Phylogenetic comparative methods

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When applied to comparative data, conventional statistical methods assume, in effect, that all species are completely unrelated. Such a scenario can be depicted as a "star" phylogeny (left). Most comparative studies will involve species that have descended in a hierarchical fashion from common ancestors, as shown on the right. Comparative data sets may include species that have gone extinct, and rates of evolution may vary among branches. Therefore, trees used in phylogenetic comparative methods may not be "ultrametric" (have tips that are contemporaneous).

Phylogenetic comparative methods (PCMs) use information on the evolutionary relationships of organisms (phylogenetic trees) to compare species (Harvey and Pagel, 1991). The most common applications are to test for correlated evolutionary changes in two or more traits, or to determine whether a trait contains a phylogenetic signal (the tendency for related species to resemble each other [Blomberg et al. 2003]). However, several methods are available to relate particular phenotypic traits to variation in rates of speciation and/or extinction, including attempts to identify evolutionary key innovations. Although most studies that employ PCMs focus on extant organisms, the methods can also be applied to extinct taxa and can incorporate information from the fossil record.

Owing to their computational requirements, they are usually implemented by computer programs (see list below). PCMs can be viewed as part of evolutionary biology, systematics, phylogenetics, bioinformatics or even statistics, as most methods involve statistical procedures and principles for estimation of various parameters and drawing inferences about evolutionary processes.

What distinguishes PCMs from most traditional approaches in systematics and phylogenetics is that they typically do not attempt to infer the phylogenetic relationships of the species under study. Rather, they use an independent estimate of the phylogenetic tree (topology plus branch lengths) that is derived from a separate phylogenetic analysis, such as comparative DNA sequences that have been analyzed by maximum parsimony, maximum likelihood or Bayesian methods. The main objective of PCMs is to study the evolution of qualitative and quantitative traits as well as identifying patterns of origination and extinction in phylogenies. Most comparative models assume the phylogenetic tree is known without error in order to estimate parameters of interest. Therefore, PCMs use phylogenies which are already available and do not produce them. Accordingly, the list of phylogenetics software shows little overlap with the programs for PCMs, with the exception to a large series of R packages such as 'ape' and 'geiger' and standalone phylogenetic software such as 'Mesquite' (see below).

Comparison of species to elucidate aspects of biology has a long history. Charles Darwin relied on such comparisons as a major source of evidence when writing The Origin of Species. Many other fields of biology use interspecific comparison as well, including behavioral ecology, ethology, ecophysiology, comparative physiology, evolutionary physiology, functional morphology, comparative biomechanics, and the study of sexual selection.

The comparative method is also used heavily in linguistics.


PCMs can be used to analyze the origin and maintenance of biodiversity. Biodiversity is most commonly discussed in terms of the number of species, but it can also be phrased in terms of the amount of phenotypic (e.g., physiological, morphological) space that a given set of species occupies (see also Cambrian explosion).

Home range areas of 49 species of mammals in relation to their body size. Larger-bodied species tend to have larger home ranges, but at any given body size members of the order Carnivora (carnivores and omnivores) tend to have larger home ranges than ungulates (all of which are herbivores). Whether this difference is considered statistically significant depends on what type of analysis is applied (Garland et al., 1993).
Testes mass of various species of Primates in relation to their body size and mating system. Larger-bodied species tend to have larger testes, but at any given body size species in which females tend to mate with multiple males have males with larger testes.

Phylogenetic comparative methods are commonly applied to such questions as:

Example: how does brain mass vary in relation to body mass?

  • Do different clades of organisms differ with respect to some phenotypic trait?

Example: do canids have larger hearts than felids?

Example: do carnivores have larger home ranges than herbivores?

Example: where did endothermy evolve in the lineage that led to mammals?

Example: where, when, and why did placentas and viviparity evolve?

  • Does a trait exhibit significant phylogenetic signal in a particular group of organisms? Do certain types of traits tend to "follow phylogeny" more than others?

Example: are behavioral traits more labile during evolution?

  • Do species differences in life history traits trade-off, as in the so-called fast-slow continuum?

Example: why do small-bodied species have shorter life spans than their larger relatives?

Phylogenetically independent contrasts[edit]

The standardized contrasts are used in conventional statistical procedures, with the constraint that all regressions, correlations, analysis of covariance, etc., must pass through the origin.

Felsenstein (1985) proposed the first general statistical method for incorporating phylogenetic information, i.e., the first that could use any arbitrary topology (branching order) and a specified set of branch lengths. The method is now recognized as an algorithm that implements a special case of what are termed phylogenetic generalized least-squares models (Grafen, 1989). The logic of the method is to use phylogenetic information (and an assumed Brownian motion like model of trait evolution) to transform the original tip data (mean values for a set of species) into values that are statistically independent and identically distributed.

The algorithm involves computing values at internal nodes as an intermediate step, but they are generally not used for inferences by themselves. An exception occurs for the basal (root) node, which can be interpreted as an estimate of the ancestral value for the entire tree (assuming that no directional evolutionary trends [e.g., Cope's rule] have occurred) or as a phylogenetically weighted estimate of the mean for the entire set of tip species (terminal taxa). The value at the root is equivalent to that obtained from the "squared-change parsimony" algorithm and is also the maximum likelihood estimate under Brownian motion. The independent contrasts algebra can also be used to compute a standard error or confidence interval.

Phylogenetic generalized least squares (PGLS)[edit]

Grafen (1989) first proposed the use of generalized least squares to incorporate phylogenetic information into standard statistical methods. He noted that his procedures built upon phylogenetically independent contrasts: "Similarity due to recognized phylogeny is treated by developing the standard regression, a generalization of Felsenstein's (1985) comparative method to the case of non-binary trees, which also incorporates a degree of flexibility in assumptions about the covariance structure." Grafen (1989) proposed a method to deal with soft polytomies (unrecognized phylogeny) and also allow the branch lengths of the "working phylogeny" to be stretched or compressed to consider trees ranging between a star phylogeny (see figure above) and the original hierarchical tree, as well as trees even more hierarchical than the working phylogeny. The optimal degree of stretching (his rho parameter) was estimated by maximum likelihood, simultaneously with the parameters (e.g., regression slopes) in the statistical model. These modifications of the "standard regression" (= Felsenstein's [1985] phylogenetically independent contrasts) make the procedure no longer generalized least squares.[1] Since Grafen's original proposal, various alternatives or enhancements have been proposed, using different ways of transforming the branch lengths, some of them tied to particular models of (residual) trait evolution,[2][3][4] and other ways of dealing with unrecognized phylogeny have been proposed.[5] Some applications employ an Ornstein-Uhlenbeck model of residual trait evolution,[6][7] as originally suggested by Fenselstein (1988) to mimic stabilizing selection.[8]

Phylogenetically informed Monte Carlo computer simulations[edit]

Data for a continuous-valued trait can be simulated in such a way that taxa at the tips of a hypothetical phylogenetic tree will exhibit phylogenetic signal, i.e., closely related species will tend to resemble each other.

Martins and Garland (1991) proposed that one way to account for phylogenetic relations when conducting statistical analyses was to use computer simulations to create many data sets that are consistent with the null hypothesis under test (e.g., no correlation between two traits, no difference between two ecologically defined groups of species) but that mimic evolution along the relevant phylogenetic tree. If such data sets (typically 1,000 or more) are analyzed with the same statistical procedure that is used to analyze a real data set, then results for the simulated data sets can be used to create phylogenetically correct (or "PC" [Garland et al., 1993]) null distributions of the test statistic (e.g., a correlation coefficient, t, F). Such simulation approaches can also be combined with such methods as phylogenetically independent contrasts or PGLS (see above).

Phylogenetic Pseudoreplication.jpg

See also[edit]


  1. ^ Lavin, S. R., W. H. Karasov, A. R. Ives, K. M. Middleton, and T. Garland Jr. 2008. Morphometrics of the avian small intestine compared with that of nonflying mammals: a phylogenetic approach. Physiological and Biochemical Zoology 81:526–550.
  2. ^ Martins, E. P., and T. F. Hansen. 1997. Phylogenies and the comparative method: a general approach to incorporating phylogenetic information into the analysis of interspecific data. American Naturalist 149:646–667. Erratum 153:___.
  3. ^ Garland, Jr., T., and A. R. Ives. 2000. Using the past to predict the present: confidence intervals for regression equations in phylogenetic comparative methods. American Naturalist 155:346–364.
  4. ^ Freckleton, R. P., P. H. Harvey, and M. Pagel. 2002. Phylogenetic analysis and comparative data: a test and review of evidence. The American Naturalist 160:712–726.
  5. ^ Purvis, A., and T. Garland, Jr. 1993. Polytomies in comparative analyses of continuous characters. Systematic Biology 42:569–575.
  6. ^ Butler, M. A., and A. A. King. 2004. Phylogenetic comparative analysis: a modeling approach for adaptive evolution. The American Naturalist 164:683–695.
  7. ^ Lavin, S. R., W. H. Karasov, A. R. Ives, K. M. Middleton, and T. Garland Jr. 2008. Morphometrics of the avian small intestine compared with that of nonflying mammals: a phylogenetic approach. Physiological and Biochemical Zoology 81:526–550.
  8. ^ Felsenstein, J. 1988. Phylogenies and quantitative characters. Annual Review of Ecology and Systematics 19:445–471.
  • Felsenstein, J. 1985. Phylogenies and the comparative method. American Naturalist 125:1-15.
  • Garland, T., Jr., A. W. Dickerman, C. M. Janis, and J. A. Jones. 1993. Phylogenetic analysis of covariance by computer simulation. Systematic Biology 42:265-292. PDF
  • Grafen, A. 1989. The phylogenetic regression. Philosophical Transactions of the Royal Society of London B 326:119-157. PDF
  • Harvey, P. H., and M. D. Pagel. 1991. The comparative method in evolutionary biology. Oxford University Press, Oxford. 239 pp.
  • Martins, E. P., and T. Garland, Jr.. 1991. Phylogenetic analyses of the correlated evolution of continuous characters: a simulation study. Evolution 45:534-557. PDF

Further reading[edit]

  • Ackerly, D. D. 1999. Comparative plant ecology and the role of phylogenetic information. Pages 391-413 in M. C. Press, J. D. Scholes, and M. G. Braker, eds. Physiological plant ecology. The 39th symposium of the British Ecological Society held at the University of York 7–9 September 1998. Blackwell Science, Oxford, U.K.
  • Berenbrink, M., P. Koldkjær, O. Kepp, and A. R. Cossins. 2005. Evolution of oxygen secretion in fishes and the emergence of a complex physiological system. Science 307:1752-1757.
  • Blomberg, S. P., T. Garland, Jr., and A. R. Ives. 2003. Testing for phylogenetic signal in comparative data: behavioral traits are more labile. Evolution 57:717-745. PDF
  • Brooks, D. R., and D. A. McLennan. 1991. Phylogeny, ecology, and behavior: a research program in comparative biology. Univ. Chicago Press, Chicago. 434 pp.
  • Cheverud, J. M., M. M. Dow, and W. Leutenegger. 1985. The quantitative assessment of phylogenetic constraints in comparative analyses: sexual dimorphism in body weight among primates. Evolution 39:1335-1351.
  • Eggleton, P., and R. I. Vane-Wright, eds. 1994. Phylogenetics and ecology. Linnean Society Symposium Series Number 17. Academic Press, London.
  • Felsenstein, J. 2004. Inferring phylogenies. Sinauer Associates, Sunderland, Mass. xx + 664 pp.
  • Freckleton, R. P., P. H. Harvey, and M. Pagel. 2002. Phylogenetic analysis and comparative data: a test and review of evidence. American Naturalist 160:712-726.
  • Garland, T., Jr., and A. R. Ives. 2000. Using the past to predict the present: Confidence intervals for regression equations in phylogenetic comparative methods. American Naturalist 155:346-364. PDF
  • Garland, T., Jr., Jr., A. F. Bennett, and E. L. Rezende. 2005. Phylogenetic approaches in comparative physiology. Journal of Experimental Biology 208:3015-3035. PDF
  • Garland, T., Jr., P. H. Harvey, and A. R. Ives. 1992. Procedures for the analysis of comparative data using phylogenetically independent contrasts. Systematic Biology 41:18-32. PDF
  • Gittleman, J. L., and M. Kot. 1990. Adaptation: statistics and a null model for estimating phylogenetic effects. Systematic Zoology 39:227-241.
  • Hadfield, J. D, and S. Nakagawa. 2010. General quantitative genetic methods for comparative biology: phylogenies, taxonomies and multi-trait models for continuous and categorical characters. Journal of Evolutionary Biology 23: 494-508
  • Herrada, E. A., C. J. Tessone, K. Klemm, V. M. Eguiluz, E. Hernandez-Garcia, and C. M. Duarte. 2008. Universal Scaling in the Branching of the Tree of Life. PLoS One 3(7): e2757. doi:10.1371/journal.pone.0002757. PDF open access publication - free to read
  • Housworth, E. A., E. P. Martins, and M. Lynch. 2004. The phylogenetic mixed model. American Naturalist 163:84-96. PDF
  • Ives, A. R., P. E. Midford, and T. Garland, Jr. 2007. Within-species variation and measurement error in phylogenetic comparative methods. Systematic Biology 56:252-270.
  • Maddison, D. R. 1994. Phylogenetic methods for inferring the evolutionary history and process of change in discretely valued characters. Annual Review of Entomology 39:267-292.
  • Maddison, W. P. 1990. A method for testing the correlated evolution of two binary characters: Are gains or losses concentrated on certain branches of a phylogenetic tree? Evolution 44:539-557.
  • Maddison, W. P., and D. R. Maddison. 1992. MacClade. Analysis of phylogeny and character evolution. Version 3. Sinauer Associates, Sunderland, Mass. 398 pp.
  • Martins, E. P., ed. 1996. Phylogenies and the comparative method in animal behavior. Oxford University Press, Oxford. 415 pp.
  • Martins, E. P., and T. F. Hansen. 1997. Phylogenies and the comparative method: a general approach to incorporating phylogenetic information into the analysis of interspecific data. American Naturalist 149:646-667. Erratum Am. Nat. 153:448.
  • Nunn, C. L., and R. A. Barton. 2001. Comparative methods for studying primate adaptation and allometry. Evolutionary Anthropology 10:81-98.
  • Oakley, T. H., Z. Gu, E. Abouheif, N. H. Patel, and W.-H. Li. 2005. Comparative methods for the analysis of gene-expression evolution: an example using yeast functional genomic data. Molecular Biology and Evolution 22:40-50. PDF
  • O’Meara, B. C., C. M. Ané, M. J. Sanderson, and P. C. Wainwright. 2006. Testing for different rates of continuous trait evolution in different groups using likelihood. Evolution 60:922-933. PDF
  • Organ, C. L., A. M. Shedlock, A. Meade, M.. Pagel, and S. V. Edwards. 2007. Origin of avian genome size and structure in non-avian dinosaurs. Nature 446:180-184.
  • Page, R. D. M., ed. 2003. Tangled trees: phylogeny, cospeciation, and coevolution. University of Chicago Press, Chicago.
  • Pagel, M. D. 1993. Seeking the evolutionary regression coefficient: an analysis of what comparative methods measure. Journal of Theoretical Biology 164:191-205.
  • Pagel, M. 1999. Inferring the historical patterns of biological evolution. Nature 401:877-884.
  • Paradis, E. 2005. Statistical analysis of diversification with species traits. Evolution 59:1-12.
  • Paradis, E., and J. Claude. 2002. Analysis of comparative data using generalized estimating equations. Journal of Theoretical Biology 218:175-185.
  • Purvis, A., and T. Garland, Jr. 1993. Polytomies in comparative analyses of continuous characters. Systematic Biology 42:569-575. PDF
  • Rezende, E. L., and T. Garland, Jr. 2003. Comparaciones interespecíficas y métodos estadísticos filogenéticos. Pages 79–98 in F. Bozinovic, ed. Fisiología Ecológica & Evolutiva. Teoría y casos de estudios en animales. Ediciones Universidad Católica de Chile, Santiago. PDF
  • Rezende, E.L., and J.A.F Diniz-Filho. 2012. Phylogenetic analyses: comparing species to infer adaptations and physiological mechanisms. Comprehensive Physiology 2:639-674. PDF
  • Ridley, M. 1983. The explanation of organic diversity: The comparative method and adaptations for mating. Clarendon, Oxford, U.K.
  • Rohlf, F. J. 2001. Comparative methods for the analysis of continuous variables: geometric interpretations. Evolution 55:2143-2160.
  • Rohlf, F. J. 2006. A comment on phylogenetic correction. Evolution 60:1509-1515.
  • Sanford, G. M., W. I. Lutterschmidt, and V. H. Hutchison. 2002. The comparative method revisited. BioScience 52:830-836.
  • Schluter, D., T. Price, A. O. Mooers, and D. Ludwig. 1997. Likelihood of ancestor states in adaptive radiation. Evolution 51:1699-1711.
  • Smith, R. J., and J. M. Cheverud. 2002. Scaling of sexual size dimorphism in body mass: a phylogenetic analysis of Rensch's rule in primates. International Journal of Primatology 23:1095-1135.
  • Steppan, S. J., P. C. Phillips, and D. Houle. 2002. Comparative quantitative genetics: evolution of the G matrix. Trends in Ecology and Evolution 17:320-327. PDF
  • Vanhooydonck, B., and R. Van Damme. 1999. Evolutionary relationships between body shape and habitat use in lacertid lizards. Evolutionary Ecology Research 1:785-805.

External links[edit]


Software packages (incomplete list)[edit]