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Biomedical subjects

J Felsenstein

Publications and source records attributed to J Felsenstein.

At least 19 recordsLinked to original sources
PubMed2001

Maximum likelihood estimation of a migration matrix and effective population sizes in n subpopulations by using a coalescent approach.

A maximum likelihood estimator based on the coalescent for unequal migration rates and different subpopulation sizes is developed. The method uses a Markov chain Monte Carlo approach to investigate possible genealogies with branch lengths and with migration events. Properties of the new method are shown by using simulated data from a four-population n-island model and a source-sink population model. Our estimation method as coded in migrate is tested against genetree; both programs deliver a very similar likelihood surface. The algorithm converges to the estimates fairly quickly, even when the Markov chain is started from unfavorable parameters. The method was used to estimate gene flow in the Nile valley by using mtDNA data from three human populations.

Genetics, Population↗
PubMed2000

Sampling among haplotype resolutions in a coalescent-based genealogy sampler.

Analysis of the coalescent structure of a population may provide information useful in mapping disease loci. Current coalescent-based genealogy samplers require haplotyped data, but haplotypes are not always available, and it is not practical to sum over all haplotype assignments for large data sets. We describe a method of adding haplotype re-evaluation to the sampler, so that it samples not only among genealogies explaining a given haplotype configuration, but also among different haplotype configurations. Several different haplotype-rearrangement strategies are considered, but the simplest-inverting the phase of a single site in a single individual-appears to be the most successful. The straightforward haplotype sampler does not mix well; heating approaches can greatly improve its performance.

Computer Simulation↗
PubMed2000

Usefulness of single nucleotide polymorphism data for estimating population parameters.

Single nucleotide polymorphism (SNP) data can be used for parameter estimation via maximum likelihood methods as long as the way in which the SNPs were determined is known, so that an appropriate likelihood formula can be constructed. We present such likelihoods for several sampling methods. As a test of these approaches, we consider use of SNPs to estimate the parameter Theta = 4N(e)micro (the scaled product of effective population size and per-site mutation rate), which is related to the branch lengths of the reconstructed genealogy. With infinite amounts of data, ML models using SNP data are expected to produce consistent estimates of Theta. With finite amounts of data the estimates are accurate when Theta is high, but tend to be biased upward when Theta is low. If recombination is present and not allowed for in the analysis, the results are additionally biased upward, but this effect can be removed by incorporating recombination into the analysis. SNPs defined as sites that are polymorphic in the actual sample under consideration (sample SNPs) are somewhat more accurate for estimation of Theta than SNPs defined by their polymorphism in a panel chosen from the same population (panel SNPs). Misrepresenting panel SNPs as sample SNPs leads to large errors in the maximum likelihood estimate of Theta. Researchers collecting SNPs should collect and preserve information about the method of ascertainment so that the data can be accurately analyzed.

Computer Simulation↗
PubMed2000

Maximum likelihood estimation of recombination rates from population data.

We describe a method for co-estimating r = C/mu (where C is the per-site recombination rate and mu is the per-site neutral mutation rate) and Theta = 4N(e)mu (where N(e) is the effective population size) from a population sample of molecular data. The technique is Metropolis-Hastings sampling: we explore a large number of possible reconstructions of the recombinant genealogy, weighting according to their posterior probability with regard to the data and working values of the parameters. Different relative rates of recombination at different locations can be accommodated if they are known from external evidence, but the algorithm cannot itself estimate rate differences. The estimates of Theta are accurate and apparently unbiased for a wide range of parameter values. However, when both Theta and r are relatively low, very long sequences are needed to estimate r accurately, and the estimates tend to be biased upward. We apply this method to data from the human lipoprotein lipase locus.

Genetics, Population↗
PubMed1999

Maximum-likelihood estimation of migration rates and effective population numbers in two populations using a coalescent approach.

A new method for the estimation of migration rates and effective population sizes is described. It uses a maximum-likelihood framework based on coalescence theory. The parameters are estimated by Metropolis-Hastings importance sampling. In a two-population model this method estimates four parameters: the effective population size and the immigration rate for each population relative to the mutation rate. Summarizing over loci can be done by assuming either that the mutation rate is the same for all loci or that the mutation rates are gamma distributed among loci but the same for all sites of a locus. The estimates are as good as or better than those from an optimized FST-based measure. The program is available on the World Wide Web at http://evolution.genetics. washington.edu/lamarc.html/.

Animals↗
PubMed1998

Maximum likelihood estimation of population growth rates based on the coalescent.

We describe a method for co-estimating 4Nemu (four times the product of effective population size and neutral mutation rate) and population growth rate from sequence samples using Metropolis-Hastings sampling. Population growth (or decline) is assumed to be exponential. The estimates of growth rate are biased upwards, especially when 4Nemu is low; there is also a slight upwards bias in the estimate of 4Nemu itself due to correlation between the parameters. This bias cannot be attributed solely to Metropolis-Hastings sampling but appears to be an inherent property of the estimator and is expected to appear in any approach which estimates growth rate from genealogy structure. Sampling additional unlinked loci is much more effective in reducing the bias than increasing the number or length of sequences from the same locus.

Forecasting↗
PubMed1997

An alternating least squares approach to inferring phylogenies from pairwise distances.

A computational method is presented for minimizing the weighted sum of squares of the differences between observed and expected pairwise distances between species, where the expectations are generated by an additive tree model. The criteria of Fitch and Margoliash (1967, Science 155:279-284) and Cavalli-Sforza and Edwards (1967, Evolution 21:550-570) are both weighted least squares, with different weights. The method presented iterates lengths of adjacent branches in the tree three at a time. The weighted sum of squares never increases during the process of iteration, and the iterates approach a stationary point on the surface of the sum of squares. This iterative approach makes it particularly easy to maintain the constraint that branch lengths never become negative, although negative branch lengths can also be allowed. The method is implemented in a computer program, FITCH, which has been distributed since 1982 as part of the PHYLIP package of programs for inferring phylogenies, and is also implemented in PAUP*. The present method is compared, using some simulated data sets, with an implementation of the method of De Soete (1983, Psychometrika 48:621-626); it is slower than De Soete's method but more effective at finding the least squares tree. The relationship of this method to the neighbor-joining method is also discussed.

Algorithms↗
PubMed1996

A Hidden Markov Model approach to variation among sites in rate of evolution.

The method of Hidden Markov Models is used to allow for unequal and unknown evolutionary rates at different sites in molecular sequences. Rates of evolution at different sites are assumed to be drawn from a set of possible rates, with a finite number of possibilities. The overall likelihood of phylogeny is calculated as a sum of terms, each term being the probability of the data given a particular assignment of rates to sites, times the prior probability of that particular combination of rates. The probabilities of different rate combinations are specified by a stationary Markov chain that assigns rate categories to sites. While there will be a very large number of possible ways of assigning rates to sites, a simple recursive algorithm allows the contributions to the likelihood from all possible combinations of rates to be summed, in a time proportional to the number of different rates at a single site. Thus with three rates, the effort involved is no greater than three times that for a single rate. This "Hidden Markov Model" method allows for rates to differ between sites and for correlations between the rates of neighboring sites. By summing over all possibilities it does not require us to know the rates at individual sites. However, it does not allow for correlation of rates at nonadjacent sites, nor does it allow for a continuous distribution of rates over sites. It is shown how to use the Newton-Raphson method to estimate branch lengths of a phylogeny and to infer from a phylogeny what assignment of rates to sites has the largest posterior probability. An example is given using beta-hemoglobin DNA sequences in eight mammal species; the regions of high and low evolutionary rates are inferred and also the average length of patches of similar rates.

Animals↗
PubMed1995

Estimating effective population size and mutation rate from sequence data using Metropolis-Hastings sampling.

We present a new way to make a maximum likelihood estimate of the parameter 4N mu (effective population size times mutation rate per site, or theta) based on a population sample of molecular sequences. We use a Metropolis-Hastings Markov chain Monte Carlo method to sample genealogies in proportion to the product of their likelihood with respect to the data and their prior probability with respect to a coalescent distribution. A specific value of theta must be chosen to generate the coalescent distribution, but the resulting trees can be used to evaluate the likelihood at other values of theta, generating a likelihood curve. This procedure concentrates sampling on those genealogies that contribute most of the likelihood, allowing estimation of meaningful likelihood curves based on relatively small samples. The method can potentially be extended to cases involving varying population size, recombination, and migration.

Base Sequence↗
PubMed1994

A simulation comparison of phylogeny algorithms under equal and unequal evolutionary rates.

Using simulated data, we compared five methods of phylogenetic tree estimation: parsimony, compatibility, maximum likelihood, Fitch-Margoliash, and neighbor joining. For each combination of substitution rates and sequence length, 100 data sets were generated for each of 50 trees, for a total of 5,000 replications per condition. Accuracy was measured by two measures of the distance between the true tree and the estimate of the tree, one measure sensitive to accuracy of branch lengths and the other not. The distance-matrix methods (Fitch-Margoliash and neighbor joining) performed best when they were constrained from estimating negative branch lengths; all comparisons with other methods used this constraint. Parsimony and compatibility had similar results, with compatibility generally inferior; Fitch-Margoliash and neighbor joining had similar results, with neighbor joining generally slightly inferior. Maximum likelihood was the most successful method overall, although for short sequences Fitch-Margoliash and neighbor joining were sometimes better. Bias of the estimates was inferred by measuring whether the independent estimates of a tree for different data sets were closer to the true tree than to each other. Parsimony and compatibility had particular difficulty with inaccuracy and bias when substitution rates varied among different branches. When rates of evolution varied among different sites, all methods showed signs of inaccuracy and bias.

Algorithms↗
PubMed1992

Inching toward reality: an improved likelihood model of sequence evolution.

Our previous evolutionary model is generalized to permit approximate treatment of multiple-base insertions and deletions as well as regional heterogeneity of substitution rates. Parameter estimation and alignment procedures that incorporate these generalizations are developed. Simulations are used to assess the accuracy of the parameter estimation procedure and an example of an inferred alignment is included.

Animals↗
PubMed1992

Estimating effective population size from samples of sequences: inefficiency of pairwise and segregating sites as compared to phylogenetic estimates.

It is known that under neutral mutation at a known mutation rate a sample of nucleotide sequences, within which there is assumed to be no recombination, allows estimation of the effective size of an isolated population. This paper investigates the case of very long sequences, where each pair of sequences allows a precise estimate of the divergence time of those two gene copies. The average divergence time of all pairs of copies estimates twice the effective population number and an estimate can also be derived from the number of segregating sites. One can alternatively estimate the genealogy of the copies. This paper shows how a maximum likelihood estimate of the effective population number can be derived from such a genealogical tree. The pairwise and the segregating sites estimates are shown to be much less efficient than this maximum likelihood estimate, and this is verified by computer simulation. The result implies that there is much to gain by explicitly taking the tree structure of these genealogies into account.

Likelihood Functions↗
PubMed1992

Estimating effective population size from samples of sequences: a bootstrap Monte Carlo integration method.

We would like to use maximum likelihood to estimate parameters such as the effective population size N(e) or, if we do not know mutation rates, the product 4N(e) mu of mutation rate per site and effective population size. To compute the likelihood for a sample of unrecombined nucleotide sequences taken from a random-mating population it is necessary to sum over all genealogies that could have led to the sequences, computing for each one the probability that it would have yielded the sequences, and weighting each one by its prior probability. The genealogies vary in tree topology and in branch lengths. Although the likelihood and the prior are straightforward to compute, the summation over all genealogies seems at first sight hopelessly difficult. This paper reports that it is possible to carry out a Monte Carlo integration to evaluate the likelihoods approximately. The method uses bootstrap sampling of sites to create data sets for each of which a maximum likelihood tree is estimated. The resulting trees are assumed to be sampled from a distribution whose height is proportional to the likelihood surface for the full data. That it will be so is dependent on a theorem which is not proven, but seems likely to be true if the sequences are not short. One can use the resulting estimated likelihood curve to make a maximum likelihood estimate of the parameter of interest, N(e) or of 4N(e) mu. The method requires at least 100 times the computational effort required for estimation of a phylogeny by maximum likelihood, but is practical on today's work stations. The method does not at present have any way of dealing with recombination.

Base Sequence↗
PubMed1991

Counting phylogenetic invariants in some simple cases.

An informal degrees of freedom argument is used to count the number of phylogenetic invariants in cases where we have three or four species and can assume a Jukes-Cantor model of base substitution with or without a molecular clock. A number of simple cases are treated and in each the number of invariants can be found. Two new classes of invariants are found: non-phylogenetic cubic invariants testing independence of evolutionary events in different lineages, and linear phylogenetic invariants which occur when there is a molecular clock. Most of the linear invariants found by Cavender (1989, Molec. Biol. Evol. 6, 301-316) turn out in the Jukes-Cantor case to be simple tests of symmetry of the substitution model, and not phylogenetic invariants.

Animals↗
PubMed1991

An evolutionary model for maximum likelihood alignment of DNA sequences.

Most algorithms for the alignment of biological sequences are not derived from an evolutionary model. Consequently, these alignment algorithms lack a strong statistical basis. A maximum likelihood method for the alignment of two DNA sequences is presented. This method is based upon a statistical model of DNA sequence evolution for which we have obtained explicit transition probabilities. The evolutionary model can also be used as the basis of procedures that estimate the evolutionary parameters relevant to a pair of unaligned DNA sequences. A parameter-estimation approach which takes into account all possible alignments between two sequences is introduced; the danger of estimating evolutionary parameters from a single alignment is discussed.

Algorithms↗