addressed this issue in the ciliate Tetrahymena thermophila, a highly successful model system in cell and molecular biology. We found that this species has a distribution that is restricted to the Eastern United States, with high diversity in the northeast and low diversity across the rest of its distribution. We find high levels of population subdivision, low rates of migration and significant isolation by distance, supporting the moderate endemicity model of protist biogeography. This restricted gene flow may be a result of small population size, which would reduce the probability of migration events, or the inability to establish after migration. This work lays the foundation for T. thermophila to become a valuable model system for studying population biology.     

Model choice for phylogeographic inference using a large set of models

Model‐based analyses are common in phylogeographic inference because they parameterize processes such as population division, gene flow and expansion that are of interest to biologists. Approximate Bayesian computation is a model‐based approach that can be customized to any empirical system and used to calculate the relative posterior probability of several models, provided that suitable models can be identified for comparison. The question of how to identify suitable models is explored using data from Plethodon idahoensis, a salamander that inhabits the North American inland northwest temperate rainforest. First, we conduct an ABC analysis using five models suggested by previous research, calculate the relative posterior probabilities and find that a simple model of population isolation has the best fit to the data (PP = 0.70). In contrast to this subjective choice of models to include in the analysis, we also specify models in a more objective manner by simulating prior distributions for 143 models that included panmixia, population isolation, change in effective population size, migration and range expansion. We then identify a smaller subset of models for comparison by generating an expectation of the highest posterior probability that a false model is likely to achieve due to chance and calculate the relative posterior probabilities of only those models that exceed this expected level. A model that parameterized divergence with population expansion and gene flow in one direction offered the best fit to the P. idahoensis data (in contrast to an isolation‐only model from the first analysis). Our investigation demonstrates that the determination of which models to include in ABC model choice experiments is a vital component of model‐based phylogeographic analysis.     

Impacts of seed and pollen flow on population genetic structure for plant genomes with three contrasting modes of inheritance

The classical island and one-dimensional stepping-stone models of population genetic structure developed for animal populations are extended to hermaphrodite plant populations to study the behavior of biparentally inherited nuclear genes and organelle genes with paternal and maternal inheritance. By substituting appropriate values for effective population sizes and migration rates of the genes concerned into the classical models, expressions for genetic differentiation and correlation in gene frequency between populations can be derived. For both models, differentiation for maternally inherited genes at migration-drift equilibrium is greater than that for paternally inherited genes, which in turn is greater than that for biparentally inherited nuclear genes. In the stepping-stone model, the change of genetic correlation with distance is influenced by the mode of inheritance of the gene and the relative values of long- and short-distance migration by seed and pollen. In situations where it is possible to measure simultaneously Fst for genes with all three types of inheritance, estimates of the relative rates of pollen to seed flow can be made for both the short- and long-distance components of migration in the stepping-stone model.