Search PubMed⌕ Search

Biomedical subjects

M Slatkin

Publications and source records attributed to M Slatkin.

At least 19 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

FST in a hierarchical island model.

It is shown that in a hierarchical island model, in which demes within a neighborhood exchange migrants at a much higher rate than do demes in different neighborhoods, hierarchical F statistics introduced by S. Wright can indicate the extent of gene flow within and between neighborhoods. At equilibrium, the within-neighborhood inbreeding coefficient, FSN, is approximately 1/(1 + 4Nm1) where N is the deme size and m1 is the migration rate among demes in the same neighborhood. The between-neighborhood inbreeding coefficient, FNT, is approximately 1/(1 + 4Ndm2) where d is the number of demes in a neighborhood and m2 is the migration rate among demes in different neighborhoods.

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↗
PubMed1990

Genealogy of neutral genes in two partially isolated populations.

Gene genealogy in two partially isolated populations which diverged at a given time t in the past and have since been exchanging individuals at a constant rate m is studied based upon an analytic method for large t and a simulation method for any t. Particular attention is paid to the conditions under which neutral genes sampled from populations are mono-, para-, and polyphyletic in terms of coalescence (divergence) times of genes. It is shown tha the probability of monophyly is high if M = 2Nm less than 0.5 and T = t/(2N) greater than 1, where N is the size of ancestral and descendant haploid populations, in which case most gene genealogies are likely to be concordant with the population relatedness. This probbility decreases as the sample size of genes increases. On the other hand, the case where the probability of monophyly is low will be either that of M greater than 1 and any T or that of M less than 1 and T less than 1, but the clear distinction between these conditions appears very difficult to make. These results are also examined if the gene genealogy is reconstructed from nucleotide differences. It is then shown that the results based upon coalescence times remain valid if the number of nucleotide differences between any pair of genes is not much smaller than 10. To observe such large nucleotide differences in small populations and therefore infer a reliable gene genealogy, we must examine a fairly long stretch of DNA sequences.

Computer Simulation↗
PubMed1990

The distribution of allelic effects under mutation and selection.

The Price (1970, 1972) equation is applied to the problem of describing the changes in the moments of allelic effects caused by selection, mutation and recombination at loci governing a quantitative genetic character. For comparable assumptions the resulting equations are the same as those obtained by different means by Barton & Turelli (1987; Turelli & Barton, 1989). The Price equation provides a natural framework within which to examine certain kinds of non-additive allelic effects, recombination and assortative mating. The use of the Price equation is illustrated by finding the equilibrium genetic variance under multiplicative dominance and epistasis and under assortative mating at an additive locus. The limitations of the use of recursion equations for the moments of allelic effects are also discussed.

Alleles↗
PubMed1990

The quantitative genetic consequences of pleiotropy under stabilizing and directional selection.

The independence of two phenotypic characters affected by both pleiotropic and nonpleiotropic mutations is investigated using a generalization of M. Slatkin's stepwise mutation model of 1987. The model is used to determine whether predictions of either the multivariate normal model introduced in 1980 by R. Lande or the house-of-cards model introduced in 1985 by M. Turelli can be regarded as typical of models that are intermediate between them. We found that, under stabilizing selection, the variance of one character at equilibrium may depend on the strength of stabilizing selection on the other character (as in the house-of-cards model) or not (as in the multivariate normal model) depending on the types of mutations that can occur. Similarly, under directional selection, the genetic covariance between two characters may increase substantially (as in the house-of-cards model) or not (as in the multivariate normal model) depending on the kinds of mutations that are assumed to occur. Hence, even for the simple model we consider, neither the house-of-cards nor the multivariate normal model can be used to make predictions, making it unlikely that either could be used to draw general conclusions about more complex and realistic models.

Genes↗
PubMed1990

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.

Computer Simulation↗
PubMed1989

Mutation and selection in bacterial populations: alternatives to the hypothesis of directed mutation.

Bacterial populations have served as model systems for studying evolutionary processes ever since the classic experiments of Luria and Delbrück, which demonstrated the occurrence of mutations prior to selection for the traits they conferred. However, several authors have recently presented experiments suggesting that bacteria may have mechanisms for directing which mutations occur, such that the rate of adaptive mutations is enhanced. Before the hypothesis of directed mutation is accepted, it is imperative to consider alternative hypotheses that might account for the same observations. To this end, we expand upon existing mathematical theory of the dynamics of mutation and selection in clonal populations for two cases of particular interest. The first case concerns selection against mutants before plating; this selection occurs as the result of differences in growth rate between mutants and nonmutants. We demonstrate that this selection model gives rise to distributions of mutants, obtained by plating from sister cultures, that are very similar to those expected when some mutations are induced by the selective environment. The second case concerns the sequential incorporation of two mutations as the result of selection for an intermediate genotype after plating. We demonstrate that this two-step mutation model also yields distributions that are similar to those expected when some mutations are induced by the selective environment. These two cases therefore provide alternatives to the hypothesis of directed mutation. We suggest experiments that might be used to examine our alternative hypotheses. We also contrast the hypothesis of directed mutation with the notion of inheritance of acquired characteristics.

Bacteria↗
PubMed1989

Detecting small amounts of gene flow from phylogenies of alleles.

The method of coalescents is used to find the probability that none of the ancestors of alleles sampled from a population are immigrants. If that is the case for samples from two or more populations, then there would be concordance between the phylogenies of those alleles and the geographic locations from which they are drawn. This type of concordance has been found in several studies of mitochondrial DNA from natural populations. It is shown that if the number of sequences sampled from each population is reasonably large (10 or more), then this type of concordance suggests that the average number of individuals migrating between populations is likely to be relatively small (Nm less than 1) but the possibility of occasional migrants cannot be excluded. The method is applied to the data of E. Bermingham and J. C. Avise on mtDNA from the bowfin, Amia calva.

Alleles↗
PubMed1989

A cladistic measure of gene flow inferred from the phylogenies of alleles.

A method for estimating the average level of gene flow among populations is introduced. The method provides an estimate of Nm, where N is the size of each local population in an island model and m is the migration rate. This method depends on knowing the phylogeny of the nonrecombining segments of DNA that are sampled. Given the phylogeny, the geographic location from which each sample is drawn is treated as multistate character with one state for each geographic location. A parsimony criterion applied to the evolution of this character on the phylogeny provides the minimum number of migration events consistent with the phylogeny. Extensive simulations show that the distribution of this minimum number is a simple function of Nm. Assuming the phylogeny is accurately estimated, this method provides an estimate of Nm that is as nearly as accurate as estimates obtained using FST and other statistics when Nm is moderate. Two examples of the use of this method with mitochondrial DNA data are presented.

Alleles↗
PubMed1989

Population structure and evolutionary progress.

Wright's shifting-balance theory is discussed as an example of a process that can cause species to evolve combinations of characters that could not evolve under natural selection alone. A review of the existing theory of peak shifts indicates that the conditions of extreme isolation that are necessary to permit genetic drift to alter the outcome of natural selection in local populations would make gene flow too weak to spread a new combination of genes to other populations in a reasonable time. Instead, it seems likely that major demographic changes must occur in a species for the shifting-balance process to work. A discussion of direct and indirect studies of gene flow in natural populations suggests that the current genetic structure of many species is likely to reflect past demographic events rather than ongoing gene flow. It is possible then that demographic processes could be responsible for spreading new traits in a species, but that would be true whether those new traits evolved only owing to natural selection or owing in addition to genetic drift and other forces.

Animals↗
PubMed1988

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.

Biological Evolution↗
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↗