Joseph Felsenstein

Evolutionary trees from DNA sequences: A maximum likelihood approach

SummaryThe application of maximum likelihood techniques to the estimation of evolutionary trees from nucleic acid sequence data is discussed. A computationally feasible method for finding such maximum likelihood estimates is developed, and a computer program is available. This method has advantages over the traditional parsimony algorithms, which can give misleading results if rates of evolution differ in different lineages. It also allows the testing of hypotheses about the constancy of evolutionary rates by likelihood ratio tests, and gives rough indication of the error of the estimate of the tree.

Phylogenies and the comparative method.

Comparative studies of the relationship between two phenotypes, or between a phenotype and an environment, are frequently carried out by invalid statistical methods. Most regression, correlation, and contingency table methods, including nonparametric methods, assume that the points are drawn independently from a common distribution. When species are taken from a branching phylogeny, they are manifestly nonindependent. Use of a statistical method that assumes independence will cause overstatement of the significance in hypothesis tests. Some illustrative examples of these phenomena have been given, and limitations of previous proposals of ways to correct for the nonindependence have been discussed. A method of correcting for the phylogeny has been proposed. It requires that we know both the tree topology and the branch lengths, and that we be willing to allow the characters to be modeled by Brownian motion on a linear scale. Given these conditions, the phylogeny specifies a set of contrasts among species, contrasts that are statistically independent and can be used in regression or correlation studies. The considerable barriers to making practical use of this technique have been discussed.

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.

Skepticism towards santa rosalia or why are there so few kinds of animals

In a classic paper, Hutchinson (1959) set the tone for much of the ecological work done during the past 20 years by suggesting that ecologists try to explain the numbers of species of animals. Hutchinsons approach was ecological, explaining diversity by explaining how the species could coexist. There can be little question that competitive exclusion sets an upper limit on species diversity, but it is not obvious that this upper limit will be achieved. There may be additional constraints on the process of speciation, constraints set by genetics rather than ecology. It has been usual for evolutionists to reject the possibility of sympatric speciation, and this amounts to asserting the existence of such genetic constraints. Even if the ecological opportunity for coexistence is present, under the conventional view lack of geographic isolation can prevent speciation. The attempt by Rosenzweig (1975) to give a comprehensive explanation of continental species diversity takes as its starting point the assumption that geographic isolation is a necessary prerequisite to species formation. A number of workers have made and analyzed detailed population genetic models of sympatric or parapatric speciation, in particular Maynard Smith (1966), Dickinson and Antonovics (1973), and Caisse and Antonovics (1978). Balkau and Feldman (1973) made a model of migration modification which can also be regarded as a model of parapatric speciation. The upshot of these models is that it is not difficult for sympatric speciation to occur. While these authors have largely been concerned with showing that sym-

Numerical Methods for Inferring Evolutionary Trees

Despite a century of evolutionary theory, only in the last few decades have clearly defined procedures for inferring phylogenies been stated. For discrete characters whose ancestral states are known, the prescriptions of Henning are well defined, but they are applicable only when there is no incompatibility between different characters. This limitation has led to the elaboration of a number of methods for dealing with such incompatibilities. One category consists of the parsimony methods, which choose that phylogeny on which the fewest changes of character state need be assumed. Another category consists of the compatibility methods, which choose that phylogeny which is perfectly compatible with the largest number of characters, irrespective of how many changes need be assumed in other characters. Other approaches include the use of phenetic clustering algorithms and methods fitting trees to similarity or distance matrices. Each method has a different set of implicit assumptions concerning the biology of the characters and the information available from the data. If the methods are considered in a statistical framework as different estimators of an unknow quantity (the phylogeny), these asseumptions are more clearly seen. Standard statistical approaches, such as maximum likelihood, can be used to obtain methods whose properties are known and for which one can determine the amount of uncertainty in the resulting estimates of the phylogeny. Although existing statistical models are highly oversimplified and do not reflect the complexity of evolutionary processes, it is by viewing the problem as a statistical one that we can place all these methods in common fremework, within which their behavior and assumptions can be compared. It is essential that we not adopt a single methods as a universal panacea, but that an attempt be made to understand the biological assumptions and statistical behavior of each method.

The number of evolutionary trees

A simple method of counting the number of possible evolutionary trees is presented. The trees are assumed to be rooted, with labelled tips but unlabelled root and unlabelled interior nodes. The method allows multifurcations as well as bifurcations. It makes use of a simple recurrence relation for T(n,m), the number of trees with n labelled tips and m unlabelled interior nodes. A table of the total number of trees is presented up to n = 22. There are 282,137,824 different trees having 10 tip species, and over 8.87 x 10/sup 23/ different trees having 20 tip species. The method is extended to count trees some of whose interior nodes may be labelled. The principal uses of these numbers will be to double-check algorithms and notation systems, and to frighten taxonomists.

An evolutionary model for maximum likelihood alignment of DNA sequences

SummaryMost 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.

Inferring Species Trees Directly from Biallelic Genetic Markers: Bypassing Gene Trees in a Full Coalescent Analysis

The multispecies coalescent provides an elegant theoretical framework for estimating species trees and species demographics from genetic markers. However, practical applications of the multispecies coalescent model are limited by the need to integrate or sample over all gene trees possible for each genetic marker. Here we describe a polynomial-time algorithm that computes the likelihood of a species tree directly from the markers under a finite-sites model of mutation effectively integrating over all possible gene trees. The method applies to independent (unlinked) biallelic markers such as well-spaced single nucleotide polymorphisms, and we have implemented it in SNAPP, a Markov chain Monte Carlo sampler for inferring species trees, divergence dates, and population sizes. We report results from simulation experiments and from an analysis of 1997 amplified fragment length polymorphism loci in 69 individuals sampled from six species of Ourisia (New Zealand native foxglove).

Inching toward reality: An improved likelihood model of sequence evolution

SummaryOur 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.

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.