ISOLATION BY DISTANCE

A method for the estimation of gene flow parameters from a population structure caused by restricted gene flow and genetic drift

A method has been developed which enables the estimation of the plant gene flow parameters σp (pollen dispersal), σs (seed dispersal) and t (outcrossing rate) from a selection-free continuously structured population in equilibrium. The method uses Wright's F-coefficients and introduces a new F-function which describes the genetic similarity as a function of the spatial distance. The method has been elaborated for wind pollinated plant species but can be modified for insect pollination and for animal species. In practice allozymes will provide for the necessary neutral genetic variation. The more loci used and the more intermediate the gene frequencies, the more reliable the results. For the estimation of σp and t together (when the outcrossing rate is not known) at least two chromosomally unlinked loci are required. The method for estimating σs depends on whether the plant species is annual or perennial. The mechanism of selfing has been analysed by the explanation of the value of t by three components: population density (d), pollen flow (σp) and relative fertilization potential of own pollen (Z). The concepts of neighbourhood size and isolation by distance, developed by Wright, who used a single gene flow parameter σ, have been extended to the situation which is realistic for seed plants, using all three parameters σp, σs and t. When σp is large with respect to σs, σs largely determines the value of the neighbourhood size, whereas σp is the most dominating factor in isolation by distance. The use of "local effective population size" and "mean gene transport per generation" instead of "neighbourhood size" and "neighbourhood area", respectively, is proposed to avoid confusion. Computer simulations have been carried out to check the validity and the reliability of the method. Populations of 200 plants, using two or three loci with intermediate allele frequencies, gave good results in the calculation of σp with known value of t and of σs and Ne. With unknown t, especially with lower values of t, larger populations of at least 1,000 plants are necessary to obtain reasonably accurate results for σp and mean gene transport per generation M.

The genetic consequences of primate social organization: a review of macaques, baboons and vervet monkeys

Primates, as long-lived, iteroparous, socially complex mammals, offer the opportunity to assess the effects of behavior and demography on genetic structure. Because it is difficult to obtain tissue samples from wild primate populations, research in this area has largely been confined to terrestrial and semi-terrestrial old world monkeys (e.g., rhesus and Japanese macaques, vervets and several subspecies of baboons). However, these species display a multi-male, multi-female social structure commonly found in many other primate and non-primate mammals. Electrophoretic analyses of blood proteins from individually recognized and/or marked wild Himalayan rhesus monkeys, themselves the subject of long-term behavioral and demographic research, have begun to reveal the genetic consequences of such phenomena as social group fission, male-limited dispersion, non-consanguineous mating patterns, and agonistically defined male dominance. Specifically, rhesus social groups, consisting primarily of clusters of maternal relatives, appear to be non-random samples of a population's genotypes and genes. The genetic effects of social group fission are highly dependent on each group's size, demographic structure, and average degree of relatedness. In all cases fission contributes to the degree of intergroup genetic differentiation. Male-limited dispersion appears both to retard genetic differentiation between social groups and to lead to mating patterns that result in an avoidance of consanguinity. Groups, therefore, appear to be genetically outbred. Comparing these results with studies of other free-ranging or wild cercopithecines allows several generalizations: (a) genetic variation seems to be evenly distributed throughout each local population of multi-male social groups; (b) social groups, however, because they contain clusters of relatives, are distinctive in their specific frequencies of genes; (c) the degree of genetic differentiation between a population's social groups, because of the effects of social group fission and non-deterministic forms of male dispersal, is somewhat greater than expected on the basis of migration rates alone; and (d) the asymmetrical pattern of dispersion with respect to sex effectively precludes inbreeding in any one social group or the population as a whole. These observations have important implications for understanding the unusually rapid rates of evolution among the primates.

The effect of non-random migration on genetic differences between populations

Models of genetic population structure generally assume that emigrants from each local group are drawn at random from the set of individuals born there. We show that small violations of this assumption can have disproportionately large effects on genetic population structure, and we introduce a statistical method for measuring this effect.

The effects of linkage and density-dependent regulation on gene flow

The rate of gene flow across a hybrid zone may be reduced by the presence of a physical barrier, by a reduction of population density caused by reduced fitness of hybrids (the "hybrid sink" effect), and by linkage. If the reduction in hybrid fitness is not extreme, the strength of the barrier to gene flow caused by these effects is B = w(rho *+/rho *0)2(W*+/W*0)(2/R + 1/r). Here, w is the width of the cline; rho * is the carrying capacity; W* is the mean fitness of the population, excluding effects of density; R is the strength of density-dependent regulation; and r is the harmonic mean recombination rate between the locus whose flow is being calculated, and loci under selection. +, 0 denote populations outside the hybrid zone, and at its centre, respectively. This relation is illustrated using data from hybrid zones in Bombina and Podisma, and its implications for interpretation of data from nature are discussed.

Convergence of genetic distances in a migration matrix model

A recurring problem with the use of migration matrix models of genetic differentiation has to do with their convergence properties. In practice, predictions can be drawn from these models only at equilibrium; but in the case of the standard predictors (most of which are modifications of Wright's FST), it can take an unrealistically large number of generations to approach equilibrium. An alternative set of predictors, the set of all pairwise genetic distances among the populations that define the rows and columns of the migration matrix, is investigated here. These distances are shown analytically to converge much more rapidly than the more commonly used predictors. In an application of the model to migration data on a human population from Papua New Guinea, it takes only about three to four generations for the pairwise distances to converge, in contrast to more than 100 generations for one of the standard predictors. In this case, moreover, the distances predicted by the model at equilibrium are similar to those calculated from the available genetic data.

A quasi-equilibrium theory of the distribution of rare alleles in a subdivided population

The conditional average frequency of rare alleles has been shown in simulations to provide a simple and robust estimator of the number of individuals exchanged between local populations in an island model (Nm). This statistic is defined as the average frequency of an allele in those samples in which the allele is present. Here, we show that the conditional average frequency can be calculated from the distribution of allele frequencies. It is a measure of the spread of this distribution, and so is analogous to the standardised variance, FST. Analytic predictions for the island model of migration agree well with the corresponding simulation results. These predictions are based on the assumption that the rare alleles found in samples have reached a "quasi-equilibrium" distribution. As well as relating the conditional average frequency to the underlying allele frequency distribution, our results provide a more accurate method of estimating Nm from the conditional average frequency of private alleles in samples of different sizes.

The allelic correlation structure of Gainj- and Kalam-speaking people. I. The estimation and interpretation of Wright's F-statistics

The internal patterning of allelic correlations in the Gainj and Kalam swidden horticulturalists of highland Papua New Guinea is examined within the context of Sewall Wright's F-statistic model. A multiallelic extension of the model is given first, and multivariate variance-component estimators for the parameters are suggested. Then, it is shown that the expectation of the F-statistic set depends on the age structure of the population and that knowledge of the population and sample age structure is critical for meaningful analysis. The array of F-statistics estimated jointly over five polymorphic enzyme loci reveals the following features of Gainj and Kalam population structure: (1) significant departures from panmictic expectations and (2) characteristics of a continuously distributed breeding population, rather than those expected for populations subdivided into demes with discrete boundaries. Finally, the F-statistics estimated for the Gainj and Kalam are briefly compared to estimates obtained from other tribal populations. It is seen that the level of differentiation observed in the Gainj and Kalam is only about one-third that observed in South American swidden horticulturalists. Consequently, some conventional wisdom regarding the interrelationship of socioecological settings and genetic structures may require reevaluation.

Genetic differentiation among Iranian Christian communities

From some 500 members of Christian communities in Iran (Armenians and Assyrians from six localities), blood specimens were obtained and examined for a number of blood group, red cell enzyme, and serum protein systems. The results indicate the relatively closed nature of the Christian community as a whole but that moderate differentiation has already occurred among the local groups. One factor in this diversification process that can be distinguished is the effect of urbanization in Tehran, but otherwise it seems to be largely random.

Genetic studies in four tribal populations of the Surat District, Gujarat (India)

Four tribal populations (Chaudhuri, Vasava, Kotwalia and Gamit) of the Surat District in Gujarat (India) have been investigated for the distribution of 22 polymorphic systems of the blood. The main results of this study are as follows: The allele frequencies show considerable heterogeneity among these populations. From the genetic structure analysis it is seen that only a small fraction of the total gene diversity accounts for genetic differences among them, and the major portion of it is due to genetic variation within them. Analysis of genetic distance according to Nei (1972) reveals that the Vasava and Kotwalia show a rather close genetic relationship, while the Chaudhuri and Gamit differ from both the Vasava and Kotwalia.

Group selection for a polygenic behavioral trait: estimating the degree of population subdivision

For assessing the degree of population subdivision, and therefore the extent to which group selection might favor an altruistic trait, an appropriate measure is Nei's GST, defined by (F0-F)/(1-F). F0 is the probability that two alleles drawn from the same group are identical in state and F is the probability for two alleles drawn at random from the entire population. These probabilities can be assessed from molecular polymorphisms. GST has a number of properties that make it useful for empirical studies. When the mutation rate is small relative to the migration rate and the reciprocal of the group size, GST depends mainly on the absolute number of migrants per generation, moves rapidly to near equilibrium, and is independent of the number of alleles. The relative homogenizing effect of migration in the island and stepping-stone models is not as different as might be expected; one immigrant chosen randomly from the rest of the population is only one to two times as effective as one from a neighboring group, appreciably exceeding 2 only when there are 1000 or more groups. The use of molecular data to estimate the degree of population subdivision may permit testable predictions of the extent of altruistic behavior.

Population structure in the Connecticut Valley. I. Marital migration

This study reports on an analysis of marital migration among 12 communities in the Connecticut River Valley of Massachusetts during the years 1790-1849. Genetic inferences are drawn, and the requisite assumptions considered. The effect of geographic distance on genetic kinship is predicted using Malécot's isolation-by-distance model. The resulting estimates are discussed in terms of geographic and historical factors. The configuration of communities as predicted by kinship values approximates closely their actual geographic locations. Estimated genetic heterogeneity was low for the historical Connecticut Valley population, and community isolation breaks down rapidly over time. The region thus assumes its place among a number of sedentary, agricultural populations for which the isolation-by-distance model provides an adequate representation. A regression analysis which includes variables in addition to distance indicates that historical and economic factors contribute some additional explanatory power to the distribution of mating frequencies.

Demographic components of gene frequency change in free-ranging macaques on Cayo Santiago

Gene frequency profiles from January 1973 to January 1977 for three polymorphic loci were examined in Cayo Santiago rhesus social groups. The effects of demographic components (i.e., births, deaths, immigrations, emigrations, and group fission and fusion) on total change in gene frequencies are assessed. Allelic frequencies at the carbonic anhydrase II, 6-phosphogluconate dehydrogenase, and transferrin loci were analyzed in four social groups. In the two groups that underwent fission and fusion during the study period, the timing of these processes was related to the largest short-term changes in gene frequences. However, immigration and emigration had the greatest effect on total change in gene frequency in all groups during the study period. The relative importance of births and deaths in producing gene frequency change varied among the social groups. These results suggest that the relative importance of the demographic components of gene frequency change in primate populations is determined by behavioral patterns and ecological conditions specific to the population considered.

Measuring gene flow among populations having high levels of genetic fragmentation

We present an analysis of the genetic structures of 22 species of salamanders, with regard to levels of gene flow among populations. We estimate the gene flow parameter, Nm (the product of the effective population number and rate of migration among populations) using two alternative methods described by Wright and Slatkin. For most species, these two methods give approximately congruent estimates of Nm; when estimates differ, the method of Wright produces values slightly larger than those derived by the method of Slatkin. We analyze these results in light of independently derived historical inferences of the fragmentation of populations. This analysis suggests that the Nm values calculated from protein polymorphisms may contain information more relevant to historical patterns of gene exchange than to the current population dynamics; moderately large values of Nm may be calculated for species containing populations known to be no longer exchanging genes. Application of a method for estimating the maximum possible rate of gene exchange among populations indicates that, for most species studied here, gene flow among populations probably is no greater than the mutation rate. We suggest that most plethodontid species cannot be viewed as units whose cohesion is maintained by continuing gene exchange. Furthermore, we suggest that phenotypic uniformity among populations is not easily explained by hypotheses of continual stabilizing selection and propose that future work concentrate upon clarification of the genetic and epigenetic factors conferring self-maintenance or autopoietic properties on living systems.

Estimation of fixation indices and gene diversities

Considering the multinomial sampling of genotypes, unbiased estimators of various gene diversity measures in subdivided populations are presented. Using these quantities, formulae for estimating Wright's fixation indices (FIS, FIT, and FST) from a finite sample are developed.

Demography and evolution in an immigrant ethnic community: Hungarian Settlement, Louisiana, USA

This paper describes the fertility, mortality, and marriage patterns of the Hungarian Settlement, Louisiana, USA, immigrant ethnic population and relates these demographic processes to the evolutionary forces of natural selection, genetic drift, and gene flow. The results indicate that the maximum opportunity for natural selection decreased over time, and natural selection could have operated in the case of this population at only a very moderate level. The demographic characteristics of this population suggest that genetic drift may be important as an agent of microdifferentiation. Gene flow, however, appears to be the most important evolutionary force in this population. The process, based on the increasing incorporation of non-Hungarians into the gene pool, is causing the breakdown of this ethnic/genetic isolate.

Models of mitochondrial DNA transmission genetics and evolution in higher eucaryotes

The future value of mitochondrial DNA (mtDNA) sequence information to studies in population biology will depend in part on understanding of mtDNA transmission genetics both within cell lineages and between animal generations. A series of stochastic models has been constructed here based on various possibilities concerning this transmission. Several of the models generate predictions inconsistent with available data and, hence, their assumptions are provisionally rejected. Other models cannot yet be falsified. These latter models include assumptions that (1) mtDNA's are sorted through cellular lineages by random allocation to daughter cells in germ cell lineages; (2) the effective intracellular population sizes (nM's) of mtDNA's are small; and (3) sperm may (or may not) provide a low level ‘gene-flow’ bridge between otherwise isolated female lineages. It is hoped that the models have helped to identify and will stimulate further empirical study of various parameters likely to strongly influence mtDNA evolution. In particular, critical experiments or measurements are needed to determine the effective sizes of mtDNA populations in germ (and somatic) cells and to examine possible paternal contributions to zygote mtDNA composition.

Genetic heterogeneity and population structure in north-west India

Genetic markers consisting of 11 blood group and red cell enzyme systems were investigated in 14 endogamous groups of north-west India. Genetic differentiation among the samples as indicated by FST is appreciable, reflecting the ethnic diversity characteristic of this region. Local variation within each state is lower, indicating a geographical component to the total variation. This variation is refined by calculations of genetic distances, which show that the tribals and low-caste groups are closer together but well separated from high-caste Brahmins and other non-tribal middle castes. There is a slight possibility of disruptive selection, but the analyses suggest that the differences in genetic structure in north-west India are more likely to be due to their breeding structure, differential migration and ethnic affiliation.

Genetic population structure in polygynous formica ants

Genetic population structures, both mating and interaction structures, were investigated in three polygynous Formica ants by examining how genotype frequencies are distributed among the nests in their populations. The study is based on electrophoretically analysed enzyme polymorphisms. The patterns of genotypic variation among single-nest workers suggest that polygyny is functional in all the three species. The observed genotype frequencies indicate outbreeding within the study areas, and no spatial microdifferentiation in gene frequencies is detected. The coexistent gynes in nests of both F. transkaucasica and F. polyctena are genetically related to each other, and the same holds for worker nest mates. These results support the hypothesis that polygyny is favoured by kin selection. The lack of genetic relatedness among gyne nest mates in the highly polygynous F. aquilonia suggests that additional factors, such as mutualism or parental parasitism, are probably involved in the evolution of polygyny.