ISOLATION BY DISTANCE

Blood protein variation in a population of Ethiopian vervet monkeys (Cercopithecus aethiops aethiops)

Seven small groups of vervet monkeys (Cercopithecus aethiops aethiops), totaling 124 individuals, from Awash National Park, Ethiopia, were trapped and blood samples were obtained. Twenty-three loci were examined by starch gel electrophoresis and four loci, Tf, E, ADA, and PMG2 were found to be polymorphic. The average heterozygosity (H) of the population was calculated to be 5.6%. No significant deviations from Hardy-Weinberg equilibrium proportions occurred and a chi-square test for group homogeneity was also not significant. Average Fst for all polymorphic loci was calculated to be 0.062. This suggests that the entire group functions as a single Mendelian population.

Marital structure and genetic isolation in a rural Hispanic population in northern New Mexico

An investigation of the mating structure of the rural Hispanic population of the village of abiquiu in northern New Mexico was carried out using village marriage registers. Marital movement and departure from random mating were analyzed by the distribution of birth places of marriage partners and by surname isonymy. The time periods studied were 1882 to 1910 and 1947 to 1977. The results of these analyses show marked marital isolation (median marital distances by birthplace of 11.5 and 20.0 miles, respectively) and a significant departure from random mating (F = 0.0556 and F = 0.0495, respectively). In each case the non-random component of the isonymy coeffient (Fn) greatly exceeds the random, or expected, component. Assortative mating for culture and proximity governed by the historical settlement pattern is indicated as the process producing these results. Isolation has begun to break down in recent years but as yet has had no great effect on the genetic structure of the Abiquiu population.

Isolation by distance: reply to Lalouel and Morton

Lalouel's assertion that I misinterpreted Malécot's work on isolation by distance may or may not be correct. If so, my assertions of error in Malécot's derivation are wrong, although they do apply to others who have used models involving a spatial continuum. Lalouel's other claims of error in my derivations of the consequences of a spatially continuous model of population reproduction and migration are incorrect, with the exception of one isolated misprint.

Gene diversity in Indian populations

Gene frequency data of ten protein and enzyme loci in seven populations of India were collected from the literature. The gene differentiation among seven populations relative to total population was only 0.6%, indicating that the genic variation between populations was small compared to that within them. Using 29 common protein loci, the genetic distances between Indians and three major races of man, Caucasoids, Mongoloids, and Negroids were also determined. Indians are closer to Mongoloids than to Caucasoids or Negroids as indicated by the phylogenetic tree.

Migration and mutation in stochastic models of gene frequency change. I. The island model

Migration has in the past been introduced deterministically into stochastic gene frequency models. Migration at rate m then reduces the between-population variability by a factor of (1 - m)2 each generation. We show that with stochastic migration, whether of fixed or variable numbers of individuals, a positive term delta m is added to the variance. As a result of the delta m term, the equilibrium value of the between-population variability is increased compared to the corresponding value for deterministic migration by a factor of approximately (1 - m)-2 for small m. An equivalent result is derived for mutation, using the infinite allele model for a single population. We show in addition that these results may be derived much more simply by use of identity-by-descent probability methods, but only if a modified definition of the probability of identity-by-descent is used, involving the sampling with instead of without replacement of pairs of genes from the population.

F-statistics and analysis of gene diversity in subdivided populations

It is show that Wright's F-statistics can be defined as ratios of gene diversities of heterozygosities rather than as the correlations of uniting gametes. This definition is applicable irrespective of the number of alleles involved or whether there is selection or not. The relationship between F-statistics and Nei's gene diversity analysis is discussed.

Variation in allele frequencies among caste groups of the Dhangars of Maharashtra, India: an analysis with Wright's Fst statistic

Variations in allelle frequencies at 11 serological and biochemical loci among 21 endogamous Dhangar castes of Maharashtra, India, have been studied using Wright's FST statistic. Gene differentiation among these castes is only about 4 per cent at these polymorphic loci. The distributional form of FST is explicable by random genetic drift at this early stage of differentiation of these caste groups. The empirical relationship between the average allele frequencies and the ration of within to total gene diversity of the caste groups is also studied.

Multivariate analysis of gametic disequilibrium in the Yanomama

The gametic disequilibria between all possible pairs of loci were examined for a set of eight codominant loci in each of fifty Yanomama villages, using a multivariate correlation analysis which reduces the results to a single measure of departure from multiple-locus-gametic equilibrium. Thirty-two of the fifty villages departed significantly from multiple-locus gametic equilibrium. The largest contributions to the departure from multiple-locus equilibrium were due to the disequilibria between MN and Ss and between Rh(Cc) and Rh(Ee), indicating the effects of tight linkage. After removing the effects of these obvious sources of disequilibrium, sixteen of the fifty villages still remained significantly out of equilibrium. The disequilibrium between any particular pair of loci was highly erratic from village to village, and (with the exception of the MN-Ss and Cc-Ee disequilibria) averaged out very close to zero overall, suggesting a lack of systematic forces (epistatic selection). The departure from equilibrium in any one village is in excess of that expected from random sampling alone, and is attributed primarily to the fission-fusion mode of village formation operative in the Yanomama and the fact that a single village consists of a few extended lineages. Village allele frequencies are highly correlated across loci, and most of the non-independence is accounted for by large correlations in the average allelic frequencies of different loci for related villages. It is suggested that these correlations also are due to territorial expansion and population growth. For the tribe as a whole, all but the tightly linked markers of the MNSs and Rh complexes are approximately uncorrelated, and large departures from multiple-locus Hardy-Weinberg expectation are primarily due to substantial Wahlund variance within the tribe. There is no need to postulate a role for selection in these disequilibria.

Aggregation, migration and population mechanics

A concept is developed for the regulation of populations by density-dependent movement, rather than by overt competition alone. Fitness is seen as maximising the reproductive advantage of a balance between migratory and congregatory behaviours. Population density is shown to be spatially, as well as temporally dynamic and a mechanism is proposed that accounts for observed spatial behaviour.

Population structure of Barra (Outer Hebrides)

Historical demography, surname concordance (isonymy), migration, and genealogy give a consistent description of population structure. The census size has averaged about 1400 over the last five centuries. Conjoined with an effective migration rate of 3-05 per generation as estimated by three different methods, this gives an evolutionary size of 638, random kinship of 0-008 and inbreeding of 0-007 relative to the rest of Britain. The population structure of Barra is similar to other British isolates in the recent past, but an order of magnitude less inbred than slash-and-burn agriculturalists and Pacific Islanders. Some consequences for rare genes and polymorphisms are discussed.

On some theoretical studies on gene differentiation in natural populations

Different mathematical approaches to study the extent of genetic variation of natural populations are reviewed. The modern understanding of the gene structure permits new interpretations of existing concepts like fixation or inbreeding. A more recent measure of genic divergence, which at molecular level is designed to measure net codon differences is also seen to be related with gene diversity in a substructed population. It is argued that such variations are produced and preserved possibly by simultaneous action of migration, mutation, selection, and random genetic drift. At the present moment it is very difficult to isolate out the effect of each factor because of varying degrees of variation at the different gene sites and between different sets of populations.

A model for genetic relationship among offspring from open-pollinated plant populations

Based on monoecious, diploid plant species, a model is constructed to determine genetic relationship within the seed production of an open-pollinated population, characterized by its rates of self-fertilization, population density and mode of pollen dispersal. Genetic relationship is measured by the coefficient of inbreeding of a seed produced by a mother plant located at a specified place, or by the coefficient of kinship between two seeds, produced from the same mother plant or produced from two different mother plants separated by a certain distance. The influence of the single parameters on these coefficients is demonstrated by some typical examples, which show that dimensionality of the habitat (one- or two-dimensional), as well as, range and type of pollen dispersal, has little influence on the relationship between seed produced from the same mother plant and, on the other hand, emphasize the important role of the rate of self-fertilization and population density. Some remarks on how to apply Wright's concept of neighbourhood to continuous plant populations close this paper.

The effect of population subdivision on two loci without selection

This paper is devoted to the study of the effects of population subdivision on the evolution of two linked loci. Two simple deterministic models of population subdivision without selection are investigated. One is a finite linear ‘stepping stone’ model and the other is a finite linear stepping stone chain of populations stretching between two large populations of constant genetic constitution. At equilibrium in the first model the gene frequencies in each population are equal and there is linkage equilibrium in each population. The rate of decay to zero of the linkage disequilibrium functions is the larger of (1 –c) and, where λ1is the rate of convergence of the gene frequencies to equilibrium and c is the recombination frequency. In the second model at equilibrium there will be a linear cline in gene frequencies connecting the two large constant populations. This cline will be accompanied by a ‘cline’ of linkage disequilibria. The rate of convergence to this equilibrium cline is independent of the recombination frequency, and, in fact, the gene frequencies and the linkage disequilibria converge to equilibrium at the same rate.

Gene flow and population differentiation

There are many possible spatial patterns of selection and gene flow that can produce a given cline structure; the actual geography of natural selection and gene flow must be worked out before an attempt is made to explain a given natural cline in terms of a model. The results of experimental and theoretical models show that it is possible for local differentiation to evolve parapatrically in spite of considerable gene flow if the selection gradients are relatively uniform. Irregularities in environmental gradients increase the sensitivity of clines to the effects of gene flow in proportion to the increase in the differences in gene frequencies between the emigrants and the demes receiving the immigrants. It is not necessary for a sharp spatial environmental change to be present for distinct differentiation to occur. In some cases even a gentle environmental gradient can give rise to marked spatial differentiation along a genetically continuous series of demes; such environmental differences may be below the practical limits of resolution in field studies. Any asymmetry in gene flow does not lead to dedifferentiation if the environmental gradient is smooth; it merely shifts the position of the transition zone between the differentiated areas from that which would be expected if there were no asymmetry. Abrupt geographic differences in gene, genotype, or morph frequencies should not, therefore, be interpreted as evidence for environmental changes in the immediate vicinity of the steepest part of the cline; neither should they be interpreted as evidence for geographic barriers, sharp environmental differences, or sexual isolation among the differentiated groups of populations when there are no other sources of evidence for these phenomena. Gene flow may be unimportant in the differentiation of populations along environmental gradients.

The island model of population differentiation: a general solution

The island model deals with a species which is subdivided into a number of discrete finite populations, races or subspecies, between which some migration occurs. If the number of populations is small, an assumption of equal rates of migration between each pair of populations may be reasonable approximation. Mutation at a constant rate to novel alleles may also be assumed.-A general solution is given for the process of population divergence under this model following subdivision of a single parental population, expressed in terms of the observed average frequency of heterozygotes within and between subpopulations at a randomly chosen set of independently segregating loci. No restriction is imposed on the magnitude of the migration or mutation rates involved, nor on the number of populations exchanging migrants.-The properties of two fundamental measures of genetic divergence are deduced from the theory. One is a parameter related to varphi, the coefficient of kinship, and the other, gamma, measures the rate of mutational divergence between the sub-populations.

The effect of a fusion of subpopulations on the total fixation index

A general mathematical expression is found for the decrease in the fixation index of a population where subpopulations with different gene frequencies fuse. It is shown that the use of Wright's formulas for a hierarchic structure will not necessarily give the correct result in this situation, since the conditions for their application are usually not satisfied. Two examples are given, one with fusions among subpopulations with a continuously distributed gene frequency, and one with data from real observations producing a discrete distribution.