Mark Pagel

Inferring the historical patterns of biological evolution

Phylogenetic trees describe the pattern of descent amongst a group of species. With the rapid accumulation of DNA sequence data, more and more phylogenies are being constructed based upon sequence comparisons. The combination of these phylogenies with powerful new statistical approaches for the analysis of biological evolution is challenging widely held beliefs about the history and evolution of life on Earth.

Phylogenetic Analysis and Comparative Data: A Test and Review of Evidence

The question is often raised whether it is statistically necessary to control for phylogenetic associations in comparative studies. To investigate this question, we explore the use of a measure of phylogenetic correlation, λ, introduced by Pagel (1999), that normally varies between 0 (phylogenetic independence) and 1 (species’ traits covary in direct proportion to their shared evolutionary history). Simulations show λ to be a statistically powerful index for measuring whether data exhibit phylogenetic dependence or not and whether it has low rates of Type I error. Moreover, λ is robust to incomplete phylogenetic information, which demonstrates that even partial information on phylogeny will improve the accuracy of phylogenetic analyses. To assess whether traits generally show phylogenetic associations, we present a quantitative review of 26 published phylogenetic comparative data sets. The data sets include 103 traits and were chosen from the ecological literature in which debate about the need for phylogenetic correction has been most acute. Eighty‐eight percent of data sets contained at least one character that displayed significant phylogenetic dependence, and 60% of characters overall (pooled across studies) showed significant evidence of phylogenetic association. In 16% of tests, phylogenetic correlation could be neither supported nor rejected. However, most of these equivocal results were found in small phylogenies and probably reflect a lack of power. We suggest that the parameter λ be routinely estimated when analyzing comparative data, since it can also be used simultaneously to adjust the phylogenetic correction in a manner that is optimal for the data set, and we present an example of how this may be done.

Detecting correlated evolution on phylogenies: a general method for the comparative analysis of discrete characters

I present a new statistical method for analysing the relationship between two discrete characters that are measured across a group of hierarchically evolved species or populations. The method assesses whether a pattern of association across the group is evidence for correlated evolutionary change in the two characters. The method takes into account information on the lengths of the branches of phylogenetic trees, develops estimates of the rates of change of the discrete characters, and tests the hypothesis of correlated evolution without relying upon reconstructions of the ancestral character states. A likelihood ratio test statistic is used to discriminate between two models that are fitted to the data: one allowing only for independent evolution of the two characters, the other allowing for correlated evolution. Tests of specific directional hypotheses can also be made. The method is illustrated with an application to the Hominoidea.

Bayesian Estimation of Ancestral Character States on Phylogenies

Biologists frequently attempt to infer the character states at ancestral nodes of a phylogeny from the distribution of traits observed in contemporary organisms. Because phylogenies are normally inferences from data, it is desirable to account for the uncertainty in estimates of the tree and its branch lengths when making inferences about ancestral states or other comparative parameters. Here we present a general Bayesian approach for testing comparative hypotheses across statistically justified samples of phylogenies, focusing on the specific issue of reconstructing ancestral states. The method uses Markov chain Monte Carlo techniques for sampling phylogenetic trees and for investigating the parameters of a statistical model of trait evolution. We describe how to combine information about the uncertainty of the phylogeny with uncertainty in the estimate of the ancestral state. Our approach does not constrain the sample of trees only to those that contain the ancestral node or nodes of interest, and we show how to reconstruct ancestral states of uncertain nodes using a most-recent-common-ancestor approach. We illustrate the methods with data on ribonuclease evolution in the Artiodactyla. Software implementing the methods (BayesMultiState) is available from the authors.

The Maximum Likelihood Approach to Reconstructing Ancestral Character States of Discrete Characters on Phylogenies

A phylogeny describes the hierarchical pattern of descent of some group of species from a common ancestor. If information is available on the character states of the contemporary species, thepossibility is raised of using that information in combination with the phylogeny to reconstruct the historical events of evolution. These reconstructions can be used to retrieve a picture of theworld as the species evolved alongwhatwould become the branches of the phylogeny. This, in turn, provides a way to test hypotheses about evolution and adaptation. Methods based on the principle of parsimony reconstruct the ancestral character states to minimize the number of historical character changes required to produce the diversity observed among the contemporary species (seeMaddison et al., 1984, for a general account). An alternative to parsimony approaches makes use of the principle of maximum likelihood. Maximum likelihood solutions make the observed data most likely given somemodel of the process under investigation (see Edwards, 1972). In a phylogenetic context this means reconstructing the ancestral character states to make the character states observed among the contemporary species most probable, given some statistical model of the way evolution proceeds. Maximum likelihood solutions may or may not be the mostparsimonious solution. I restrict myself here to using maximum likelihood models to infer ancestral character states for binary discrete characters, that is, for characters that can adopt only two states, although the generalization to more than two states requires no new concepts.My approach to reconstructing ancestral states makes use of a Markov model of binary character evolution on phylogenies (Pagel, 1994). Sanderson (1993) describes a related model for investigating rates of gains and losses of characters for which the ancestral states are assumed to be known. Schluter (1995), Yang et al. (1995), and Koshi and Goldstein (1996) derive methods that are similar to the procedures I will describe here. However, Yang et al. (1995) and Koshi and Goldstein (1996) use what I shall term “global” methods for estimating ancestral characters, I argue for a “local” approach on grounds that the global method does not produce a maximum-likelihood estimate of the hypothesis of interest. Schluter (1995) reported global and local estimators in his investigation of artiodactyl ribonucleases, and Schluter et al. (1997) reported global estimators. In several recent papers, Schluter (1995; Schluter et al., 1997) called attention to the usefulness of reconstructing ancestral character states for testing ideas about adaptation and evolution, and much of what I say here owes its inspiration to these investigations. Mooers and Schluter (1999) now provide important additional examples of how maximum likelihood methods can return both more information about ancestral character states thanparsimony approaches, as well as information that is at odds with parsimony reconstructions. I intend this article to act as a primer to thosewhoare interested in usingmaximumlikelihood methods but who may not be familiar with the mathematics of the approach. Accordingly, I begin with the simplest case of estimating the ancestral state of two species.

Inferring evolutionary processes from phylogenies

Evolutionary processes shape the regular trends of evolution and are responsible for the diversity and distribution of contemporary species. They include correlated evolutionary change and trajectories of trait evolution, convergent and parallel evolution, differential rates of evolution, speciation and extinction, the order and direction of change in characters, and the nature of the evolutionary process itself—does change accumulate gradually, episodically, or in punctuational bursts. Phylogenies, in combination with information on species, contain the imprint of these historical evolutionary processes. By applying comparative methods based upon statistical models of evolution to well resolved phylogenies, it is possible to infer the historical evolutionary processes that must have existed in the past, given the patterns of diversity seen in the present. I describe a set of maximum likelihood statistical methods for inferring such processes. The methods estimate parameters of statistical models for inferring correlated evolutionary change in continuously varying characters, for detecting correlated evolution in discrete characters, for estimating rates of evolution, and for investigating the nature of the evolutionary process itself. They also anticipate the wealth of information becoming available to biological scientists from genetic studies that pin down relationships among organisms with unprecedented accuracy.

A method for the analysis of comparative data

Felsenstein (1985) developed a method for analyzing comparative data that calculates a set of mutually independent comparisons among the species. The method was designed to be used with phylogenies for which the true dichotomous branching pattern is known. However, available phylogenies often contain many incompletely resolved nodes, or nodes from which three or more branches emanate. This paper reports a generalization of Felsensteins method that permits the analysis of incompletely resolved phylogenies. The method is general to any sort of phylogeny and, like Felsensteins model can accommodate more than one model of evolutionary change. The method is implemented in a computer program which can make use of information on branch lengths, or, if branch length information is not available, an algorithm is used to calculate a set of branch lengths. The wider implications of the method are that it makes explicit the assumptions about unknown branching patterns and branch lengths that all comparative methods that are applied to incompletely resolved phylogenies must make.

Bayesian analysis of correlated evolution of discrete characters by reversible-jump Markov chain Monte Carlo.

We describe a Bayesian method for investigating correlated evolution of discrete binary traits on phylogenetic trees. The method fits a continuous‐time Markov model to a pair of traits, seeking the best fitting models that describe their joint evolution on a phylogeny. We employ the methodology of reversible‐jump (RJ) Markov chain Monte Carlo to search among the large number of possible models, some of which conform to independent evolution of the two traits, others to correlated evolution. The RJ Markov chain visits these models in proportion to their posterior probabilities, thereby directly estimating the support for the hypothesis of correlated evolution. In addition, the RJ Markov chain simultaneously estimates the posterior distributions of the rate parameters of the model of trait evolution. These posterior distributions can be used to test among alternative evolutionary scenarios to explain the observed data. All results are integrated over a sample of phylogenetic trees to account for phylogenetic uncertainty. We implement the method in a program called RJ Discrete and illustrate it by analyzing the question of whether mating system and advertisement of estrus by females have coevolved in the Old World monkeys and great apes.

RECENT DEVELOPMENTS IN THE ANALYSIS OF COMPARATIVE DATA

Comparative methods can be used to test ideas about adaptation by identifying cases of either parallel or convergent evolutionary change across taxa. Phylogenetic relationhips must be known or inferred if comparative methods are to separate the cross-taxonomic covariation among traits associated with evolutionary change from that attributable to common ancestry. Only the former can be used to test ideas linking convergent or parallel evolutionary change to some aspect of the environment. The comparative methods that are currenlty available differ in how they manage the effects brought about by phylogenetic relationships. One method is applicable only to discrete data, and uses cladistic techniques to identify evolutionary events that depart from phylogenetic trends. Techniques for continuous variables attempt to control for plylogenetic effects in a variety of ways. One method examines the taxonomic distribution of variance to identify the taxa within which character variation is small. The method assumes that taxa with small amounts of variation are those in which little evolutionary change has occurred, and thus variation is unlikely to be independent of ancestral trends. Analyses are then concentrated among taxa that show more variation, on the assumption that greater evolutionary change in the character has taken place. Several methods estimate directly the extent to which ancestry can predict the observed variation of a character, and subtract the ancestral effect to reveal variation independent of phylogeny. Yet another can remove phylogenetic effects if the true phylogeny is known. One class of comparative methods controls for phylogenetic effects by searching for comparative trends within rather than across taxa. With current knowledge of phylogenies, there is a trade-off in the choice of a comparative method: those that control phylogenetic effects with greater certainty are either less applicable to real data, or they make restrictive or untestable assumptions. Those that rely on statistical patterns to infer phylogenetic effects may not control phylogeny as efficiently but are more readily applied to existing data sets.

Detecting Regular Sound Changes in Linguistics as Events of Concerted Evolution

Summary Background Concerted evolution is normally used to describe parallel changes at different sites in a genome, but it is also observed in languages where a specific phoneme changes to the same other phoneme in many words in the lexicon—a phenomenon known as regular sound change. We develop a general statistical model that can detect concerted changes in aligned sequence data and apply it to study regular sound changes in the Turkic language family. Results Linguistic evolution, unlike the genetic substitutional process, is dominated by events of concerted evolutionary change. Our model identified more than 70 historical events of regular sound change that occurred throughout the evolution of the Turkic language family, while simultaneously inferring a dated phylogenetic tree. Including regular sound changes yielded an approximately 4-fold improvement in the characterization of linguistic change over a simpler model of sporadic change, improved phylogenetic inference, and returned more reliable and plausible dates for events on the phylogenies. The historical timings of the concerted changes closely follow a Poisson process model, and the sound transition networks derived from our model mirror linguistic expectations. Conclusions We demonstrate that a model with no prior knowledge of complex concerted or regular changes can nevertheless infer the historical timings and genealogical placements of events of concerted change from the signals left in contemporary data. Our model can be applied wherever discrete elements—such as genes, words, cultural trends, technologies, or morphological traits—can change in parallel within an organism or other evolving group.