Biomedical subjects

B Rannala

Publications and source records attributed to B Rannala.

12 recordsLinked to original sources

PubMed1998

Likelihood analysis of disequilibrium mapping, and related problems.

In this paper a theory is developed that provides the sampling distribution of alleles at a diallelic marker locus closely linked to a low-frequency allele that arose as a single mutant. The sampling distribution provides a basis for maximum-likelihood estimation of either the recombination rate, the mutation rate, or the age of the allele, provided that the two other parameters are known. This theory is applied to (1) the data of Hästbacka et al., to estimate the recombination rate between a locus associated with diastrophic dysplasia and a linked RFLP marker; (2) the data of Risch et al., to estimate the age of a presumptive allele causing idiopathic distortion dystonia in Ashkenazi jews; and (3) the data of Tishkoff et al., to estimate the date at which, at the CD4 locus, non-African lineages diverged from African lineages. We conclude that the extent of linkage disequilibrium can lead to relatively accurate estimates of recombination and mutation rates and that those estimates are not very sensitive to parameters, such as the population age, whose values are not known with certainty. In contrast, we also conclude that, in many cases, linkage disequilibrium may not lead to useful estimates of allele age, because of the relatively large degree of uncertainly in those estimates.

Africa↗

PubMed1997

Detecting immigration by using multilocus genotypes.

Immigration is an important force shaping the social structure, evolution, and genetics of populations. A statistical method is presented that uses multilocus genotypes to identify individuals who are immigrants, or have recent immigrant ancestry. The method is appropriate for use with allozymes, microsatellites, or restriction fragment length polymorphisms (RFLPs) and assumes linkage equilibrium among loci. Potential applications include studies of dispersal among natural populations of animals and plants, human evolutionary studies, and typing zoo animals of unknown origin (for use in captive breeding programs). The method is illustrated by analyzing RFLP genotypes in samples of humans from Australian, Japanese, New Guinean, and Senegalese populations. The test has power to detect immigrant ancestors, for these data, up to two generations in the past even though the overall differentiation of allele frequencies among populations is low.

Emigration and Immigration↗

PubMed1997

Phylogenetic methods come of age: testing hypotheses in an evolutionary context.

The use of molecular phylogenies to examine evolutionary questions has become commonplace with the automation of DNA sequencing and the availability of efficient computer programs to perform phylogenetic analyses. The application of computer simulation and likelihood ratio tests to evolutionary hypotheses represents a recent methodological development in this field. Likelihood ratio tests have enabled biologists to address many questions in evolutionary biology that have been difficult to resolve in the past, such as whether host-parasite systems are cospeciating and whether models of DNA substitution adequately explain observed sequences.

Animals↗

PubMed1997

On the genealogy of a rare allele.

The gene genealogy is derived for a rare allele that is descended from a mutant ancestor that arose at a fixed time in the past. Following Thompson (1976, Amer. J. Human Genet. 28, 442-452), the fractional linear branching process is used as a model of the demography of a rare allele. The model does not require the total population size to be constant or the mutant class to be neutral; so long as individuals in the class are selectively equivalent, the class as a whole may have a selective advantage, or disadvantage, relative to other alleles in the population. An exact result is given for the joint probability distribution of the coalescence times among a sample of alleles descended from the mutant. A method is described for rapidly simulating these coalescence times. The relationship between the genealogical structure of a discrete generation branching process and a continuous generation birth-death process is elucidated. The theory may be applied to the problem of estimating the ages of rare nonrecurrent mutations.

Alleles↗

PubMed1997

Gene genealogy in a population of variable size.

The genealogical properties of a small population with continuous overlapping generations that fluctuates randomly in size are studied using a model based on a stochastic birth-death process. The distribution of the coalescence times is presented, as well as a method for computing the expected overall length of the genealogy as a function of the individual birth rate gamma, the individual death rate mu, and the present population size. The relationship between the birth and death rates and the shape of the resulting genealogy is studied. The total length of the genealogy is shown to be maximized when gamma = mu. The joint distribution of the coalescence times is shown to be invariant in gamma and mu, conditional on the current population size, so that exponential growth of a population cannot be distinguished from exponential decline based on the shape of the resulting genealogy. The model is used to predict the probability that all genetic variation is lost from a recent founder population.

Founder Effect↗

PubMed1997

The sampling distribution of disease-associated alleles.

A theory is developed that provides the sampling distribution of low frequency alleles at a single locus under the assumption that each allele is the result of a unique mutation. The numbers of copies of each allele is assumed to follow a linear birth-death process with sampling. If the population is of constant size, standard results from theory of birth-death processes show that the distribution of numbers of copies of each allele is logarithmic and that the joint distribution of numbers of copies of k alleles found in a sample of size n follows the Ewens sampling distribution. If the population from which the sample was obtained was increasing in size, if there are different selective classes of alleles, or if there are differences in penetrance among alleles, the Ewens distribution no longer applies. Likelihood functions for a given set of observations are obtained under different alternative hypotheses. These results are applied to published data from the BRCA1 locus (associated with early onset breast cancer) and the factor VIII locus (associated with hemophilia A) in humans. In both cases, the sampling distribution of alleles allows rejection of the null hypothesis, but relatively small deviations from the null model can account for the data. In particular, roughly the same population growth rate appears consistent with both data sets.

Alleles↗

PubMed1997

Bayesian phylogenetic inference using DNA sequences: a Markov Chain Monte Carlo Method.

An improved Bayesian method is presented for estimating phylogenetic trees using DNA sequence data. The birth-death process with species sampling is used to specify the prior distribution of phylogenies and ancestral speciation times, and the posterior probabilities of phylogenies are used to estimate the maximum posterior probability (MAP) tree. Monte Carlo integration is used to integrate over the ancestral speciation times for particular trees. A Markov Chain Monte Carlo method is used to generate the set of trees with the highest posterior probabilities. Methods are described for an empirical Bayesian analysis, in which estimates of the speciation and extinction rates are used in calculating the posterior probabilities, and a hierarchical Bayesian analysis, in which these parameters are removed from the model by an additional integration. The Markov Chain Monte Carlo method avoids the requirement of our earlier method for calculating MAP trees to sum over all possible topologies (which limited the number of taxa in an analysis to about five). The methods are applied to analyze DNA sequences for nine species of primates, and the MAP tree, which is identical to a maximum-likelihood estimate of topology, has a probability of approximately 95%.

Algorithms↗

PubMed1997

Estimating the age of alleles by use of intraallelic variability.

A method is presented for estimating the age of an allele by use of its frequency and the extent of variation among different copies. The method uses the joint distribution of the number of copies in a population sample and the coalescence times of the intraallelic gene genealogy conditioned on the number of copies. The linear birth-death process is used to approximate the dynamics of a rare allele in a finite population. A maximum-likelihood estimate of the age of the allele is obtained by Monte Carlo integration over the coalescence times. The method is applied to two alleles at the cystic fibrosis (CFTR) locus, deltaF508 and G542X, for which intraallelic variability at three intronic microsatellite loci has been examined. Our results indicate that G542X is somewhat older than deltaF508. Although absolute estimates depend on the mutation rates at the microsatellite loci, our results support the hypothesis that deltaF508 arose < 500 generations (approximately 10,000 years) ago.

Alleles↗

PubMed1996

The Sampling Theory of Neutral Alleles in an Island Population of Fluctuating Size

The sampling distribution of neutral alleles under a stochastic birth, death, and immigration (BDI) process, proposed as a model of fluctuating island populations, is studied by analytical methods. A new result is presented for the distribution of allele types in a sample of N individuals from an island when the allele frequencies among immigrants are constant. The sampling distribution of allele types depends on the sample size N, the array of allele frequencies among immigrants p, and the parameter theta=phi/lambda, where phi is the immigration rate and lambda is the individual birth rate. The sampling distribution of alleles does not depend on time or population size, and no "genetic equilibrium" assumption is therefore needed to apply the model to natural populations. The moments of the sampling distribution of allele types are used to calculate the expectation and variance of a sample identity by descent estimate (fN 0) within islands under the BDI model.

Journal Article↗

PubMed1996

Probability distribution of molecular evolutionary trees: a new method of phylogenetic inference.

A new method is presented for inferring evolutionary trees using nucleotide sequence data. The birth-death process is used as a model of speciation and extinction to specify the prior distribution of phylogenies and branching times. Nucleotide substitution is modeled by a continuous-time Markov process. Parameters of the branching model and the substitution model are estimated by maximum likelihood. The posterior probabilities of different phylogenies are calculated and the phylogeny with the highest posterior probability is chosen as the best estimate of the evolutionary relationship among species. We refer to this as the maximum posterior probability (MAP) tree. The posterior probability provides a natural measure of the reliability of the estimated phylogeny. Two example data sets are analyzed to infer the phylogenetic relationship of human, chimpanzee, gorilla, and orangutan. The best trees estimated by the new method are the same as those from the maximum likelihood analysis of separate topologies, but the posterior probabilities are quite different from the bootstrap proportions. The results of the method are found to be insensitive to changes in the rate parameter of the branching process.

Animals↗

PubMed1996

Estimating gene flow in island populations.

A new method is presented for estimating the rate of gene flow into island populations using the distribution of alleles in samples from a number of islands. The pseudo maximum likelihood estimator (PMLE) that we derive may be applied to species with either discrete or continuous generation times. For Wright's discrete-generation island model, the method provides an estimate of theta = 2Nm where N is the (haploid) population size on each island and m is the fraction of individuals replaced by immigrants in each generation. For a continuous-generation island model, the corresponding parameter theta is the ratio of the immigration rate phi to the individual birth rate lambda. Monte Carlo simulations are used to compare the statistical properties of the PMLE with those of two alternative estimators of theta derived from Wright's F-statistics. The PMLE is shown to have greatest efficiency (least mean square error) in most cases for a wide range of sample sizes and parameter values. The PMLE is applied to estimate theta using mtDNA haplotypes and allozymes for subdivided populations of African elephants and Channel Island foxes.

Alleles↗

PubMed1995

Identity by descent in island-mainland populations.

A new model is presented for the genetic structure among a collection of island populations, with fluctuating population sizes and continuous overlapping generations, using a stochastic birth, death and immigration (BDI) process. Immigrants enter each island from a large mainland population, with constant gene frequencies, according to a Poisson process. The average probability of identity by descent (IBD) for two haploid individuals randomly selected from an island population is f0 = (phi f1 + lambda)/(phi + lambda), where f1 is the probability of IBD for two randomly selected immigrants, lambda is the birth-rate for each individual, and phi is the arrival rate of immigrants into each island. The value of f0 is independent of the death process, time and N. The expected level of genetic differentiation among island populations is FST = (1 - 1/n)lambda/(phi + lambda), where n is the total number of islands receiving immigrants. Because f0 and FST are independent of the death process, for a BDI model, the population genetic structure for several general demographic situations may be examined using our equations. These include stochastic exponential, or logistic (regulated by death rate) growth within islands, or a ""source-sink" population structure. Because the expected values of both f0 and FST are independent of time, these are achieved immediately, for a BDI model, with no need to assume the island populations are at genetic equilibrium.

Demography↗