Gene flow and genetic drift in a species subject to frequent local extinctions

Two models of the effect of extinction and recolonization on the genetic differentiation of local populations are analyzed. One model is Wright's “island model” in which there is gene flow from a source of fixed gene frequency. The other is an island model with a continuous production of new alleles and gene flow among all the populations. Individual and group selection are not considered. It is shown that the extent of population differentiation and the direction of the effect of the colonization and extinction process depend on the manner in which the propagules that establish new colonies are formed. Two extreme cases are considered. In the “propagule pool” model all the individuals in a single propagule are derived from one population while in the “migrant pool” model, the individuals in a propagule are derived from a random sample of the entire collection of populations.     

Detecting Isolation by Distance Using Phylogenies of Genes

We introduce a method for analyzing phylogenies of genes sampled from a geographically structured population. A parsimony method can be used to compute s, the minimum number of migration events between pairs of populations sampled, and the value of s can be used to estimate the effective migration rate M, the value of Nm in an island model with local populations of size N and a migration rate m that would yield the same value of s. Extensive simulations show that there is a simple relationship between M and the geographic distance between pairs of samples in one- and two-dimensional models of isolation by distance. Both stepping-stone and lattice models were simulated. If two demes k steps apart are sampled, then, s, the average value of s, is a function only of k/(Nm) in a one-dimensional model and is a function only of k/(Nm)2 in a two-dimensional model. Furthermore, log(M) is approximately a linear function of log(k). In a one-dimensional model, the regression coefficient is approximately -1 and in a two-dimensional model the regression coefficient is approximately -0.5. Using data from several locations, the regression of log(M) on log(distance) may indicate whether there is isolation by distance in a population at equilibrium and may allow an estimate of the effective migration rate between adjacent sampling locations. Alternative methods for analyzing DNA sequence data from a geographically structured population are discussed. An application of our method to the data of R. L. Cann, M. Stoneking and A. C. Wilson on human mitochondrial DNA is presented.     

A strategy of movement and resource utilization

A set of age-specific rates of birth and death implies expected numbers of kin. An individual girl or woman chosen at random out of a population whose birth and death rates are specified can be expected to have a certain number of older sisters, younger sisters, nieces, cousins; expressions for these values are provided for both total kin and kin who are still living. Included also are the probabilities of living mother, grandmother, and great grandmother for girls and women of various ages. The methods are applicable to the size of the nuclear and the extended family. All formulas have been programmed and specimen numerical values are given.     

Linkage Disequilibrium in Human Ribosomal Genes: Implications for Multigene Family Evolution

Members of the rDNA multigene family within a species do not evolve independently, rather, they evolve together in a concerted fashion. Between species, however, each multigene family does evolve independently indicating that mechanisms exist which will amplify and fix new mutations both within populations and within species. In order to evaluate the possible mechanisms by which mutation, amplification and fixation occur we have determined the level of linkage disequilibrium between two polymorphic sites in human ribosomal genes in five racial groups and among individuals within two of these groups. The marked linkage disequilibrium we observe within individuals suggests that sister chromatid exchanges are much more important than homologous or nonhomologous recombination events in the concerted evolution of the rDNA family and further that recent models of molecular drive may not apply to the evolution of the rDNA multigene family.     

Epistatic selection opposed by immigration in multiple locus genetic systems

A model of “complete” epistatis is considered in which all “plus” alleles must be present in an individual before the adaptive phenotype is expressed. The conditions under which the plus alleles and hence the adaptive phenotype can increase and reach a stable equilibrium in the presence of immigration of gametes carrying minus alleles are found. In haploids and diploids in which the plus alleles are recessive, frequencies of the plus alleles are the same at all loci, regardless of the linkage relationships. Tight linkage favors the existence of a locally stable polymorphic equilibrium, but the equilibrium with only minus alleles is locally stable unless there is very tight linkage or very strong selection. Thus, this kind of epistasis, which provides a simple model for a character that requires several components to be present at the same time, is very sensitive to even a small amount of immigration. Hence, the evolution of such characters is likely only in completely rather than partially isolated populations.