Gene genealogies in geographically structured populations.

Population genetics theory has dealt only with the spatial or geographic pattern of degrees of relatedness or genetic similarity separately for each point in time. However, a frequent goal of experimental studies is to infer migration patterns that occurred in the past or over extended periods of time. To fully understand how a present geographic pattern of genetic variation reflects one in the past, it is necessary to build genealogy models that directly relate the two. For the first time, space-time probabilities of identity by descent and coalescence probabilities are formulated and characterized in this article. Formulations for general migration processes are developed and applied to specific types of systems. The results can be used to determine the level of certainty that genes found in present populations are descended from ancient genes in the same population or nearby populations vs. geographically distant populations. Some parameter combinations result in past populations that are quite distant geographically being essentially as likely to contain ancestors of genes at a given population as the past population located at the same place. This has implications for the geographic point of origin of ancestral, "Eve," genes. The results also form the first model for emerging "space-time" molecular genetic data.     

Sex ratios in geographically structured populations

In his book on sexual selection (1), Darwin documented evidence that the primary sex ratio (the proportion of males at conception) is about 1/2 in a wide variety of species. Otherwise, he explained, a newly conceived member of the rare sex will, on average, have more offspring than one of the common sex, since each offspring has one mother and one father; thus there is frequency-dependent selection in favour of parents producing the rare sex. Darwin formulated this explanation in the first edition (1871) for monogamous species, but he failed to extend it to polygamous species, and in the second edition (1874) he retracted it completely. It was left to Fisher (2) to develop the theory in the more general form that there should be equal parental expenditure on the two sexes, allowing for the possibility that one sex may cost more to produce than the other. Despite the wide applicability of Fisher's principle, recent work on sex ratio evolution has focused on situations where it breaks down (3). Hamilton (4) first pointed out that Fisher's argument assumes population-wide competition for mates, whereas most natural populations have a geographical population structure in which limited dispersal imposes constraints on mating patterns. What are the consequences for the sex ratio?     

Host resistance and coevolution in spatially structured populations

Natural, agricultural and human populations are structured, with a proportion of interactions occurring locally or within social groups rather than at random. This within-population spatial and social structure is important to the evolution of parasites but little attention has been paid to how spatial structure affects the evolution of host resistance, and as a consequence the coevolutionary outcome. We examine the evolution of resistance across a range of mixing patterns using an approximate mathematical model and stochastic simulations. As reproduction becomes increasingly local, hosts are always selected to increase resistance. More localized transmission also selects for higher resistance, but only if reproduction is also predominantly local. If the hosts disperse, lower resistance evolves as transmission becomes more local. These effects can be understood as a combination of genetic (kin) and ecological structuring on individual fitness. When hosts and parasites coevolve, local interactions select for hosts with high defence and parasites with low transmissibility and virulence. Crucially, this means that more population mixing may lead to the evolution of both fast-transmitting highly virulent parasites and reduced resistance in the host.     

The strong-migration limit in geographically structured populations

Summary Some strong-migration limits are established for geographically structured populations. A diploid monoecious population is subdivided into a finite number of colonies, which exchange migrants. The migration pattern is fixed and ergodic, but otherwise arbitrary. Generations are discrete and nonoverlapping; the analysis is restricted to a single locus. In all the limiting results, an effective population number N _e ( N _T ) appears instead of the actual total population number N _T . 1. If there is no selection, every allele mutates at rate u to types not preexisting in the population, and the (finite) subpopulation numbers N _i are very large, then the ultimate rate and pattern of convergence of the probabilities of allelic identity are approximately the same as for panmixia. If, in addition, the N _i are proportional to 1/u, as N _T 8, the equilibrium probabilities of identity converge to the panmictic value. 2. With a finite number of alleles, any mutation pattern, an arbitrary selection scheme for each colony, and the mutation rates and selection coefficients proportional to 1/N _T , let P _j be the frequency of the allele A _j in the entire population, averaged with respect to the stationary distribution of the backward migration matrix M. As N _T 8, the deviations of the allelic frequencies in each of the subpopulations from P _j converge to zero; the usual panmictic mutation-selection diffusion is obtained for P _j , with the selection intensities averaged with respect to the stationary distribution of M. In both models, N _e = N _T and all effects of population subdivision disappear in the limit if, and only if, migration does not alter the subpopulation numbers.Supported by the National Science Foundation (Grant No. DEB77-21494)     

The coalescent and the genealogical process in geographically structured population

We shall extend Kingman's coalescent to the geographically structured population model with migration among colonies. It is described by a continuous-time Markov chain, which is proved to be a dual process of the diffusion process of stepping-stone model. We shall derive a system of equations for the spatial distribution of a common ancestor of sampled genes from colonies and the mean time to getting to one common ancestor. These equations are solved in three particular models; a two-population model, the island model and the one-dimensional stepping-stone model with symmetric nearest-neighbour migration.     

The strong-migration limit for the genealogical process in geographically structured populations

In this article we assume that the entire population is subdivided into a finite number of panmictic colonies, each of which consists of a respective number of haploid individuals. We also assume that random genetic drift occurs in each colony and migration among colonies, which is independent of time and ergodic. We study the genealogical process of sampled genes from geographically structured populations. We prove that if the actual total population number is replaced by the effective population number, the mean coalescence time converges to that in a panmictic population in the strong migration limit. We also obtain the geographical distribution of the common ancestor.     

The decay of genetic variability in geographically structured populations. II

The ultimate rate of approach to equilibrium in the infinite stepping-stone model is calculated. The analysis is restricted to a single locus in the absence of selection, and every mutant is assumed to be new to the population. Let f(t, x) be the probability that two homologous genes separated by the vector x in generation t are the same allele. It is supposed that $\text{f(}\text{0, x}\text{) = O(x}{}^{\mathrm{?2?\eta }}\text{), η > 0,}\text{as}\text{x ≡ ¦}\text{x}\text{¦ → ∞}$. In the absence of mutation, f(t, x) tends to unity at the rate $\text{t}{}^{\mathrm{<mtext>?1</mtext><mtext>2</mtext>}}$ in one dimension and (ln t)^?1 in two dimensions. Thus, the loss of genetic variability in two dimensions is so slow that evolutionary forces not considered in this model would supervene long before a two-dimensional natural population became completely homogeneous. If the mutation rate, u, is not zero f(t, x) asymptotically approaches equilibrium at the rate $\text{(1 ? u)}{}^{\mathrm{2t}}\text{t}{}^{\mathrm{<mtext>?3</mtext><mtext>2</mtext>}}$ in one dimension and (1 ? u)^2tt^?1(lnt)^?2 in two dimensions. Integral formulas are presented for the spatial dependence of the deviation of f(t, x) from its stationary value as t → ∞, and for large separations this dependence is shown to be (const + x) in one dimension and (const + ln x) in two dimensions. All the results are the same for the Malécot model of a continuously distributed population provided the number of individuals per colony is replaced by the population density. The relatively slow algebraic and logarithmic rates of convergence for the infinite habitat contrast sharply with the exponential one for a finite habitat.     

The rate of allelism of lethal genes in a geographically structured population

The expected rate of allelism, E[I(x)], of lethal genes between two colonies with distance x in a structured population is studied by using one- and two-dimensional stepping-stone models. It is shown that E[I(x)] depends on the magnitude of selection in heterozygous condition (h), the rate of migration among adjacent colonies (m), the number of loci which produce lethal mutations (n) and the effective population size of each colony (N).——E[I(x)] always decreases with distance x. The rate of decrease is affected strongly by the magnitude of m. The rate of decrease is faster when m is small. E[I(x)] also decreases with increasing N and n. The effect of h on E[I(x)] is somewhat complicated. However, E[I(0)] is always smaller when h is small than when it is large.——For large x, the following approximate formulae may be obtained: (see PDF) where q and Var (q) are the mean and the variance of gene frequencies in each colony, t is approximated as t=h, (see PDF), -h for the partially recessive, completely recessive, and overdominant lethals, respectively, and C₀ is a function of m and t. It is clear that E[I(x)] declines exponentially with x in a one-dimensional habitat. The decrease E[I(x)] is faster in a two-dimensional habitat than in a one-dimensional habitat. The present result is applied to some of the existing data and the estimation of population parameters is also discussed.     

The genealogical process of neutral genes with mutation in geographically structured populations

The genealogical process of neutral genes with mutation in geographically structured populations is investigated. Following Watterson [24], the sampled genes are partitioned into two types, old equivalence classes and new equivalence classes. The model is described by a bivariate continuous time Markov chain as an interactive particle system. Some results are obtained in the two-population model and the stepping stone model with symmetric nearest-neighbour migration.     

Natural genetic variation of Arabidopsis thaliana is geographically structured in the Iberian peninsula

To understand the demographic history of Arabidopsis thaliana within its native geographical range, we have studied its genetic structure in the Iberian Peninsula region. We have analyzed the amount and spatial distribution of A. thaliana genetic variation by genotyping 268 individuals sampled in 100 natural populations from the Iberian Peninsula. Analyses of 175 individuals from 7 of these populations, with 20 chloroplast and nuclear microsatellite loci and 109 common single nucleotide polymorphisms, show significant population differentiation and isolation by distance. In addition, analyses of one genotype from 100 populations detected significant isolation by distance over the entire Iberian Peninsula, as well as among six Iberian subregions. Analyses of these 100 genotypes with different model-based clustering algorithms inferred four genetic clusters, which show a clear-cut geographical differentiation pattern. On the other hand, clustering analysis of a worldwide sample showed a west–east Eurasian longitudinal spatial gradient of the commonest Iberian genetic cluster. These results indicate that A. thaliana genetic variation displays significant regional structure and consistently support the hypothesis that Iberia has been a glacial refugium for A. thaliana. Furthermore, the Iberian geographical structure indicates a complex regional population dynamics, suggesting that this region contained multiple Pleistocene refugia with a different contribution to the postglacial colonization of Europe.     

Metacommunity process rather than continental tectonic history better explains geographically structured phylogenies in legumes

Penalized likelihood estimated ages of both densely sampled intracontinental and sparsely sampled transcontinental crown clades in the legume family show a mostly Quaternary to Neogene age distribution. The mode ages of the intracontinental crown clades range from 4-6 Myr ago, whereas those of the transcontinental crown clades range from 8-16 Myr ago. Both of these young age estimates are detected despite methodological approaches that bias results toward older ages. Hypotheses that resort to vicariance or continental history to explain continental disjunct distributions are dismissed because they require mostly Palaeogene and older tectonic events. An alternative explanation centring on dispersal that may well explain the geographical as well as the ecological phylogenetic structure of legume phylogenies is Hubbell's unified neutral theory of biodiversity and biogeography. This is the only dispersalist theory that encompasses evolutionary time and makes predictions about phylogenetic structure.     

Gene flow among geographically diverse housefly populations (Musca domestica L.): a worldwide survey of mitochondrial diversity

Single-strand conformation polymorphisms at 16S2 and COII mitochondrial genes were surveyed in 111 housefly samples from North, Central, and South America, Europe, Asia, Africa, and the Western Pacific. Forty-eight phenotypes were detected, of which none were ubiquitous, and 21 (44%) were confined to a single zoogeographical region. Nei's gene diversity index (H(S)) was 0.27 and was heterogeneous among zoogeographical regions. Phenotypes were the most diverse in the Ethiopian region and least diverse in the Palearctic and Nearctic regions. Hierarchical partitioning of the total diversity among regions (Nei's G(RT) = 0.49) indicated only a small proportion was shared. The differentiation of populations within regions (G(SR)) was 0.32. All pairwise estimates of gene flow between zoogeographical regions were less than 0.31 reproducing females per generation (mean 0.19). We conclude that housefly populations are highly structured even though the flies are mobile and easily capable of passive transport by ship and air.     

Native range genetic variation in Arabidopsis thaliana is strongly geographically structured and reflects Pleistocene glacial dynamics

Despite Arabidopsis thaliana 's pre-eminence as a model organism, major questions remain regarding the geographic structure of its genetic variation due to the geographically incomplete sample set available for previous studies. Many of these questions are addressed here with an analysis of genome-wide variation at 10 loci in 475 individuals from 167 globally distributed populations, including many from critical but previously un-sampled regions. Rooted haplotype networks at three loci suggest that A. thaliana arose in the Caucasus region. Identification of large-scale metapopulations indicates clear east–west genetic structure, both within proposed Pleistocene refugia and post-Pleistocene colonized regions. The refugia themselves are genetically differentiated from one another and display elevated levels of within-population genetic diversity relative to recolonized areas. The timing of an inferred demographic expansion coincides with the Eemian interglacial (approximately 120 000 years ago). Taken together, these patterns are strongly suggestive of Pleistocene range dynamics. Spatial autocorrelation analyses indicate that isolation by distance is pervasive at all hierarchical levels, but that it is reduced in portions of Europe.     

An adaptive explanation for geographically structured allozyme variation inDichroplus elongatus (Orthoptera: Acrididae)

Previous studies on allozyme variation in five populations of the grasshopperDichroplus elongatus along a geographical gradient in Argentina revealed a significant degree of population structuring and a significant association between one of the loci (Aat-1) and latitude. As this could not be entirely explained by historical factors, the possible adaptive significance of this locus or loci in linkage disequilibrium was investigated in the present study, with an emphasis on the role of environmental variables correlated with latitude. The present paper reports a study of the geographical organization of allozyme diversity over a wider range of the distribution ofD. elongatus. The relation of allelic frequencies with geographic climatic variables was analysed. We have found (i) that different loci (Aat-1 andPep-1) covary significantly with different variables, (ii) discordance between genetic and geographical distances, (iii) copious gene flow that would mask allelic frequency differences due solely to genetic drift, (iv) and temporal stability of the gradient found. The results suggest that causes other than drift and migration may explain the observed directional patterns of variation inD. elongatus.