Deme

Abstract: Closely related species often differ karyotypically due to the fixation of chromosomal translocations and inversions which are generally deleterious when heterozygous but have normal fitnesses when homozygous (White, 1973; Muller, 1954, 1956). The fixation of such chromosomal rearrangements requires small population sizes, because they are selected against when in the minority but favored when in the majority, and hence they can become established in a local area only through random genetic drift. Naturalists have long known that most species exist in subdivided populations where each individual has a limited number of potential mates; and recent biogeographic studies, especially on islands, have emphasized the high turnover rates of local populations by extinction and colonization (Simberloff, 1974; Spight, 1974). The present paper develops population genetic models to determine how the fixation rates of negatively heterotic chromosomal rearrangements are influenced by the spontaneous occurrence rates, strengths of selection against heterozygotes, the effective size of demes (or local populations), interdeme migration rates, local extinction and colonization, and other factors. Data on chromosomal rearrangements concerning spontaneous occurrence, selection coefficients, and fixation rates in phylogeny are then used to draw inferences about the breeding structure of species during longterm evolution, particularly the effective size of demes. The effective size of a population through time, Ne, is the number of breed-

Abstract: Many species, including humans, have dramatically expanded their range in the past, and such range expansions had certainly an impact on their genetic diversity. For example, mutations arising in populations at the edge of a range expansion can sometimes surf on the wave of advance and thus reach a larger spatial distribution and a much higher frequency than would be expected in stationary populations. We study here this surfing phenomenon in more detail, by performing extensive computer simulations under a two-dimensional stepping-stone model. We find that the probability of survival of a new mutation depends to a large degree on its proximity to the edge of the wave. Demographic factors such as deme size, migration rate, and local growth rate also influence the fate of these new mutations. We also find that the final spatial and frequency distributions depend on the local deme size of a subdivided population. This latter result is discussed in the light of human expansions in Europe as it should allow one to distinguish between mutations having spread with Paleolithic or Neolithic expansions. By favoring the spread of new mutations, a consequence of the surfing phenomenon is to increase the rate of evolution of spatially expanding populations.

Abstract: We report here a simulation study examining the effect of a recent spatial expansion on the pattern of molecular diversity within a deme. We first simulate a range expansion in a virtual world consisting in a two-dimensional array of demes exchanging a given proportion of migrants (m) with their neighbors. The recorded demographic and migration histories are then used under a coalescent approach to generate the genetic diversity in a sample of genes. We find that the shape of the gene genealogies and the overall pattern of diversity within demes depend not only on the age of the expansion but also on the level of gene flow between neighboring demes, as measured by the product Nm, where N is the size of a deme. For small Nm values (< approximately 20 migrants sent outwards per generation), a substantial proportion of coalescent events occur early in the genealogy, whereas with larger levels of gene flow, most coalescent events occur around the time of the onset of the spatial expansion. Gene genealogies are star shaped, and mismatch distributions are unimodal after a range expansion for large Nm values. In contrast, gene genealogies present a mixture of both very short and very long branch lengths, and mismatch distributions are multimodal for small Nm values. It follows that statistics used in tests of selective neutrality like Tajima's D statistic or Fu's F(S) statistic will show very significant negative values after a spatial expansion only in demes with high Nm values. In the context of human evolution, this difference could explain very simply the fact that analyses of samples of mitochondrial DNA sequences reveal multimodal mismatch distributions in hunter-gatherers and unimodal distributions in post-Neolithic populations. Indeed, the current simulations show that a recent increase in deme size (resulting in a larger Nm value) is sufficient to prevent recent coalescent events and thus lead to unimodal mismatch distributions, even if deme sizes (and therefore Nm values) were previously much smaller. The fact that molecular diversity within deme is so dependent on recent levels of gene flow suggests that it should be possible to estimate Nm values from samples drawn from a single deme.

Abstract: This paper derives the long-term effective size, Ne, for a general model of population subdivision, allowing for differential deme fitness, variable emigration and immigration rates, extinction, colonization, and correlations across generations in these processes. We show that various long-term measures of Ne are equivalent. The effective size of a metapopulation can be expressed in a variety of ways. At a demographic equilibrium, Ne can be derived from the demography by combining information about the ultimate contribution of each deme to the future genetic make-up of the population and Wright's FST's. The effective size is given by Ne = 1/(1 + var (upsilon) ((1 - FST)/Nin), where n is the number of demes, theta i is the eventual contribution of individuals in deme i to the whole population (scaled such that sigma theta i = n), and denotes an average weighted by theta i. This formula is applied to a catastrophic extinction model (where sites are either empty or at carrying capacity) and to a metapopulation model with explicit dynamics, where extinction is caused by demographic stochasticity and by chaos. Contrary to the expectation from the standard island model, the usual effect of population subdivision is to decrease the effective size relative to a panmictic population living on the same resource.