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S Tavaré

Publications and source records attributed to S Tavaré.

34 records · Page 2Linked to original sources
PubMed1995

Coalescents and genealogical structure under neutrality.

Genealogical or coalescent methods have proved very useful in interpreting and understanding a wide range of population genetic data. Our aim is to illustrate some of the central ideas behind this approach. The primary focus is genealogy in neutral genetic models, for which the effects of demography can be separated from those of mutation. We describe the coalescent for panmictic populations of fixed size, and its extensions to incorporate various assumptions about variation in population size and nonrandom mating caused by geographical population subdivision. The effects of such genealogical structure on patterns and correlations in genetic data are discussed. An urn model is useful for simulating samples at loci with complex mutation mechanisms. We give two applications of the genealogical approach. The first concerns methods for estimating the mutation rate from infinitely-many-sites data, and the second relates to inference about recent common ancestors and population history.

Genealogy and Heraldry↗
PubMed1994

Sampling theory for neutral alleles in a varying environment.

We develop a sampling theory for genes sampled from a population evolving with deterministically varying size. We use a coalescent approach to provide recursions for the probabilities of particular sample configurations, and describe a Monte Carlo method by which the solutions to such recursions can be approximated. We focus on infinite-alleles, infinite-sites and finite-sites models. This approach may be used to find maximum likelihood estimates of parameters of genetic interest, and to test hypotheses about the varying environment. The methods are illustrated with data from the mitochondrial control region sampled from a North American Indian tribe.

Alleles↗
PubMed1992

Estimating substitution rates from molecular data using the coalescent.

A coalescent model is used to estimate the rate at which neutral substitutions occur in a DNA sequence, without the necessity for an independent estimate of divergence times. Given a random sample of molecular sequences from a finite population, the distribution of the time to a common ancestor can be obtained from the coalescent model. With this principle, summary statistics are developed that use the distribution of molecular diversity within the sample to estimate the relative magnitude of nucleotide substitution rates. If, in addition, the effective population size is known, absolute substitution rates can also be estimated. These techniques are illustrated by estimating the transition rates that underlie the evolution of the first 360 nucleotides of the mitochondrial control region in an Amerindian tribal population.

Biological Evolution↗
PubMed1992

Modeling the evolution of the human mitochondrial genome.

Mitochondrial DNA data have been used extensively to study evolution and early human origins. These applications require estimates of the rate at which nucleotide substitutions occur in the DNA sequence. We consider the problem of estimating substitution rates in the presence of site-to-site rate variation. A coalescent model is presented that allows for different substitution rates for purines and pyrimidines, as well as more detailed models that allow fast and slow rates within each of the purine and pyrimidine classes. A method for estimating such rates is presented. Even for these simple models of site heterogeneity, there are, typically, insufficient data to obtain reliable estimates of site-specific substitution rates. However, estimates of the average rate across all sites appear to be relatively stable even in the presence of site heterogeneity. Simulations of models with site-to-site variation in mutation rate show that hypervariable sites can produce peaks in the pairwise difference curves that have previously been attributed to population dynamics.

Biological Evolution↗
PubMed1991

Genomic mapping by anchoring random clones: a mathematical analysis.

A complete physical map of the DNA of an organism, consisting of overlapping clones spanning the genome, is an extremely useful tool for genomic analysis. Various methods for the construction of such physical maps are available. One approach is to assemble the physical map by "fingerprinting" a large number of random clones and inferring overlap between clones with sufficiently similar fingerprints. E.S. Lander and M.S. Waterman (1988, Genomics 2:231-239) have recently provided a mathematical analysis of such physical mapping schemes, useful for planning such a project. Another approach is to assemble the physical map by "anchoring" a large number of random clones--that is, by taking random short regions called anchors and identifying the clones containing each anchor. Here, we provide a mathematical analysis of such a physical mapping scheme.

Chromosome Mapping↗
PubMed1989

Codon preference and primary sequence structure in protein-coding regions.

The stochastic complexity of a data base of 365 protein-coding regions is analysed. When the primary sequence is modeled as a spatially homogeneous Markov source, the fit to observed codon preference is very poor. The situation improves substantially when a non-homogeneous model is used. Some implications for the estimation of species phylogeny and substitution rates are discussed.

Amino Acids↗
PubMed1989

Is knowing the age-order of alleles in a sample useful in testing for selective neutrality?

The most powerful, and most frequently used, test of selective neutrality, based on data consisting of observed allelic frequencies in a sample of genes at some locus, is the procedure of G. A. Watterson. This procedure uses the sample homozygosity F* as the test statistic, and in effect leads to rejection of the hypothesis of selective neutrality if the observed value of F* differs significantly from neutral theory expectations. The homozygosity statistic is invariant under relabeling of the alleles and thus cannot use any further information on the alleles which might be available. We present results which suggest that information concerning the age order of the alleles cannot be used to provide a more powerful testing procedure than that of Watterson.

Alleles↗
PubMed1987

The birth process with immigration, and the genealogical structure of large populations.

This paper studies a version of the birth and immigration process in which families are followed in the order of their appearance. This age structure is related to a number of results from population genetics, in particular the genealogical structure of the infinitely-many neutral alleles model. The asymptotic behavior of this genealogy is an easy consequence of the structure of the age-ordered family size process.

Biometry↗
PubMed1987

The population genealogy of the infinitely--many neutral alleles model.

A process analogous to Kingman's coalescent is introduced to describe the genealogy of populations evolving according to the infinitely- many neutral alleles model. The process records population frequencies in old and new classes, and labels the new classes in order of decreasing age. Its marginal distribution is characterized in a form which is amenable to explicit calculations and the transition densities of the associated K-allele models follow readily from this representation.

Alleles↗
PubMed1984

Line-of-descent and genealogical processes, and their applications in population genetics models.

A variety of results for genealogical and line-of-descent processes that arise in connection with the theory of some classical selectively neutral population genetics models are reviewed. While some new results and derivations are included, the principle aim is to demonstrate the central importance and simplicity of genealogical Markov chains in this theory. Considerable attention is given to "diffusion time scale" approximations of such genealogical processes. A wide variety of results pertinent to (diffusion approximations of) the classical multiallele single-locus Wright-Fisher model and its relatives are simplified and unified by this approach. Other examples where such genealogical processes play an explicit role, such as the infinite sites and infinite alleles models, are discussed.

Alleles↗
PubMed1983

Some stochastic models for plasmid copy number.

Some stochastic models for the copy number of plasmids in a cell line are studied. When considering the behavior of copy number in the whole cell line, the theory of multitype branching processes is appropriate. Attention is paid to the cure rate in the cell line, and the asymptotic fractions of cells containing a given number of plasmids. These quantities are used to compare the models numerically.

DNA Replication↗
PubMedDate not supplied

The effect of nonhomogeneous clone length distribution on the progress of an STS mapping project.

We provide both theoretical and simulation results on the progress of an STS mapping project in the presence of clone length inhomogeneity. For an example in which the genome comprises alternating regions of clones with short and long average length, the main conclusion is that the efficiency of the project is clearly decreased in the presence of such inhomogeneity. The case of deterministic clone length gives the worst progress. The general simulation algorithm we propose shows that strategies that space the anchors as regularly as possible do best: fewer contigs of larger average length are expected. The simulation algorithm can be used to study many statistical properties of the progress of any anchoring project.

Algorithms↗