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1 Introduction

A comparison of apples and oranges occurs when two items or groups of items are compared that cannot be practically compared. … However, apples are actually more closely related to pears (both are rosaceae) than to oranges.

—WikipediaFootnote 1

The phylogenetic comparative method has undoubtedly been one of the most important phenomena of evolutionary biology during the last few decades. Comparative methods exist in many fields such as anthropology (Bock 1966), law (Kiekbaev 2003), linguistics (Forster et al. 1998), and evolutionary biology (Harvey and Pagel 1991). The concepts and uses of these different comparative methods vary widely. Since the present book is specifically concerned with biological evolution, it is thus useful to define our subject.

We may define the comparative method as an analytical approach based on the comparison of different objects with the aim to elucidate the mechanisms at the origin of their diversity. From this, we can define the phylogenetic comparative method as the analytical study of species, populations, and individuals in a historical framework with the aim to elucidate the mechanisms at the origin of the diversity of life.

It is important to note that the phylogenetic comparative method (PCM) is distinct from but not independent of phylogenetics, the study and reconstruction of the historical relationships among species. For instance, in linguistics or in anthropology, the goal of the comparative method is the historical reconstruction of spoken languages or of human cultures (e.g., Forster et al. 1998, with some historical references therein; see Sect. 1.7 below).

The goal of this chapter is to give a general introduction to the PCM by examining some topics. The next section presents the main historical milestones of phylogenetics and the comparative method—since both have been tightly linked through their history. The following sections give some essential elements on statistical inference of evolutionary processes with comparative data. The last two sections aim to put the PCM in a broader perspective by looking at its relationships with anthropology and speculating about some of its current advances and its future.

2 History of Phylogenetics and the Comparative Method

2.1 Early Developments

In the nineteenth century, trees were essential graphical tools for the development of evolutionary ideas. Lamarck (1809) used a downward-growing tree to represent the relationships among the main groups of animals with a caption indicating that this “table displays the origin of the different animals.” History was central in Lamarck’s argumentation: “A strong reason prevents us to identify the changes that have successively diversified the animals as we know them today: we have never witnessed these changes.” This could be taken as a manifesto of today’s comparative method in evolutionary biology.

Cuvier was Lamarck’s great rival and strong opponent to the idea of evolution. However, Cuvier acknowledged that species are more or less closely related so that they can be classified in a hierarchical system and that different characters of these species are relevant at different levels, especially through his gradual characters (caractères gradués, Cuvier 1798). In spite of his backward ideas on fixism (Laurent 1986), Cuvier had a profound impact on comparative anatomy through the numerous illustrations and drawings included in his books—which could appear in a modern textbook on evolution after updating the captions.

It has been widely appreciated that Darwin (1859) used a phylogenetic tree as the only figure in the Origin of Species. He also used comparative data to support several of his points; for instance, “Genera which are polymorphic in one country seem to be, with some few exceptions, polymorphic in other countries, and likewise, judging from Brachiopod shells, at former periods of time.” Thus, Darwin characterized the patterns of diversity in space and in time and also used these facts to infer the processes of diversification of species: “…the larger genera also tend to break up into smaller genera. And thus, the forms of life throughout the universe become divided into groups subordinate to groups.”

The end of the nineteenth century has witnessed the wide acceptance of the idea of evolution, particularly with the contributions of Haeckel, the father of phylogenetics: “For the purpose of constructing a hypothetical genealogical tree of the Radiolaria, as of all other organisms, three sources of information are open to us, viz., palæontology, comparative ontogeny, and comparative anatomy.” (Haeckel 1887).

During the first half of the twentieth century, phylogenetics and biological comparative studies have followed separate paths. The discovery of the physical support of heredity (genes, chromosomes, and later DNA) led scientists to focus their interest on the genetic mechanisms of evolution. Fisher (1930) certainly best illustrates this change of paradigm where history was less important than previously thought: “For mutations to dominate the trend of evolution it is thus necessary to postulate mutation rates immensely greater than those which are known to occur…” For Fisher, mutations could not explain evolutionary novelties and we should rather look at other evolutionary forces such as selection or population structure to explain the diversity of life. At the same time, phylogenetics made fundamental contributions to evolutionary thinking. Paleontologists integrated phylogenetic ideas, mainly because of the historical nature of their data (Simpson 1944). Phylogenetic trees became the analytical tool of a school of systematists (cladistics), leading to the first numerical treatments of phylogenies (see a historical account in Felsenstein 2004).

2.2 Modern Developments

The late 1960s have witnessed some crucial turns. The development of statistical methods to reconstruct phylogenies from genetic data was a major step accomplished by Cavalli-Sforza and Edwards (1967). Because the approach they developed was statistical, it was possible to extend it to other kinds of data such as continuous characters. This next step was achieved by Felsenstein (1973) who proposed a method to calculate the likelihood of a tree for a set of continuous traits. The significance of this work was not obvious until the same author published a related method to calculate the phylogenetically independent contrasts (PICs), a major difference being that the calculations under this new method could be done with a hand calculator (Felsenstein 1985).

Until the 1970s, comparative biology developed its statistical tools independently of phylogenetic or historical ideas. Comparative data from n species used to be analyzed with standard statistical methods, assuming that they were n independent observations. This separation between comparative biology and the historical dimension of biological evolution seems surprising when considering that the idea of evolution, and particularly adaptation, was at the heart of most comparative studies (Clutton-Brock and Harvey 1979).

The 1980s can be seen as the golden age of PCMs when a great variety of methods were published (reviewed by Pagel and Harvey 1988). Two important papers were published in the same year: Cheverud et al. (1985), who proposed an approach based on auto-regression including the possibility to account for intraspecific variation, and Felsenstein (1985), already cited. A few years later, Grafen (1989), in a very rich and dense paper, proposed the use of generalized least squares (GLS) to derive a method now widely known as the phylogenetic generalized least squares (PGLS). Gittleman and Kot (1990) further developed the use of auto-correlation functions to assess phylogenetic signal in diverse settings, including using taxonomic levels when a phylogeny is not available. Nevertheless, the power of these methods to infer evolutionary models and parameters was not yet fully acknowledged, and the view that phylogeny was a confounding effect in comparative analyses still prevailed: “Confounding effects of phylogeny and other variables may lurk behind any comparative relationship, and they must be removed or controlled prior to considering adaptive arguments.” (Pagel and Harvey 1988).

During the 1990s, the developments of the previous decade were confirmed and strengthened. Lynch (1991) made a link between models of quantitative genetics and phylogenetics. He developed a method to partition the variance of a trait into an environmental and a phylogenetic component. Importantly, the same decomposition can be done for the covariance between two traits, thus providing a formal way to quantify the historical component of the link between two characters. New methods were proposed for the analysis of discrete traits (Pagel 1994; Grafen and Ridley 1997). In two important papers, Hansen and Martins (1996) and Martins and Hansen (1997) showed how GLS can be used to address evolutionary questions beyond the basic Brownian motion model.

In the 2000s, some efforts were given to issues left temporarily aside such as fitting more complicated models combining continuous and discrete traits (Paradis and Claude 2002; Felsenstein 2005; Hadfield and Nakagawa 2010) or combining interspecific and intraspecific data (Felsenstein 2008; Garamszegi and Møller 2010; Stone et al. 2011; see Chap. 7). At the end of the decade, three papers by Revell (2009), Jombart et al. (2010), and Pavoine et al. (2010) defined a general framework for multivariate statistical analyses in a phylogenetic context. The concept of phylogenetic signal has also attracted significant interest with the aim of clarifying previous ideas on phylogenetic confounding effect (Blomberg et al. 2003; Ollier et al. 2006; Pavoine et al. 2008; Münkemuller et al. 2012). At the same time, PCMs have achieved maturity with some generalizations such as the development of a Brownian model with variable parameters (O’Meara et al. 2006) or the use of sophisticated model-fitting techniques such as Monte Carlo Markov chains (MCMC) to fit complicated models (Pagel et al. 2004; Pagel and Meade 2006; Hadfield and Nakagawa 2010).

Remarkable progress in phylogenetics also contributed to PCMs, particularly with the publication of more and more phylogenies, some of them being complete over a very large number of species (Bininda-Emonds et al. 2007; Smith et al. 2011; Jetz et al. 2012; see Chap. 3). Some methods have been developed to combine different sources of phylogenetic information in order to build trees for comparative analyses (Kuhn et al. 2011; Eastman et al. 2013; Thomas et al. 2013; see Chap. 2).

Figure 1.1 gives the number of citations of two earlier papers over the years together with another major contribution to the development of PCMs. After almost three decades, the range of applications of PCMs has grown to reach all branches of biological science: 6,533 citations of Felsenstein (1985) or Harvey and Pagel (1991) are found in 771 periodical titles. The PCM, through the development of a wide range of analytical tools, has contributed insights into many questions on evolution and the diversity of life.

Fig. 1.1
figure 1

The annual number of citations of three major contributions to the phylogenetic comparative method (Source Web of Science)

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3 The Covariance Structure of Comparative Data

A central issue with comparative data is the non-independence of observations. A similar problem is found in other fields such as geography (Cliff and Ord 1981), climatology (Tiao et al. 1990), ecology (Legendre 1993), or medical research (Houwing-Duistermaat et al. 1998).

In a very general way, a data set can be arranged in a matrix where the rows are the observations (individuals, populations, species, sequences, cells, etc.) and the columns are variables (size, area, nucleotide sites, RNA transcription levels, etc.). Data analyses seek for relationships among the columns of this matrix, and common statistical methods assume that the rows are independent observations; in other words, the values observed on a given row are not affected by the values at others (Fig. 1.2).

Fig. 1.2
figure 2

A general depiction of a data set

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To statistically handle non-independence of observations, a general approach is to assume that two observations (rows), say i and j, are related through a covariance parameter denoted as \( \sigma_{ij}^{2} \). This parameter specifies the strength of the relation between the values of the same variable (column) observed for these two observations. The way this parameter enters in the analyses depends on the method used, the kinds of variables, and the question asked. The covariance parameters are usually arranged in a symmetric matrix with the diagonal elements equal to the variances and the off-diagonal elements being the covariances (see Chap. 5). This matrix has n rows and n columns and so contains \( n(n - 1)/2 \) off-diagonal elements.

There are many ways to define the values of \( \sigma_{ij}^{2} \): they may be all equal or not, they may follow a specific distribution or may be related to another variable, they may be fixed or estimated from the data, etc. For instance, with spatial data, it is common to use a covariance function related to geographical distance.

In the case of comparative data from several species, it is possible to calculate a priori the covariances among species traits if we know how these traits have evolved. For instance, if we assume that a trait has evolved under a Brownian motion (BM) model, these covariances can be calculated from the phylogenetic tree linking these species without observing the trait itself. The PIC and PGLS methods were directly derived from this assumption. Both methods are identical though they are computationally very different (Blomberg et al. 2012). PGLSs directly use the covariances by calculating a correlation matrix among observations, which is simply a covariance matrix scaled to have values between −1 and 1 (see Chap. 5).

4 Statistical Inference

The covariance matrix is at the core of most PCMs. Fortunately, it is possible to calculate it for other models of trait evolution, in particular for the Ornstein–Uhlenbeck (OU) model which is appropriate to model evolution of traits under constraints (see Chaps. 13, 14 and 15). Using this and other models, it is thus possible to relax the assumption underlying the BM model. This feature of PCMs allows us to go beyond the paradigm that phylogeny is a confounding effect that must simply be corrected (see Rohlf 2006).

We can illustrate this point with a small simulation exercise. Taking the phylogeny in Fig. 1.3, we simulate two independent traits that evolve according to either a BM or an OU model. In this second model, the traits are constrained to evolve toward an optimal value with a strength controlled by the parameter denoted as \( \alpha \). The simulated traits were analyzed with two methods: a standard regression (assuming the species are independent) and a regression using the PICs calculated with the original phylogeny (which was thus assumed to be perfectly known). Table 1.1 shows the estimated rejection rates for both methods. Since both traits are independent, we expect these rates to be close to 5 %. The PIC-based analyses gave the correct answer with the data simulated from a BM model or from an OU model with a small value of \( \alpha \). On the other hand, for the large values of \( \alpha \), the PIC-based analyses had a high type I error rate, whereas the standard regression had a rejection rate close to 5 %.

Fig. 1.3
figure 3

A simulated phylogeny with \( n = 20 \)

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Table 1.1 Rejection rate of the test of correlation between two independent traits simulated on the phylogeny in Fig. 1.3 using the model indicated in the table
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Figure 1.4 shows the correlation matrices among the 20 leaves of the tree under different models of trait evolution. These matrices would be used in PGLS analyses (see Chap. 5). This shows clearly that an OU model with small \( \alpha \) is close to a Brownian motion one, whereas when \( \alpha \) is large, the observations are expected to be almost independent.

Fig. 1.4
figure 4

Correlation matrices among the 20 tips of the tree in Fig. 1.3. The speciational model is one where change occurs only after a speciation event

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The critical point in a PCM-based analysis is to use the correct correlation structure among observations. The more distant the assumed correlation structure from the real one, the more biased the analysis will be. This property explains the statement that “in a comparative analysis a wrong phylogeny is better than no phylogeny at all” (Losos 1994; Martins 1996). Indeed, if the traits evolved on a phylogeny and another phylogeny is used for data analysis, the latter will result in a correlation structure closer to the correct one than assuming no correlation at all (i.e., independence of observations).

From the point of view of data analysis, one problem often encountered in published studies is that the phylogenetic correlation structure of the data is usually not assessed. This certainly comes from the view traditionally defended by most authors that only the phylogenetically controlled analyses are relevant. We now know that this can lead to wrong inference. This seems relatively easy to fix with tests of phylogenetic signal and model selection with information criteria such as the AIC (see Chap. 5). Remarkably, when different correlation structures are compared with real data, the Brownian motion model is rejected against more complex models such as the OU one (Whitney et al. 2011; Lapiedra et al. 2013).

5 Inferring Adaptation

Perhaps because of its history, the comparative method is most often used to infer adaptation. However, the scope and power of the PCM to reveal adaptation have been criticized several times over the years (e.g., Leroi et al. 1994; Martins 2000; Grandcolas et al. 2011). Such criticism is not really surprising: It has been discussed since a long time ago that characterizing the adaptative nature of a trait is a complicated endeavor (Bock 1959). Even the characterization of adaptation in viruses, which are far simpler than the organisms studied by most evolutionists, appears to be an arduous task (Pepin et al. 2010). The use of traits such as “habitat use” or “environment” with PCMs has been questioned because the analysis of such variables in a phylogenetic framework is meaningless (Grandcolas et al. 2011). On the other hand, it is hard to not consider these variables in evolutionary models since the assessment of the adaptive value of a trait cannot be separated from extrinsic variables such as habitat, resources, or climate (Bock 2003; Losos 2011; Watt 2013).

Some recent developments in PCMs provide a solution to the limitations underlined by the critiques cited above. As we have seen in the previous sections, the PCM does not simply aim at correcting for phylogenetic dependence or inferring repeated evolution of the same trait in different lineages, but rather to provide tools to analyze comparative data in a historical framework, and this includes fitting complex models of trait evolution that can handle various complications of the study design. For instance, some methods make possible to analyze several traits that evolve under different models: Bartoszek et al. (2012) developed a multi-trait model where traits can evolve following different processes of BM or OU.

One situation illustrated by Losos (2011) is the one of “incomplete convergence.” Convergence toward similar phenotypes among distantly related species is often viewed as evidence for adaptation. However, adaptive evolution can proceed in different ways in different groups, and the patterns thus produced are likely to be masked or obscured by other variables (such as the taxonomical background). Losos (2011) gives the example of the head shape of lizards which is mainly related to phylogenetic relatedness; however, within distinct clades, some species evolved independently toward herbivory and share some similarities, but the convergence is incomplete as they retain their respective phylogenetic background. In this case, a standard comparative analysis will likely fail to characterize the limited convergence among species affected by similar selective forces. On the other hand, statistical methods in a historical framework, including models of trait evolution, are helpful to characterize such patterns of adaptation. The use of these and other recently developed models of trait evolution may help to solve this “paradox” of using non-heritable traits in comparative analyses.

6 Inferring Causality

Correlation is not causality, and PCMs do not escape this reality. In spite of the importance of causality in evolutionary theory (see Watt 2013, for a recent view), the application of PCMs is generally oblivious of this point. This has led to some debate about the applicability of the PCM in order to identify evolutionary mechanisms. The vast majority of publications do not elaborate much on correlation and causality in their predictions: A simple linear correlation is usually derived from the hypotheses under test.

In general statistical inference, the causal relationship between two variables (say \( x \) and \( y \)) can be assessed if one of them can be controlled and then used as a predictor in data analyses. With comparative data, \( x \) and \( y \) cannot be controlled: They are evolving traits (or intrinsic variables) which are measured “on the species” (or they are extrinsic variables, like habitat, which cannot generally be controlled). Therefore, in the situation of a PCM with two variables, it is not possible to determine which regression (\( x \) on \( y \) or \( y \) on \( x \)) best describes the data. In other words, we cannot infer the causal relationship between these two variables.

When three or more uncontrolled variables are analyzed, it is possible to assess alternative causal relationships among them with a method known as path analysis (Freedman 2009). This method considers explicitly the causal relationships among variables under alternative hypotheses. A causal relationship can be expressed as “the variation in \( y \) is caused by the variation in the value of \( x \)” and has the statistical consequence that the regression of \( y \) on \( x \) is meaningful. Under a given hypothesis of the causal relationships among variables, some regressions are meaningful, while others are not. Using a procedure called the d-sep, it is possible to test which hypothesis best describes the data (Shipley 2013). Santos and Cannatella (2011) and von Hardenberg and Gonzalez-Voyer (2013) proposed to extend the framework of path analysis to PCMs (see Chap. 8). In a traditional path analysis, the regressions are done assuming independence of observations. Therefore, it is straightforward to generalize this method to cases where the observations are not independent, using tools such as (P)GLS.

Causality in general, and in evolution in particular, is fundamental, but this is a difficult concept to apply in practice. Hopefully, future applications of PCMs will help to progress on this issue.

7 Phylogenetic Comparative Method and Anthropology

As mentioned above, the present book focuses on the uses of the comparative method in evolutionary biology. One reason for this restriction is that other scientists do not see the comparative approach in the same way than evolutionists do. For instance, Bock (1966) described the comparative method as follows (italics as original):

It should be recalled at the outset that the primary objective of users of the comparative method is historical reconstruction. What history or whose history is by no means clear in the nineteenth century literature, and this question has hardly been resolved in recent controversy.

Thus, what anthropologists call “comparative method” seems close to what evolutionists call “phylogenetics.” Mace and Pagel (1994) revisited this issue by introducing a phylogenetic approach to anthropology directly inspired from evolutionary biology. Considering the links between comparative biology and phylogenetics, their message does not differ radically from the one formulated 28 years before by Bock.

In practice, the application of PCMs in anthropology differs substantially compared to evolutionary biology. A remarkable difference is that with anthropological data, the historical sequence of changes in traits (cultures, political systems, etc.) is often recorded—at least more often than in biology. For instance, Lindenfors et al. (2011) studied changes in political systems in the world between 1800 and 2008. Using several variables, they built a score ranging between −10 (total autocracy) and +10 (full democracy) and measured transitions among these different scores. They showed that most political changes occurred from autocratic systems (with a peak around −6) toward democratic ones (with a peak around +8). However, one interesting point about this study is their comment with respect to the historical dimension of the problem:

A reconstruction of democracy as a political system on a language phylogeny would almost certainly indicate democracy as the ancestral state for large sections of the phylogeny. However, since we have exact information of all transitions, we know this not to be true.

In biological terms, there is a trend (or directional evolution) from autocracy toward democracy so that the second system is the most widespread today among countries. If we ignore this historical trend, we would make wrong inference. Here also, we see that using the wrong model of evolution can be misleading. Similar situations can be found with evolutionary data; for instance, if a trend exists in the evolution of a trait (say, increase in body size), then ancestral inference will likely be misleading if this trend is not taken into account (Grafen 1989). Anthropological data have other peculiarities, like the ubiquity of horizontal transfers (Borgerhoff Mulder et al. 2006), so that a full comparison between cultural and biological evolution would require a much longer discussion.

8 The Future of the Phylogenetic Comparative Method

The comparative method in biology has evolved through several centuries to reach its present status. Today, PCMs have attained a level of maturity and sophistication that the readers can appreciate in the chapters of this book. The directions of future progress are certainly multiple.

We have seen the importance of the evolutionary models in statistical inference with the PCM. Some researchers currently explore the possibility to analyze complex models with several variables and an explicit formulation of the relationships among them. Hadjipantelis et al. (2013) analyzed an evolutionary model of “function-valued traits” by combining dimensionality reduction and a “bagging” (bootstrap aggregating) procedure. Complex relational models fitted with structural equation models seem also a very promising approach for future comparative analyses (Chap. 8).

It has not been widely appreciated that some PCMs link a model of microevolution (random evolution through genetic drift or stabilizing selection) with the patterns of interspecific variation in a trait and thus with macroevolution. Further works in this direction will likely lead to some interesting investigations on evolutionary mechanisms.

During many decades, the fossil record has been considered as the only source of information about evolutionary change. This paradigm has been broken by two steps forward in evolutionary biology: phylogenetic methods which try to reconstruct the past from the present and observations of real evolutionary changes over recent years such as the spread of resistance alleles in pathogens. However, the divorce between paleobiology and PCMs does not seem natural, and several researchers try to reconcile them (Pennell and Harmon 2013). This task will surely be very difficult but considering the many contributions of fossils to evolutionary biology, this is worth the effort (Chap. 22).

A scientific discipline is sometimes judged by how it contributes to everyone’s well-being. The PCM may well move very positively in this direction as comparative analyses could have concrete applications. Spreitzer et al. (2005) used simple comparisons between different plant and alga species to create new enzymes involved in photosynthesis by targeted mutations on “phylogenetic residues.” The resulting enzyme is one with original characteristics, a kind of “phylogenetic chimaera.” Such an approach of “phylogenetic engineering” may be promising to design new proteins or even new organisms based on predictions from evolutionary phylogenetic models.

Yan et al. (2012) used a phylogenetic analysis of a number of bacteria in order to propose cocktails of probiotic bacteria to reduce pathogens in food. Their approach is based on an investigation of a protein, MazF, which has an antimicrobial activity, and for which they propose an engineered variant. The phylogeny of the studied bacteria was instrumental in designing this new protein. The combination of molecular structure approaches with phylogenetic comparative analyses seems a promising venue to develop a variety of new molecules with desired properties.

Rich of its long history, the PCM seems to have a bright future both for addressing fundamental questions and for delivering applications.