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First published online August 4, 2005
Journal of Experimental Biology 208, 3015-3035 (2005)
Published by The Company of Biologists 2005
doi: 10.1242/jeb.01745

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Commentary

Phylogenetic approaches in comparative physiology

Theodore Garland, Jr¹, Albert F. Bennett^2,* and Enrico L. Rezende¹

¹ Department of Biology, University of California, Riverside, CA 92521, USA
² Department of Ecology and Evolutionary Biology, University of California, Irvine, CA 92697, USA

^* Author for correspondence (e-mail: abennett{at}uci.edu)

Accepted 13 June 2005

	Summary

TOP Summary Introduction Phylogeny and modern... An example of how... When and why to... Examples of the utility... Some notes of caution Summary and perspectives Appendix References

 
Over the past two decades, comparative biological analyses have undergone profound changes with the incorporation of rigorous evolutionary perspectives and phylogenetic information. This change followed in large part from the realization that traditional methods of statistical analysis tacitly assumed independence of all observations, when in fact biological groups such as species are differentially related to each other according to their evolutionary history. New phylogenetically based analytical methods were then rapidly developed, incorporated into `the comparative method', and applied to many physiological, biochemical, morphological and behavioral investigations. We now review the rationale for including phylogenetic information in comparative studies and briefly discuss three methods for doing this (independent contrasts, generalized least-squares models, and Monte Carlo computer simulations). We discuss when and how to use phylogenetic information in comparative studies and provide several examples in which it has been helpful, or even crucial, to a comparative analysis. We also consider some difficulties with phylogenetically based statistical methods, and of comparative approaches in general, both practical and theoretical. It is our personal opinion that the incorporation of phylogeny information into comparative studies has been highly beneficial, not only because it can improve the reliability of statistical inferences, but also because it continually emphasizes the potential importance of past evolutionary history in determining current form and function.

Key words: allometry, comparative method, evolutionary physiology, model of evolution, phylogeny, statistical analysis

	Introduction

TOP Summary Introduction Phylogeny and modern... An example of how... When and why to... Examples of the utility... Some notes of caution Summary and perspectives Appendix References

 
Studies of organismal form and function rely on multiple types of scientific investigation, including theory, description, experimentation and comparison. Comparing species is an ancient human enterprise, done for a variety of reasons (Sanford et al., 2002). Since Charles Darwin, the `comparative method' – comparing populations, species or higher taxa – has been the most common and productive means of elucidating past evolutionary processes (Harvey and Pagel, 1991; Brooks and McClennan, 2002). Comparative methods have been used extensively to infer evolutionary adaptation, that is, changes in response to natural selection (for alternate physiological meanings of `adaptation', see Garland and Adolph, 1991; Bennett, 1997). They are most often promoted and criticized (e.g. Leroi et al., 1994) within this context. However, comparative methods are not used to infer adaptation alone (Garland and Adolph, 1994; Sanford et al., 2002), but are also employed to analyze the effects of sexual selection (e.g. Hosken et al., 2001; Nunn, 2002; Smith and Cheverud, 2002; Aparicio et al., 2003; Cox et al., 2003), which may be nonadaptive or even maladaptive with respect to natural selection. These methods can also be used to compare rates of evolution across clades or the amount of morphospace occupied by clades or by ecologically defined groups (Garland, 1992; Clobert et al., 1998; Ricklefs and Nealen, 1998; Garland and Ives, 2000; Hutcheon and Garland, 2004; McKechnie and Wolf, 2004). Of particular interest for the present review, they are also widely used to explore trade-offs (e.g. Clobert et al., 1998; Vanhooydonck and Van Damme, 2001) and to examine functional (mechanistic) relationships among traits (e.g. Lauder, 1990; Iwaniuk et al., 1999; Mottishaw et al., 1999; Autumn et al., 2002; Hale et al., 2002; Gibbs et al., 2003; Johnston et al., 2003; Herrel et al., 2005), including allometric scaling with body size (e.g. Garland, 1994; Reynolds and Lee, 1996; Williams, 1996; Clobert et al., 1998; Garland and Ives, 2000; Nunn and Barton, 2000; Herrel et al., 2002; Perry and Garland, 2002; Rezende et al., 2002, 2004; Schleucher and Withers, 2002; McGuire, 2003; Al-kahtani et al., 2004; McKechnie and Wolf, 2004; Muñoz-Garcia and Williams, in press).

Comparative methods have been radically restructured over the past two decades, and now routinely incorporate both phylogenetic information and explicit models of character evolution. Indeed, Sanford et al. (2002) suggest that this new emphasis be termed the `comparative phylogenetic method'. As outlined in Blomberg and Garland (2002), this revolution in comparative phylogenetic methodology followed from several conceptual advances: (1) adaptation should not be casually inferred from comparative data; (2) the incorporation of phylogenetic information increases both the quality and even the type of inference from comparative data alone; (3) because all organisms are differentially related to each other, taxa cannot be assumed to be independent of each other for statistical purposes; (4) statistical analyses of comparative data must assume some model of character evolution for effective inference; (5) taxa used in comparative analyses should be chosen in regard to their phylogenetic affinities as well as the area of functional investigation; and (6) even phylogenetically based comparisons are purely correlational and inferences of causation drawn from them can be enhanced by other approaches, including experimental manipulations.

To expand on some of these points, `quality' in point 2 includes the simple fact that adding an independent estimate of phylogenetic relationships to a comparative analysis increases – often greatly – the amount of basic data that is brought to bear on a given question, whereas `type' refers to analyses that are simply impossible without a phylogenetic perspective, such as reconstructing ancestral values or comparing rates of evolution among lineages. Although phylogenetic information and a suitable analytical method may allow any comparative data set to be `rescued' from phylogenetic nonindependence (e.g. avoid inflated Type I error rates; point 3), phylogenetically informed choice of species (point 5) can accomplish more, such as actually increasing statistical power to detect relationships among traits (Garland et al., 1993; Garland, 2001). Finally, we note that point 6 was recognized long ago, but has been re-emphasized as phylogenetically explicit methods of statistical inference have been developed (e.g. see Lauder, 1990; Garland and Adolph, 1994; Leroi et al., 1994; Autumn et al., 2002).

The intent of this commentary is to provide a review of some advances that have occurred in the comparative method, with an emphasis on their place in comparative physiology. We examine the underlying reasons for the incorporation of phylogenetic information into comparative studies. In an Appendix, we give a brief overview of the three most commonly used and best understood phylogenetically based statistical methods: independent contrasts (IC; worked example in Fig. 5), generalized least-squares (GLS) models, and Monte Carlo computer simulations. These methods apply mainly to analysis of continuously varying (or at least quantitative) traits, which is the nature of most physiological traits (e.g. blood pressure, metabolic rate, enzyme activity). However, they can also easily incorporate independent variables that are treated as discrete categories, such as diet (e.g. insectivore, frugivore, sanguivore) or habitat (e.g. fresh or salt water). Discussions of methods for categorical traits and computer programs to implement them are available from Mark Pagel (e.g. see Pagel, 1999), in MacClade (Maddison and Maddison, 2000), and in Mesquite (http://mesquiteproject.org/mesquite/mesquite.html; see also Paradis and Claude, 2002). For a general listing of phylogeny-related programs, see the website maintained by Joe Felsenstein (http://evolution.genetics.washington.edu/phylip/software.html).

We discuss when phylogenetically based statistical methods should be used and give some practical examples of where a phylogenetic perspective has improved our understanding of comparative data and evolutionary processes. We also discuss some of the practical and theoretical limitations of such methods. Throughout, we try to emphasize that the incorporation of phylogeny can greatly enhance comparative studies, deliver new insights, and open new areas for research. This is of necessity only a brief summary and readers are directed to more extensive discussions of the topics and issues raised here (e.g. Ridley, 1983; Lauder, 1981, 1982, 1990; Harvey and Pagel, 1991; Garland et al., 1992, 1999; Garland and Adolph, 1994; Harvey, 1996; Ricklefs and Nealen, 1998; Ackerly, 1999, 2000, 2004; Pagel, 1999; Purvis and Webster, 1999; Diniz-Filho, 2000; Feder et al., 2000; Garland and Ives, 2000; Maddison and Maddison, 2000; Garland, 2001; Rohlf, 2001; Autumn et al., 2002; Blomberg and Garland, 2002; Brooks and McLennan, 2002; Blomberg et al., 2002, 2003; Rezende and Garland, 2003; Housworth et al., 2004). We have intentionally not cited some `forum' and `perspective' type papers because we felt that their rhetoric was misleading, and in some cases they contain outright errors.

The empirical examples cited here are idiosyncratic, reflecting mainly our own research interests. Thus, we emphasize examples that involve physiological phenotypes, but include others when they are lacking. Our enthusiasm for phylogenetic approaches in comparative physiology should not be taken to imply, however, that we think they are more important than other approaches, such as measurement of selection acting in natural populations, experimental evolution (e.g. see Garland and Carter, 1994; Bennett and Lenski, 1999; Ackerly et al., 2000; Feder et al., 2000; Garland, 2001, 2003; Bennett, 2003; Swallow and Garland, 2005), or more purely mechanistic investigations (e.g. Mangum and Hochachka, 1998; Hochachka and Somero, 2002).

We are concerned that some of our discussion of assumptions and intricacies of phylogenetically based statistical methods may be off-putting to those who simply want to analyze their data (see also Felsenstein, 1985). However, it must be acknowledged that statistical analyses in general are not always simple and have underlying assumptions that cannot be ignored. Most of the tools that we use in everyday research (e.g. correlation, regression, analysis of variance, analysis of covariance) have been around for 50 years or even a century. Nonetheless, the field of statistics (both theoretical and applied) continues to refine these methods. Such questions as what type of line is best for describing functional relationships (e.g. Rayner, 1985; chapter 6 in Harvey and Pagel, 1991; Riska, 1991; McGuire, 2003; Garland et al., 2004), how to deal with non-linear relationships (Quader et al., 2004) or random effects in ANOVA models, when to include or exclude interaction terms, how best to transform data, or when to employ nonparametric methods, still do not have simple, general answers. Moreover, new statistical methods continue to be developed, including computer-intensive approaches that were not possible 50 years ago (e.g. see Lapointe and Garland, 2001; Roff, in press). For many statistical parameters, including comparative methodologies, several different approaches (and attendant algorithms) may be used for estimation, none of which performs `best' in all situations. We believe that it is important that a comparative biologist understand the assumptions and approaches underlying these methodologies, and does not just resort to their rote application, and that is the basis for our more detailed presentation.

	Phylogeny and modern (statistical) comparative methods

TOP Summary Introduction Phylogeny and modern... An example of how... When and why to... Examples of the utility... Some notes of caution Summary and perspectives Appendix References

 
The beginning of the transition into modern comparative phylogenetic methods is marked by the publication of Ridley's book on mating adaptations (Ridley, 1983) and by Felsenstein's article entitled `Phylogenies and the comparative method' (Felsenstein, 1985). Both argued for the necessity of incorporating an explicitly phylogenetic perspective into analyses of comparative data. These authors were not the first to claim that comparative data generally violate the assumptions of conventional statistical methods (see Harvey and Pagel, 1991), but Felsenstein (1985) proposed the first fully phylogenetic method, i.e. one that could incorporate detailed information on topology and branch lengths, which he termed independent contrasts (IC). Although the full-blown IC method (see Appendix for description and worked example in Fig. 5) requires detailed information on phylogenetic topology, branch lengths (Fig. 1), and model of character evolution (Fig. 2) in order to be maximally reliable, Felsenstein (1985) also considered how one might make use of partial information, such as might be derived from a taxonomy that had some resemblance to actual phylogenetic relationships, e.g. by comparing several pairs of species within a series of genera, an approach that is now commonly used (e.g. Monkkonen, 1995; for a review of plant examples, see Ackerly, 1999). Nonetheless, the requirements of the method seemed daunting to many, and its use in comparative physiology grew slowly. Indeed, one of us even helped to develop an alternative phylogenetic method, partly because of a lack of information on branch lengths (see Figs 1, 2) in a comparative study that seemed to preclude the use of IC (Huey and Bennett, 1987; and see extensions in Garland et al., 1991; Martins and Garland, 1991).

View larger version (14K): [in this window] [in a new window]   Fig. 1. Hypothetical evolutionary relationships among 17 species of organisms. Vertical axis represents time in relative units, with the top of the `phylogenetic tree' representing the present. Hence, species 1–7 and 8–13 are alive now (extant), whereas species e1–e4 are extinct. Statements about phylogenetic relationships are based solely on recency of common ancestry. For example, species 1 and 2 are each other's closest relative because they share a more recent common history with each other than with any other species depicted in this figure. The horizontal axis is arbitrary, and note that nodes could be rotated for graphical convenience with no implication for evolutionary relationships. `Clades' are hierarchically arranged, `monophyletic' groups of species, including all species that have descended from a common ancestor as well as that basal ancestor. All species within a given clade are more closely related to each other (they share a more recent common ancestor) than to any species in another clade. In the strict sense, a clade includes all species that have ever existed within it. Thus, Clade B includes species 7 as well as e1–e4. However, as it is impossible to know of all extinct species within a given clade and as physiologists rarely include extinct taxa in their studies, the term `clade' is often used in a relative way with respect to a particular collection of species that are included in a given study. Consider a comparative physiological study of species 1–13. Species 1–6 might be referred to as Clade 1, while species 7–13 might be referred to as Clade 2. However, note that species 7 is relatively distantly related to the other extant species in Clade 2 (i.e. species 8–13 shared a last common ancestor much more recently than the last common ancestor of them with species 7). Hence, a researcher studying species 1–13 might prefer to write in terms of Clades A, B and C in order to highlight the fact that, a priori, she would expect species 7 to be somewhat different from species 8–13. (Importantly, a priori hypotheses about particular single species can be tested with well-established phylogenetically based statistical methods, although they may not be convincing to some regardless of the level of statistical significance; see Garland et al., 1993; Garland and Adolph, 1994; Garland and Ives, 2000.) Branch lengths in this figure are proportional to divergence times. All phylogenetically based statistical methods use branch lengths in their calculations, although some assume (arbitrarily) that each branch segment is equal in length. Alternatively, under the commonly assumed Brownian motion model of character evolution (see Fig. 2), branch lengths are assumed to be in units proportional to (relative) divergence times and hence to the variance of character evolution along each branch segment (i.e. longer branches imply greater variance of character change; see Felsenstein, 1985).

View larger version (17K): [in this window] [in a new window]   Fig. 2. Illustration of a Brownian motion (random walk in continuous time) model of character evolution, as might be implemented in a computer program (e.g. PDSIMUL of Garland et al., 1993). The goal is to simulate the evolution of two traits, beginning at the bottom of the phylogenetic tree and ending at the three tips, species A, B and C. A computer program begins at the bottom of the tree (internal node `F') with user-specified starting values, in this example 10 and 10 for Traits 1 and 2, respectively. It then draws a random datum from a bivariate normal distribution of hypothetical evolutionary changes for the two traits. This distribution is illustrated by concentric rings proportional to density of data points in the z axis (projecting out of the page), with darker indicating a higher density of points; the tails of the distribution diminish to infinity). In this example, we assume that the means of this distribution are 0 for both traits, such that no general tendency for either to increase or decrease will be modeled. We also specify 0 correlation between them, such that they will `evolve' independently, on average. For the amount of evolutionary change from node F to tip species C, we happen to draw values of –4 and –2 (red). Thus, species C has values of 6 and 8. For the change from node F to G, we draw +3 and +2 (blue). Above this, we draw two separate sets of changes: +1 and –2 leading to tip species A (green); –1 and +2 leading to tip species B (purple). Note that the amount of change tends to be greater for longer branches, reflecting a greater opportunity for evolutionary change. In practice, a computer program might achieve this by expanding or contracting the widths of the bivariate normal distribution for relatively longer or shorter branch lengths, respectively. Thus, under Brownian motion, for a given character, the variance of this distribution is set to be proportional to divergence time (along the length of each branch segment sequentially; Felsenstein, 1985, 1988). Note also that the distribution from which changes are drawn does not need to be (bivariate) normal (see Felsenstein, 1985, 1988). Moreover, the means of the distribution can be set to positive or negative values to impose directional trends in character evolution (Garland et al., 1993). These sorts of changes create models that are no longer simple Brownian motion.

Concern about the possible influence of phylogeny in comparative and ecological physiology antedated Felsenstein's (1985) publication. For example, explicit comparisons of marsupial with placental mammals (MacMillen and Nelson, 1969; Dawson and Hulbert, 1970) and of passerine with non-passerine birds (Lasiewski and Dawson, 1967) were motivated by cognizance of phylogeny, and some workers tried to partition the effects of phylogeny on physiological relationships (e.g. Andrews and Pough, 1985). Moreover, some workers voiced concerns about specific adaptive interpretations of characters shared more widely in their clades (e.g. Dawson and Schmidt-Nielsen, 1964; Dawson et al., 1977). What those earlier studies lacked was not necessarily a general perspective on the importance of phylogeny, but rather a formal logical and statistical methodology for incorporating detailed phylogenetic information. Analytical techniques have been greatly expanded and modified since 1985 (see below and Appendix), but Felsenstein's IC method is still the most widely used and his insights were pivotal to modernization of the comparative method. Moreover, the realization that IC is a special case of generalized least-squares (GLS) methods (see Appendix) means that the former can always serve as a useful entry point for the latter, and one that retains the major heuristic of `tree thinking' (sensu Maddison and Maddison, 2000).

Traditional interspecific comparative analyses applied conventional statistical methods to test for associations between traits (e.g. metabolic rate and body size), or between a trait and an environmental variable (e.g. blood oxygen carrying capacity and altitude). This approach treats all data points (e.g. mean values for a series of species) as statistically independent of each other. Unfortunately, mean phenotypes of biological taxa usually will not be statistically independent because they are all related through their hierarchical phylogenetic history. Empirically, more closely related species do indeed tend to resemble one another; put simply, hummingbirds look like hummingbirds, and turtles look like turtles, and the same is true for physiological traits (Blomberg et al., 2003; see below). This general tendency exists for several good biological reasons (Harvey and Pagel, 1991), including time lags for change to occur after speciation, occupation of similar niches by close relatives, and conservative phenotype-dependent responses to selection. Thus, the extent of these phylogenetic relationships – and hence the expected degree of resemblance – must also be figured into comparative analyses. Analytical techniques that do not incorporate phylogenetic information make the tacit statistical assumption that all the species studied are equally distantly related to each other, that is, that they descended along a `star phylogeny' (Fig. 3A), when in fact their ancestral associations are hierarchical (Fig. 3C).

View larger version (19K): [in this window] [in a new window]   Fig. 3. (A) Illustration of what conventional statistical analyses assume when applied to comparative data (`star' phylogeny with equal-length branches). This model implies that values at tips of the tree (phenotypic means for some trait for 10 species) are statistically independent and identically distributed. (B) Phylogenetic tree that might be inferred from taxonomic information, e.g. if five genera within a single family were represented that contained, from left to right, one, one, three, three and two species in the data set. This assumes that the genera are an unrelated series of `mini-stars' with no hierarchical structure within any of them. It also assumes that the taxa actually represent separate evolutionary lineages (monophyletic groups or clades), but such is not always the case for taxonomies. (C) Estimates of real phylogenies usually indicate hierarchical relationships and branches that do not necessarily line up along the tips of the tree. Non-contemporaneous tips can indicate that extinct taxa are included in the data set or that the rate of evolution has varied among branches. Real phylogenies like this cause various statistical problems, stemming from the non-independence of species' phenotypes, so phylogenetically based statistical methods are required for proper analyses. Modified from Garland (2001) and Rezende and Garland (2003).

Second, it is important to consider what is meant by the `branch lengths' of a phylogenetic tree that is used for analysis. In general, proponents of phylogenetically based comparative methods assume that analyses of physiological and other traits will involve use of a phylogenetic tree that was inferred from other data, such as variation in DNA sequences, which is presumed to be independent of the data being analyzed. Otherwise, it seems intuitively obvious that analyses may involve some circularity. However, this is actually a complicated subject and beyond the scope of the present paper (Felsenstein, 1985; de Queiroz, 2000). Leaving aside the general issue of having available a phylogeny that is independent of the characters under study, the branch lengths of the working phylogenetic tree are confounded with the model and rates of character evolution that will be assumed for statistical analyses of most real data sets (see Figs 1, 2). In other words, we usually do not have independent information on, for instance, divergence times and selective regimes that may have prevailed along various branches of the tree. In any case, all of the main phylogenetically based statistical methods require branch lengths in units proportional to expected variance of evolution for the characters(s) under study (see Felsenstein, 1985, 1988; Garland et al., 1992, 1993, 1999; Garland and Ives, 2000; Rohlf, 2001; Blomberg et al., 2003; Housworth et al., 2004). Branch lengths essentially indicate our a priori expectations for how likely a given trait was to change (increase or decrease in value) from one node to another along a phylogenetic tree, and thus become an integral component of our statistical null model. Under a simple Brownian motion model, those branch lengths would necessarily be proportional to divergence times. Under any other model, such as the Ornstein–Uhlenbeck (OU) process, which is like Brownian motion while tethered to an elastic band and is used to model stabilizing selection or constraints on trait space (Felsenstein, 1988; Garland et al., 1993; Diaz-Uriarte and Garland, 1996; Martins and Hansen, 1997; Blomberg et al., 2003; Freckleton et al., 2003; Butler and King, 2004; Housworth et al., 2004), they would be more-or-less different from divergence times.

A simple hypothetical example can illustrate this distinction. Many traits evolve within limits set by physical or biological properties. Some of these are trivial. For example, body mass cannot evolve to be as small as 0 g. Others are more interesting. Apparently, for example, activity body temperatures (T_b) of squamate reptiles (lizards and snakes) cannot evolve to be more than about 42°C. We do not know the ancestral activity T_b of squamates, but it was probably substantially lower that 42°C. Thus, during their initial radiation and diversification, T_b would have been free to evolve, perhaps in a fairly Brownian motion-like fashion, with an increase or decrease about equally likely to occur along any branch of the phylogeny. However, lineages that `explored' the climate space towards higher T<sub>b</sub> would eventually be constrained by the reduction in Darwinian fitness that can be caused by exceedingly high temperatures (e.g. via failure of spermatogenesis or outright death). Thus, if we were to depict a phylogenetic tree of squamates with branch lengths proportional to expected variance of T<sub>b</sub> evolution, then we would need to know the T<sub>b</sub> at the start of each branch segment and also have the branches be, in effect, different if the lineage was near a thermal limit, either upper or lower. That is, a lineage near an upper limit would have a low probability of evolving a higher T<sub>b</sub>, but a `typical' probability of evolving a lower T_b, and vice versa. It should be obvious that our ability to specify such detailed branch-length information for any trait in any group of wild organisms is severely limited. Thus, for simplicity and/or analytical tractability, phylogenetically based statistical methods usually begin with an assumption of Brownian motion evolution along whatever branch lengths are specified in a working phylogeny (e.g. Fig. 1). And in many cases (e.g. see reviews of published studies in Blomberg et al., 2003; Ashton, 2004a), these will be arbitrary values, such as setting all segments equal to unity in length or by some other simple rule (e.g. Fig. 4B). In such cases, it is often prudent to perform computations with more than one set of branches as a sensitivity analysis for the conclusions (e.g. see Ashton, 2004b; Hutcheon and Garland, 2004; Laurin, 2004). Similarly, some studies use multiple phylogenies (topologies) (e.g. Bauwens et al., 1995; Symonds and Elgar, 2002; Hodges, 2004).

View larger version (48K): [in this window] [in a new window]   Fig. 4. Use of computer simulations to illustrate how Type I error rates for testing an association between two traits can be inflated by ignoring phylogenetic relationships. Shown are three distributions of ordinary, non-phylogenetic, Pearson product–moment correlations of tip data. In each of the three figures, data were simulated along the phylogeny shown, under a simple Brownian motion model of character evolution (see Fig. 2), with the correlation between the two traits set to zero (Martins and Garland, 1991; Garland et al., 1993). (A) Data simulated along a `star' phylogeny, here depicted as a `comb.' The upper 95th percentile is +0.504, which is statistically indistinguishable from the conventional critical value of +0.497. Compared with this distribution, the correlation for the real data on lizards (+0.585; see text) would be considered statistically significant at P<0.05. (B) Data simulated along the hierarchical topology, but with less extreme branch lengths (arbitrary values as suggested by Pagel, 1992) than for the real branch lengths shown in (C). For these simulated data, the 95th percentile is +0.641, which is larger than the conventional critical value. Judged against this empirical null distribution, the correlation for the real data would be considered statistically non-significant (P>0.05). (C) Simulations along the actual phylogeny used by Garland et al. (1991). The simulated data include an even greater number of sets for which the correlation is strongly positive, as compared with (B). The 95th percentile is +0.828, which is much larger than the nominal one-tailed critical value for testing a correlation coefficient (+0.497). If the phylogeny shown in C is close to reality, and if evolution has been similar to Brownian motion, then the results of C are more trustworthy than those of A.

These points have suggested to some that phylogenetically based analyses are so fraught with pitfalls that we should stick with non-phylogenetic ones. But a conventional statistical analysis actually has as many assumptions as a phylogenetic one. For example, it assumes that the species under analysis have not been interacting, e.g. as by character displacement (Hansen et al., 2000). It assumes that each species should be equally weighted, which is equivalent to saying that the heights of each branch from the root of the tree (assumed to be a star) are equal. And so forth.

In any case, it has become increasingly clear that, because we never know the true branch lengths and/or model of character evolution, we should pay careful attention to the branch lengths used, employing methods that can consider options ranging between a star and our working hierarchical phylogeny, and possibly something even more hierarchical. Thus, recent methods emphasize estimation of optimal branch length transformations as an essential part of phylogenetic analyses of comparative data (e.g. see Grafen, 1989; Diaz-Uriarte and Garland, 1996, 1998; Pagel, 1999; Harvey and Rambaut, 2000; Freckleton et al., 2002; Martins et al., 2002; Blomberg et al., 2003; Housworth et al., 2004). Although some researchers may be uneasy with such transformations of branch lengths, they are analogous to use of a Box–Cox procedure to find the optimal transformation of data (e.g. best approximation of normality) in conventional statistical procedures (for instance, use of a Box–Cox procedure to transform branch lengths; Reynolds and Lee, 1996). Moreover, aside from its benefits with computer-simulated data, such careful attention to branch lengths can sometimes improve statistical power to an important extent with real data (see below).

	An example of how phylogeny can affect statistical analyses

TOP Summary Introduction Phylogeny and modern... An example of how... When and why to... Examples of the utility... Some notes of caution Summary and perspectives Appendix References

 
By overestimating the true number of independent observations, conventional statistical methods applied to comparative data typically lead to inflated Type I error rates, i.e. statistical significance is claimed too often (e.g. Grafen, 1989; Martins and Garland, 1991; Purvis et al., 1994; Diaz-Uriarte and Garland, 1996). A real example of the influence of phylogeny on interpretation of comparative data comes from a study that tested the hypothesis that the preferred body temperature and the optimal temperature for sprint running speed would be positively correlated among 12 species of lizards (Huey and Bennett, 1987; Garland et al., 1991). The ordinary Pearson correlation coefficient between these two temperatures, uncorrected for phylogenetic associations, is +0.585. Is this statistically significant, or might it have been obtained by chance sampling if the true correlation among all Australian skinks were zero?

The answer depends on what is assumed about the phylogenetic relationships of the 12 species. If we assume that species are unrelated, then we can refer to conventional tables of critical values for correlation coefficients. For a one-tailed test with 12 data points (and hence 10 degrees of freedom for testing a correlation), the critical value is +0.497, so a value of +0.585 would be considered significant at P<0.025. If, instead, we want to assume that the species are related in a hierarchical fashion, then we cannot use the conventional tables. Fortunately, however, we can incorporate phylogenetic information as follows (Martins and Garland, 1991; Garland et al., 1993). We can construct different working phylogenies, model the uncorrelated evolution of these traits by a Monte Carlo computer simulation that assumes random, Brownian-motion like trait change, and calculate a correlation coefficient for each simulated data set. We can then determine the critical 5% level for the correlation coefficient for each distribution. If we assume that all species are completely independent or related by a star phylogeny (Fig. 4A), then the one-tailed probability for obtaining a correlation as large as +0.585 is 0.023 (based on this particular set of 1000 simulated data sets), so the relationship is statistically significant at P<0.05. In fact, if we do a very large number of simulations, then we will obtain exactly the same results as when referring to conventional tables.

If, however, we simulate data along our best estimate of the phylogeny of these lizards (Fig. 4C), then a correlation of +0.585 would be observed much more frequently than 5% of the time and would not be considered very unusual, hence not statistically significant (P>0.15). If a hypothetical phylogeny with different branch lengths, involving fewer deep roots, were assumed (Fig. 4B), then a value of +0.585 would have a lower probability of being observed, but in this case would still be non-significant. Thus, the assumed pattern of the relationships among the species crucially affects the statistical significance of the observations: the more the phylogeny departs from a star, the lower is the number of effectively independent observations and the more likely we are to observe an extremely large (or small) correlation just by chance. If the working topology, branch lengths, and simulation model are somewhat realistic, then we will claim significance too often if we ignore phylogeny.

Another important point is that if the simulated data of Fig. 4B or C are analyzed with IC, using the corresponding phylogenies, then the resulting distribution of correlation coefficients will be the same as in Fig. 4A (results not shown). Thus, as discussed in the Appendix, the IC method uses the specified phylogenetic information to transform the data to make them independent and identically distributed. This then allows one to refer to conventional tables of critical values for hypothesis testing.

All of the simulations shown in Fig. 4 were done under a simple Brownian motion model (Fig. 2), but the model used can have a large effect on the resulting distributions of statistics (e.g. see Garland et al., 1993; Diaz-Uriarte and Garland, 1996; Price, 1997; Harvey and Rambaut, 2000; Martins et al., 2002; Freckleton et al., 2003). Brownian motion is a very simple model of character evolution, and its analytical tractability was exploited by Felsenstein (1985) to develop IC. It is a good model for traits that evolve solely by random genetic drift, and may also be adequate for some types of `fluctuating' selection (i.e. when the direction of selection changes from generation to generation). As a basis for statistical methods to estimate and test character correlations, it may also be an adequate model for traits that are subject to certain types of selection (Felsenstein, 1985, 1988; Grafen, 1989). But most traits probably evolve in ways that are too complicated and idiosyncratic to be modeled realistically by Brownian motion (Felsenstein, 1988; Hansen et al., 2000). Fortunately, simulations can use arbitrarily complex models of character evolution, limited only by one's ability to write computer programs and imagination (e.g. Garland et al., 1993; Diaz-Uriarte and Garland, 1996, 1998; Price, 1997; Harvey and Rambaut, 2000; Freckleton et al., 2003). Of course, whether more complicated models lead to more accurate analyses depends on whether they are actually a better descriptor of past evolution by the characters under study, and that is something very difficult to know. Moreover, finding a model that fits a set of data reasonably well does not necessarily mean that it is the correct model, and other models can probably be found that would provide equally good fit (see also Blomberg et al., 2003). (As always, it is risky to attempt to infer process from pattern.) Given the near impossibility of knowing how traits actually evolved in the distant past, simulation studies are also used to gauge how robust analytical methods such as IC are to violation of their assumptions (e.g. Brownian motion, accurate knowledge of branch lengths), how diagnostic tests can alert one to such violations, and how well remedial measures (e.g. transformations of tip data or branch lengths) can rescue statistical performance when assumptions are violated (e.g. Martins and Garland, 1991; Purvis et al., 1994; Diaz-Uriarte and Garland, 1996, 1998; Harvey and Rambaut, 2000; Diniz-Filho and Torres, 2002; Freckleton et al., 2003). Still, physiologists may sometimes be able to improve the accuracy of assumed models by their knowledge of how organisms work (or could have worked), as in the case of limits to body temperature evolution discussed above. Similarly, paleontological information can be used to improve the realism of simulations (Garland et al., 1993).

We close this section by emphasizing that the use of computer simulations to obtain `phylogenetically correct' (PC) null distributions for testing hypotheses about comparative data is a very general tool that can be used for virtually any analysis (Martins and Garland, 1991; Garland et al., 1993), including bivariate (e.g. Ricklefs and Nealen, 1998) or multivariate analyses of evolutionary diversification. For example, the PHYLOGR (available at http://cran.r-project.org/) program allows one to test hypotheses about canonical correlation or principal components analysis (PCA) in relation to computer-simulated data (R. Diaz-Uriarte and T. Garland, manuscript in preparation).

	When and why to use phylogenetic information in comparative studies

TOP Summary Introduction Phylogeny and modern... An example of how... When and why to... Examples of the utility... Some notes of caution Summary and perspectives Appendix References

 
What kinds of characters are amenable to comparative phylogenetically based analyses? Basically, any measurable trait can be studied with these methods. It can be a discrete character, such as presence or absence of a structure, or a continuously distributed trait, such as the length of a bone or the value for a rate process. The methods are not confined to analysis of structure and function of individuals, but may also include aspects of ecology, such as home range size or environmental indices (e.g. mean annual temperature). However, for the analysis of evolutionary differences it is desirable to minimize the influence of the immediate environment on phenotypic characters prior to their measurement. That is, to the extent possible, all species should be exposed to common conditions (acclimated to the same environment) for some period of time prior to measurement. Ideally, they would be bred and raised under common conditions for one or two generations (Garland and Adolph, 1991). That is unfortunately not possible for many species. Moreover, given that the species under study probably vary in the conditions they inhabit, which set or sets of environmental conditions should be used? And what if the ordering of species phenotypes varies among those conditions because of genotype-by-environment interactions? These questions have no easy answers, but should be borne in mind during analysis and interpretation.

What kinds of characters demand a phylogenetic analysis? Although we may generally expect that most characters will tend to `follow phylogeny', this is an empirical question. The simplest general test for whether related organisms actually do tend to resemble each other more than they resemble those that might be chosen randomly with respect to phylogenetic position uses randomization procedures (see also Abouheif, 1994; Ackerly, 2004; Laurin, 2004; Rheindt et al., 2004). Specifically, once phylogenetically IC have been computed, it is possible to calculate the variance of those contrasts. The lower the variance of the contrasts, the better the fit of the phylogeny (topology and branch lengths) to the character in question. To determine whether a given variance indicates the presence of statistically significant `phylogenetic signal' (i.e. more closely related species tend to resemble each other more than they resemble randomly chosen species), one can compare it with the distribution of variances for a large number of data sets that have been randomized (shuffled) across the tips of the phylogeny (Blomberg and Garland, 2002; Blomberg et al., 2003). For studies with 20 or more species (for which statistical power should be reasonably high), more than 90% of the traits examined to date (including behavioral, physiological, morphological, life history and ecological/environmental traits) do exhibit a significant phylogenetic signal (P<0.05: Blomberg et al., 2003; Al-kahtani et al., 2004; Ashton, 2004a,b; Rezende et al., 2004; Ross et al., 2004; Muñoz-Garcia and Williams, in press; see also Freckleton et al., 2002).

The empirical finding of pervasive phylogenetic signal implies that hierarchical phylogenies – as presented and used in numerous publications – provide a better fit to the data under analysis than does a star phylogeny (Figs 3A, 4A). This sends a strong message that we should routinely consider phylogenetic information in statistical analyses of comparative data. However, this does not necessarily mean that, for any given set of data, we should simply obtain a phylogenetic tree, perform an IC, GLS or Monte Carlo simulation analysis, and automatically presume that the results will be more reliable than the comparable conventional statistical analysis. As we and others have emphasized for more than a decade, analyses using a given topology and branch lengths can perform relatively poorly if their assumptions are severely violated (e.g. see Grafen, 1989; Martins and Garland, 1991; Diaz-Uriarte and Garland, 1996, 1998; Price, 1997; Garland and Diaz-Uriarte, 1999; Harvey and Rambaut, 2000; Diniz-Filho and Torres, 2002; Martins et al., 2002; Freckleton et al., 2003; Housworth et al., 2004). Thus, we urge practitioners to apply robust tests for phylogenetic signal, diagnostic checks, and branch length transformations as warranted (for recent discussions and methods, see Freckleton et al., 2002; Blomberg et al., 2003), and sensitivity analyses by varying branch lengths and/or model of evolution (e.g. see Garland et al., 1993; Ashton, 2004b; Hutcheon and Garland, 2004; Laurin, 2004; Muñoz-Garcia and Williams, in press).

What sorts of branch lengths should be used? Given the uncertainties regarding branch lengths (see above), many workers have reported results with multiple branch lengths to explore consistency or the lack thereof (e.g. Ross et al., 2004). Although it is often the case that conclusions are relatively robust (insensitive) to the branch lengths used, this is not always true, and the importance of attempting to use `optimal' branch lengths transformations can be illustrated with two empirical examples. Garland et al. (1993) analyzed home range areas in relation to body size for 49 species of carnivores and ungulates. Conventional analysis of covariance (ANCOVA) indicated a highly significant (P<0.001) different in size-adjusted home range areas of the two groups. Analysis via IC (or Monte Carlo simulations), however, revealed no statistically significant difference (two-tailed P=0.126 for IC). The branch lengths used for the phylogenetic analyses were estimates of divergence times, derived from various sources. They passed the diagnostic `lack of fit' tests as described in Garland et al. (1992). However, power to detect a difference is apparently improved by applying the transformations of branch lengths as proposed by Blomberg et al. (2003) to mimic particular models of character evolution. Using the branches transformed under the OU model for log body mass, the P value is reduced to 0.099, and using their Accelerating–Decelerating (ACDC) model the P value is reduced to 0.044, thus crossing the typical threshold of <0.05 to be considered statistically significant (degrees of freedom were reduced by one in both cases to reflect the additional parameter estimated in these models; see also Diaz-Uriarte and Garland, 1996, 1998; Garland and Diaz-Uriarte, 1999). Similarly, in a recent comparison of the generic average body sizes of `megabats' and `microbats,' Hutcheon and Garland (2004) found statistical significance in the IC analysis only when using branch lengths transformed under the OU or ACDC models. We suspect that such increases in power may be more likely to occur in comparisons between groups that are fairly highly phylogenetically confounded (i.e. the independent variable of interest, such as diet, is highly clumped with respect to phylogeny, as in comparisons of clades; e.g. see Garland et al., 1993; Vanhooydonck and Van Damme, 1999; Perry and Garland, 2002; Rezende et al., 2004) than in tests of correlations between two traits.

How do we choose species for study? Traditionally, animals were chosen for comparative studies for any number of reasons, including convenience (e.g. local availability or an existing literature data base), possession of an interesting biological trait (e.g. the long neck of the giraffe), occupation of an extreme environment (e.g. a hot dry desert, the Arctic), or characteristics that make it well suited to study a particular physiological process (Garland and Adolph, 1994; Garland and Carter, 1994; Bennett, 2003). Frequently, a particular species or group living in a particular environment has been the key that originally sparked interest in the project. It is now clear that phylogenetic information should also be considered when choosing species for study (for a simulation study on the effects of taxon sampling when testing for correlated evolution, see also Purvis and Webster, 1999; Ackerly, 2000).

To increase analytical power, it is a good idea to include other species that experience a very broad range of the environmental (`independent') variable. You might then randomly sample species from a broad taxon (e.g. mammals) or focus exclusively on a particular lineage, such as bats or rodents. From a design perspective, the latter strategy is preferable because the broader comparison will involve distant relatives that vary in many traits, potentially complicating the analysis of particular traits of interest. From a phylogenetic point of view, comparisons of distant relatives are like an experiment with multiple uncontrolled variables (Garland and Adolph, 1994; Garland, 2001). To quote Felsenstein (1985, p. 465), `Comparative biologists tend to suspect comparisons of distantly related species; they hope to base their comparisons on recent evolutionary events that have not been overlaid by much subsequent change'. In principle, it might be possible to control for confounding traits that differ in distant relatives by including additional independent variables in the analysis, but it is often difficult to know a priori what those traits might be, let alone actually obtain quantitative data for them. In any case, an example in which casting too broad a net seems to reduce statistical power is provided by a study of body mass evolution in birds (Garland and Ives, 2000, p. 354). A comparison of passerines with their sister clade indicates that the former have significantly smaller log body masses, on average, whereas a comparison of passerines with all birds (including their sister clade) does not. (It should be noted that the identity of the sister clade of passerines is controversial, and the foregoing example may well change as improved phylogenetic information becomes available.) A related topic is whether one might a priori exclude certain subclades from a comparative analysis because they are `unusual' as compared with the larger clade in general. For example, many studies of lizards (e.g. Perry and Garland, 2002) exclude snakes. A recent study by Bininda-Emonds and Gittleman (2000) suggests that this sort of a priori data exclusion may be less warranted than is often presumed.

A particularly powerful comparative design is one that has several different pairs of closely related species that differ in the variable of interest (e.g. high and low temperature) and has these species pairs relatively distantly related to each other (i.e. in different branches of the phylogeny). As noted by Garland (2001), a particularly favorable distribution of this sort has the power to detect significant associations even when conventional statistical methods fail to do so. However, some workers choose species in this way, but then analyze only the pairs of tip species rather than performing a full analysis of the entire phylogeny (e.g. Lavergne et al., 2004). If that is done, Type I error rates should be correct, and the analysis should be robust with respect to errors in branch lengths and/or model of evolution, but statistical power will likely be lost (see Ackerly, 2000). A more extreme analytical variant is to perform a sign test on the tip pairs (Felsenstein, 1985), thus not using any information on branch lengths, but this comes at the extreme loss of statistical power (Ackerly, 2000).

The worst, that is, the least powerful, comparative design is one in which all species on one side of the root of the tree share, say, high values for an independent variable of interest (e.g. high temperature) and those on the other side of the root share low values (e.g. low temperature) (e.g. Garland et al., 1993; Garland, 2001). Although some methods can enhance inferential power in such situations (e.g. Schondube et al., 2001), it is not an attractive comparative scenario.

How many species or other taxa need to be included in a comparative study? In general, the statistical power of phylogenetically based analyses, when applied with an accurate phylogeny and model of character evolution, is the same as for conventional statistical methods, so standard power calculations can be employed (e.g. see fig. 5 in Garland and Adolph, 1994). However, it is also true that phylogenetic analyses sometimes uncover relationships that were not apparent in conventional analyses (see below).

	Examples of the utility of incorporating a phylogenetic perspective

TOP Summary Introduction Phylogeny and modern... An example of how... When and why to... Examples of the utility... Some notes of caution Summary and perspectives Appendix References

 
One obvious utility of phylogenetically based analytical methods is their ability to estimate ancestral values (Schluter et al., 1997; Martins and Lamont, 1998; Cunningham et al., 1998; Garland et al., 1999). Such estimations would be impossible without phylogenetic information. Using phylogenetic methods, one can ask where a particular trait arose within the evolutionary diversification of a group and whether it arose once or multiple times (e.g. Schondube et al., 2001; Reznick et al., 2002; Johnston et al., 2003; Espinoza et al., 2004; Hodges, 2004; Lane et al., 2004; Rezende et al., 2004; Berenbrink et al., 2005). Inferences about nodal values permit the estimation of evolutionary change along each branch segment of an evolutionary tree and hence analysis of features correlated with that change, including inferences regarding the order of evolution of the components of a complex trait (e.g., see Lauder, 1980, 1981, 1990; Pagel, 1999; Autumn et al., 2002; Pérez-Barbería et al., 2002; Oakley, 2003; Berenbrink et al., 2005).

We will now review just a few examples from the literature in which phylogenetic information has added to our understanding and interpretation of comparative data. The first two of these deal with the evolution of lower metabolic rate in endotherms as part of their adaptation to desert environments.

It has long been recognized that low metabolic rates, low body temperatures, and an ability to become torpid would be beneficial to endotherms in hot, arid environments, in order to minimize heat load and energy (and water) demands in environments of low productivity (e.g. Dawson and Bartholomew, 1968; Dawson and Hudson, 1970; Williams, 1996; Tieleman et al., 2003; Rezende et al., 2004). When these traits were first discovered in desert caprimulgid birds (e.g. poorwills and nighthawks), they were initially interpreted as adaptations to desert conditions (e.g. Bartholomew et al., 1962