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Biomedical subjects

M Slatkin

Publications and source records attributed to M Slatkin.

At least 73 records · Page 4Linked to original sources
PubMed1987

Gene flow and the geographic structure of natural populations.

There is abundant geographic variation in both morphology and gene frequency in most species. The extent of geographic variation results from a balance of forces tending to produce local genetic differentiation and forces tending to produce genetic homogeneity. Mutation, genetic drift due to finite population size, and natural selection favoring adaptations to local environmental conditions will all lead to the genetic differentiation of local populations, and the movement of gametes, individuals, and even entire populations--collectively called gene flow--will oppose that differentiation. Gene flow may either constrain evolution by preventing adaptation to local conditions or promote evolution by spreading new genes and combinations of genes throughout a species' range. Several methods are available for estimating the amount of gene flow. Direct methods monitor ongoing gene flow, and indirect methods use spatial distributions of gene frequencies to infer past gene flow. Applications of these methods show that species differ widely in the gene flow that they experience. Of particular interest are those species for which direct methods indicate little current gene flow but indirect methods indicate much higher levels of gene flow in the recent past. Such species probably have undergone large-scale demographic changes relatively frequently.

Animals↗
PubMed1987

The average number of sites separating DNA sequences drawn from a subdivided population.

The "infinite sites" model in the absence of recombination is examined in a subdivided population in which there is arbitrary migration among demes. It is shown that, if the migration matrix is symmetric and irreducible, the average number of sites that differ in two alleles chosen from the same deme depends only on an effective size of the whole population and not on either the elements of the migration matrix or the size of each deme separately. If there are n demes all of size N, the average number of sites that differ in two alleles chosen from the same deme is 4nN mu, where mu is the average mutation rate per site. This is the same value as for two alleles drawn from a panmictic population of size nN. The average number of sites that differ in alleles drawn from the same and from different demes can provide some information about the degree of population subdivision, as is illustrated by using the data of Kreitman and Aquadé (1986, Proc. Nat. Acad. Sci. U.S.A., 83, 3562) on Drosophila melanogaster.

Alleles↗
PubMed1986

Private alleles in a partially isolated population. II. Distribution of persistence time and probability of emigration.

Two diffusion limits were derived from a discrete Wright-Fisher model of migration, mutation, and selection with an arbitrary degree of dominance. Instantaneous killing of the process due to emigration of a mutant leads to one of two diffusion processes with a killing term. One (weak gene flow) is the boundary case of the other (strong gene flow), which can cover a wide range of gene flow. The diffusion process subject to strong gene flow is similar to that studied by S. Karlin and S. Tavaré (1983, SIAM J. Appl. Math. 43, 31-41). The spectral decomposition of the transition probability density of "private" allele frequencies is presented in the case of strong gene flow. The fate of mutant in a deme is discussed in terms of the probabilities of survival and emigration.

Alleles↗
PubMed1986

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.

Alleles↗
PubMed1986

Interchromosomal biased gene conversion, mutation and selection in a multigene family.

A mathematical model of the effects of interchromosomal biased gene conversion, mutation and natural selection on a multigene family is developed and analyzed. The model assumes two allelic states at each of n loci. The effects of genetic drift are ignored. The model is developed under the assumption of no recombination, but the analysis shows that, at equilibrium, there is no linkage disequilibrium, which implies that the conclusions are valid for arbitrary recombination among loci. At equilibrium, the balance between mutation, gene conversion and selection depends on the ratio of the mutation rates to the quantity [s + g(2 alpha - 1)/n], where s is the increment or decrement in relative fitness with each additional copy of one of the alleles, g is the conversion rate, and alpha is a measure of the bias in favor of one of the alleles. When this quantity is large relative to the mutation rates, the allele that has the net advantage, combining the effects of selection and conversion, will be nearly fixed in the multigene family. A comparison of these results with those from a comparable model of intrachromosomal biased conversion shows that biased interchromosomal conversion leads to approximately the same equilibrium copy number as does intrachromosomal conversion of the same strength. Interchromosomal conversion is much more effective in causing the substitution of one allele by another. The relative frequencies of interchromosomal and intrachromosomal conversion is indicated by the extent of the linkage disequilibrium among the loci in a multigene family.

Alleles↗
PubMed1985

Genetic differentiation of transposable elements under mutation and unbiased gene conversion.

A model is developed to predict the extent of genetic differentiation in a family of transposable elements under the combined effects of genetic drift, transposition, mutation and unbiased gene conversion. The model is based on simplifying assumptions that are valid when transposition is always to new sites and copy number per site is low. In the absence of gene conversion, the degree of differentiation as measured by the probability of identity of different elements is the same as at a single locus with the same mutation rate but in a population of effective size Nc/2, where N is the population size and c is the number of copies per individual. The inclusion of unbiased gene conversion does not significantly change this result. If, as seems to be the case, families of transposable elements are relatively homogeneous, then the model implies either that mutation rates for transposable elements are much lower than at comparable single-copy loci or that some other force, such as natural selection or biased gene conversion, is at work. Transposition is a very ineffective force for homogenizing a family of transposable elements.

DNA Transposable Elements↗
PubMed1984

Mitochondrial gene flow.

To account for the transmission of mitochondrial DNA between conspecific species Drosophila pseudoobscura and D. persimilis in sympatry reported by J.R. Powell [Powell, J.R. (1983) Proc. Natl. Acad. Sci. USA 80, 492-495], a simple model of gene flow and selection in infinite populations is analyzed. The model assumes two alleles at each of two loci, one of which is coded by an autosome and the other by mitochondrial DNA. Viability selection is presumed to be underdominant--i.e., heterozygous inferiority to the homozygotes--at an autosomal locus, and neutral or deleterious at a mitochondrial locus, with the combined action being multiplicative. Extremely strong selection against heterozygotes may prevent the transmission of mitochondrial DNA between two species, but otherwise the transmission can easily occur over species boundaries. The rate of approach to equilibrium is determined by the level of gene flow and is not affected much by selection against an autosomal locus. The divergence of the nuclear genomes of the two species is reexamined. Based on published data on enzyme loci, we conclude that there has been mitochondrial gene flow between these species for a long enough time that several nuclear loci examined could diverge because of accumulation of neutral mutations.

Animals↗
PubMed1980

The distribution of mutant alleles in a subdivided population.

The results are presented from a simulation study of the spatial distribution of mutant alleles in a subdivided population. Statistical measures of the spatial pattern are defined in such a way that the same quantities could be measured in a geographic survey of allele frequencies in natural populations. Two types of quantities are discussed in this paper: (1) the occupancy distribution provides information on the presence or absence of the mutant in different numbers of demes; and (2) the conditional frequency distribution provides information about the extent of local differentiation when the mutant is present in different numbers of demes. Properties of these distributions are found for different types of natural selection acting on the mutant. Some results are presented for the same statistical measures based on samples of individuals from a fraction of the total number of demes. The simulation results for intermediate levels of the migration rates are compared with analytic results obtained on the limits of high and low migration rates. The main conclusion is that these measures of the spatial distribution of mutants in a subdivided population have simple properties that could provide a new perspective on data from natural populations.

Alleles↗
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↗
PubMed1978

Group selection on a quantitative character.

We derive a model of group and individual selection on a quantitative character that is similar to the single-locus "metapopulation" models of group selection. Two alternative methods for the colonization of new or vacant habitats are examined and their effects are contrasted. In one model, all populations contribute migrants to a common pool, the "migrant pool," from which colonists are drawn at random to fill vacant sites. In the migrant pool there is complete mixing of individuals from different populations. This model of colonization is the one used in all previous models of group selection. In the other model, the "propagule pool" model, each propagule is made up of individuals derived from a single population and there is no mixing of colonists from different populations during propagule formation. The analysis shows that much more between-population genetic variance can be maintained with the propagule pool model than with the migrant pool model. Consequently, group selection can be much more effective in natural populations than is commonly supposed.

Journal Article↗
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↗