PubMed Health⌕ Search

Biomedical subjects

M Slatkin

Publications and source records attributed to M Slatkin.

10 recordsLinked to original sources
PubMed1992

Estimation of levels of gene flow from DNA sequence data.

We compare the utility of two methods for estimating the average levels of gene flow from DNA sequence data. One method is based on estimating FST from frequencies at polymorphic sites, treating each site as a separate locus. The other method is based on computing the minimum number of migration events consistent with the gene tree inferred from their sequences. We compared the performance of these two methods on data that were generated by a computer simulation program that assumed the infinite sites model of mutation and that assumed an island model of migration. We found that in general when there is no recombination, the cladistic method performed better than FST while the reverse was true for rates of recombination similar to those found in eukaryotic nuclear genes, although FST performed better for all recombination rates for very low levels of migration (Nm = 0.1).

Computer Simulation↗
PubMed1991

Inbreeding coefficients and coalescence times.

This paper describes the relationship between probabilities of identity by descent and the distribution of coalescence times. By using the relationship between coalescence times and identity probabilities, it is possible to extend existing results for inbreeding coefficients in regular systems of mating to find the distribution of coalescence times and the mean coalescence times. It is also possible to express Sewall Wright's FST as the ratio of average coalescence times of different pairs of genes. That simplifies the analysis of models of subdivided populations because the average coalescence time can be found by computing separately the time it takes for two genes to enter a single subpopulation and time it takes for two genes in the same subpopulation to coalesce. The first time depends only on the migration matrix and the second time depends only on the total number of individuals in the population. This approach is used to find FST in the finite island model and in one- and two-dimensional stepping-stone models. It is also used to find the rate of approach of FST to its equilibrium value. These results are discussed in terms of different measures of genetic distance. It is proposed that, for the purposes of describing the amount of gene flow among local populations, the effective migration rate between pairs of local populations, M, which is the migration rate that would be estimated for those two populations if they were actually in an island model, provides a simple and useful measure of genetic similarity that can be defined for either allozyme or DNA sequence data.

Animals↗
PubMed1991

Pairwise comparisons of mitochondrial DNA sequences in stable and exponentially growing populations.

We consider the distribution of pairwise sequence differences of mitochondrial DNA or of other nonrecombining portions of the genome in a population that has been of constant size and in a population that has been growing in size exponentially for a long time. We show that, in a population of constant size, the sample distribution of pairwise differences will typically deviate substantially from the geometric distribution expected, because the history of coalescent events in a single sample of genes imposes a substantial correlation on pairwise differences. Consequently, a goodness-of-fit test of observed pairwise differences to the geometric distribution, which assumes that each pairwise comparison is independent, is not a valid test of the hypothesis that the genes were sampled from a panmictic population of constant size. In an exponentially growing population in which the product of the current population size and the growth rate is substantially larger than one, our analytical and simulation results show that most coalescent events occur relatively early and in a restricted range of times. Hence, the "gene tree" will be nearly a "star phylogeny" and the distribution of pairwise differences will be nearly a Poisson distribution. In that case, it is possible to estimate r, the population growth rate, if the mutation rate, mu, and current population size, N0, are assumed known. The estimate of r is the solution to ri/mu = ln(N0r) - gamma, where i is the average pairwise difference and gamma approximately 0.577 is Euler's constant.

Animals↗
PubMed1979

Coevolution in structured demes.

A simple model of coevolution in a subdivided population is considered. It is shown that, when there are frequency- and density-dependent interactions in each site, the sampling variation in numbers in each local site can lead to selection both through the dispersal process and through indirect effects. The model predicts that coevolved relationships between species can result from various interactions other than direct forms of competition and predation.

Animals↗
PubMed1979

Genetic drift in sex-linked lethal disorders.

A model is considered to calculate effects of genetic drift on the expected proportion of new mutants amongst males affected by a sex-linked recessive lethal. We show how to relate the number of cases of the disorder in males to the expected deviations from the deterministic value of the proportion of new mutants. For small values of alpha (= 3N mu), where N is the size of the female population, and mu is the mutation rate from wild-type to lethal allele, the standard deviation (SD) of the proportion of new mutants is large. However, if alpha more than 50, the potential effect of genetic drift is probably less important than the many other sources of error and bias.

Gene Frequency↗
PubMed1976

Cost and benefits of lizard thermoregulation.

Lizards thermoregulate by behavioral and physiological adjustments. The resultant control over metabolic processes is generally assumed to be beneficial. However, these thermoregulatory adjustments have associated costs which, if extensive, make thermoregulation impractical. We extend this idea into an abstract mathematical, cost-benefit model of thermoregulation in lizards. Investigation of the model leads to a set of predictions which includes: (1) the physiologically optimal temperature is not always the ecologically optimal temperature; (2) thermoregulation is beneficial only when associated costs are low; (3) thermal specialists will normally thermoregulate more carefully than thermal generalists unless costs are high; and (4) lizards will thermoregulate more carefully if productivity of the habitat is increased or if exploitation competition is reduced. Data on lizards, where available, generally agree with these predicitions.

Animals↗
PubMed1975

Genetic drift in a cline.

A model is developed of genetic drift in a cline maintained by spatially varying natural selection and local dispersal of individuals. The model is analyzed by an approximation scheme which is valid for weak selection and small migration rates. The results, which are based on numerical iterations of the approximate equations, are that the cline is less steep than predicted on the basis of the deterministic theory but that for weak selection the correlation between random fluctuations in neighboring colonies is approximately the same as in models of migration and drift in the absence of selection.

Biological Evolution↗
PubMed1975

Gene flow and selection in a two-locus system.

A model of gene flow and selection in two linked loci is analyzed. The problems considered are the effects of linkage on the clines in frequencies at the two loci and the role of gene flow in producing linkage disequilibrium between the loci. Also, the possible significance of linkage as a mechanism for permitting a population of "track" spatial changes in the environment is considered. The results are that when the recombination fraction between the loci is of the same order of magnitude as the selection coefficients or smaller, then linkage is important in determining the gene frequencies and a substantial amount of linkage disequilibrium is present in the cline. Depending on the spatial pattern of selection on the two loci, linkage can either decrease or increase a population's response to local selection.

Models, Biological↗