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Modelling the Evolution of Continuously Varying Characters on Phylogenetic Trees the Case of Hominid Cranial Capacity

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Modelling the Evolution of Continuously Varying Characters on Phylogenetic Trees the Case of Hominid Cranial Capacity Chapter 13 Modelling the evolution of continuously varying characters on phylogenetic trees The case of Hominid cranial capacity Mark Pagel ABSTRACT I describe a generalised least squares model for analysing trait evolution on phyloge- netic trees, and apply the model to characterise brain-size evolution in the hominids. The model incorporates the conventional Brownian-motion or random-walk model of trait evolution, but can also estimate a directional component to trait evolution - such as would arise if the trait were getting bigger or smaller through evolutionary time. This also makes it possible to reconstruct ancestral states that fall outside the range of observed (extant) values, something that cannot occur with simple Brownian- motion models. The model can also estimate three scaling parameters relevant to testing hypotheses about the tempo and mode of trait evolution: is it punctuated or gradual, does it proceed at a constant rate or speed up (slow down), and are the sim­ ilarities among species what we would expect? Applied to hominid trait evolution, the model detects the well-known increase in brain size in this group, and as a result, estimates ancestral states more accurately than the random-walk model. The model further suggests that brain-size evolution has been gradual, but that its rate of increase has increased over time (i.e., it is accelerating). Introduction Given a collection of species, information on their attributes, and a phylogeny that describes their shared hierarchy of descent, the prospect is raised of reconstructing the characteristics of the ancestors to these species. This is an intriguing idea, holding out as it does the possibility of glimpsing the past and of seeing how the present came about. The attraction is more than just curiosity. Some ecological and evolutionary theo­ ries require a specific order and direction of evolution from ancestors to descendants. Cope's famous law' proposes that as species give way to their descendants body size tends to increase, yielding an evolutionary trend toward increasing size. Where no theory exists to make a prediction, reconstructed ancestral states provide, if accu­ rate, ideas about how and why creatures evolved as they did. Omland (1994,1997), for example, investigates empirical patterns of directional evolution in morphological traits of ducks. Schluter, Mooers and colleagues (Schluter 1995; Schluter etal 1997; Mooers et al 1999; Mooers and Schluter 1999) have been instrumental in calling attention to these and other possibilities inherent in reconstructing ancestral states 270 Mark Pagel on phytogenies. Golding and Dean (1998) emphasise the potential for reconstructing ancient genes and proteins. The attributes of species come in all shapes and sizes, but they can be broadly categorised into two classes. The so-called 'discrete' traits adopt a finite and typically small number of states and may or may not be ordered. The presence or absence of some feature is a binary discrete trait. Living solitarily, in a relationship with one other, or in a group could be an ordered discrete trait. More often, traits are defined in such a way as to constitute a continuously varying feature of the organism or its environment. Wing length, geographic range size, body size, brain volume, age at maturation, running speed, and body temperature are all examples of continuously varying traits. Here, I shall confine myself to discussing the statistical reconstruction of the probable ancestral character states of continuously varying traits, discrete traits having recently been discussed elsewhere (Schluter 1995; Yang et al. 1995; Koshi and Goldstein 1996; Schluter et al. 1997; Mooers and Schluter 1999; Pagel 1999a,b). Continuously vary­ ing traits also have received attention in recent work (Schluter et al. 1997; Garland et al. 1999; Mooers et al. 1999), but I discuss a relatively new maximum-likelihood model that can detect and characterise directional trends of evolution (see Pagel 1997, 1999b). This method can detect features of trait evolution not available to other meth­ ods, such as gradual versus punctuational change, accelerating versus decelerating trait evolution, and whether phylogenetic effects are present. By virtue of being capable of detecting directional trends the method raises the attractive possibility of reconstruct­ ing ancestral states to fall outside of the range of values observed amongst species. That is, it may be possible to infer the historical existence of traits never directly observed. I use a recent phylogeny proposed for the Hominid species (Foley 1998) and information on cranial capacity to illustrate the method in the context of brain-size evolution. General theory for statistical models of continuously varying traits The conventional approach to reconstructing ancestral states of continuous traits pro­ ceeds by choosing those values for the ancestral states that minimise some criterion of the total amount of evolution on the tree (e.g., W. P. Maddison 1991; D. R. Maddison 1994). This is the method of maximum parsimony, and the criterion that is minimised is usually the square of the amount of inferred change along the branches of the phylogeny - hence 'squared-change' parsimony. Other criteria are possible, such as minimising the absolute value of change. The chief weaknesses of this approach are that it assumes that character change is rare, and it fails to incorporate any stochastic element into the process of evolution. Character change may not be rare (e.g., Schluter 1995; Pagel 1999b), and it is impor­ tant to document the expected uncertainty in our estimates of ancestral states to know what alternative values can be safely ruled out. Maximum parsimony methods do not provide estimates of this uncertainty, although an error-rate of sorts may be possible in principle to calculate (Maddison 1995). Modelling continuously varying characters 271 The principle alternative to parsimony methods is to adopt a statistical approach to reconstructing ancestral states (e.g., Pagel 1997, 1999a,b; Schluter et al. 1997; Garland et al 1999; Mooers et al 1999; Mooers and Schluter 1999). For traits that naturally vary along a continuous scale constant-variance random-walk models (sometimes called Brownian motion) provide a useful framework within which to model character evolution. In the conventional random-walk model, traits evolve each instant of 'time' dt with a mean change of zero and unknown and constant variance σ2. Time may be chronological or some other unit of divergence such as genetic distance. The evolutionary process is presumed to unfold independently at each instant of time and along each of the branches of the phylogeny. This framework makes it possible to calculate the uncertainty associated with esti­ mates allotted to different parts of a phylogenetic tree. It is an important capability when attempting to estimate ancestral states: trait values of species or lineages that have diverged more from the root are expected to have larger variances and thus are less reliable observations for reconstructing the past, other things equal. To see why, consider that the expected variance of a given species' trait value is tσ 2, where t records the total path length (time or distance) from the root to that species. This is the vari­ ance in the trait that would be expected were the process of evolution to be re-run many times from the same starting point. The starting point is the value of the trait at the root of the tree, and is estimated from the data. Schluter et al. (1997) apply this basic model to reconstructing ancestral wing lengths in scrubwrens and to ecological diversification in lizards. Garland et al. (1999) investi­ gate the basic constant-variance model and variations on it for a range of characters and taxa. Ancestral states obtained from the popular independent-contrasts approaches for comparative studies (Felsenstein 1985; Harvey and Pagel 1991; Garland et al 1992; Pagel 1992) are equivalent to those obtained from the constant-variance random-walk model. Similarly, ancestral states estimated from 'local' squared-change parsimony, in which only the species immediately descendant from a node are used to estimate the state of the node, are also equivalent to those obtained from the constant-variance model. A limitation of the standard constant-variance model is that, by presuming that traits evolve according to an unbiased random-walk (neutral-drift), it cannot detect any directional trends of trait evolution along the branches of the tree (Pagel 1997,199b). Historical trends such as a phyletic increase in size, or more generally, greater amounts of change in the traits of lineages that have diverged more, will be masked. This model along with independent-contrast and squared-change parsimony approaches always estimates the ancestral state at the root of the phylogeny as falling somewhere within the range of observed values in the species data, as it has no route by which to place them outisde of this range. By comparison, here I shall show how a directional constant-variance model for continuous traits can detect historical trends of trait evolution, and use them to develop more plausible and accurate estimates of ancestral states. Unlike the neutral random- walk model, the directional model presumes that there has been a bias in evolution such that traits evolve at each instant of time dt with a mean of ß and unknown and constant variance a2 (Pagel 1997,1999b). Note that here ß is used to signify the bias in the random walk, and not the variance of trait evolution as in Schluter et al (1997). The directional model, in effect, examines the correlation between the species' trait 272 Mark Page! values and the total phylogenetic distance or path length from the root of the tree. If a directional trend exists, species that have diverged more from the root, will tend also to have changed more in a given direction, that is, be larger, or mature earlier, and so on.
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