Phylogenetic comparative methods (PCMs) use information on the historical relationships of lineages ( phylogenies) to test evolutionary hypotheses. The comparative method has a long history in evolutionary biology; indeed,

Charles Darwin Charles Robert Darwin ( ; 12 February 1809 – 19 April 1882) was an English natural history#Before 1900, naturalist, geologist, and biologist, widely known for his contributions to evolutionary biology. His proposition that all speci ...

used differences and similarities between species as a major source of evidence in ''

The Origin of Species ''On the Origin of Species'' (or, more completely, ''On the Origin of Species by Means of Natural Selection, or the Preservation of Favoured Races in the Struggle for Life''),The book's full original title was ''On the Origin of Species by Me ...

''. However, the fact that closely related lineages share many traits and trait combinations as a result of the process of descent with modification means that lineages are not independent. This realization inspired the development of explicitly phylogenetic comparative methods. Initially, these methods were primarily developed to control for phylogenetic history when testing for adaptation; however, in recent years the use of the term has broadened to include any use of phylogenies in statistical tests. Although most studies that employ PCMs focus on extant organisms, many methods can also be applied to extinct taxa and can incorporate information from the

fossil record A fossil (from Classical Latin , ) is any preserved remains, impression, or trace of any once-living thing from a past geological age. Examples include bones, shells, exoskeletons, stone imprints of animals or microbes, objects preserved ...

. PCMs can generally be divided into two types of approaches: those that infer the evolutionary history of some character (

phenotypic In genetics, the phenotype () is the set of observable characteristics or traits of an organism. The term covers the organism's morphology or physical form and structure, its developmental processes, its biochemical and physiological proper ...

or genetic) across a phylogeny and those that infer the process of evolutionary branching itself ( diversification rates), though there are some approaches that do both simultaneously. Typically the tree that is used in conjunction with PCMs has been estimated independently (see

computational phylogenetics Computational phylogenetics is the application of computational algorithms, methods, and programs to phylogenetic "tribe, clan, race", and wikt:γενετικός, γενετικός [] "origin, source, birth") is the study of the evolutionary hist ...

) such that both the relationships between lineages and the length of branches separating them is assumed to be known.

Applications

Phylogenetic comparative approaches can complement other ways of studying adaptation, such as studying natural populations, experimental studies, and mathematical models. Interspecific comparisons allow researchers to assess the generality of evolutionary phenomena by considering independent evolutionary events. Such an approach is particularly useful when there is little or no variation within species. And because they can be used to explicitly model evolutionary processes occurring over very long time periods, they can provide insight into macroevolutionary questions, once the exclusive domain of

paleontology Paleontology (), also spelled palaeontology or palæontology, is the scientific study of life that existed prior to, and sometimes including, the start of the Holocene epoch (roughly 11,700 years before present). It includes the study of fos ...

Phylogenetic comparative methods are commonly applied to such questions as: * What is the

slope In mathematics, the slope or gradient of a line is a number that describes both the ''direction'' and the ''steepness'' of the line. Slope is often denoted by the letter ''m''; there is no clear answer to the question why the letter ''m'' is used ...

of an allometric scaling relationship? → ''Example: how does brain mass vary in relation to body mass?'' * Do different

clades A clade (), also known as a monophyletic group or natural group, is a group of organisms that are monophyletic – that is, composed of a common ancestor and all its lineal descendants – on a phylogenetic tree. Rather than the English term ...

of organisms differ with respect to some

trait? → ''Example: do

canids Canidae (; from Latin, ''canis'', "dog") is a family (biology), biological family of dog-like carnivorans, colloquially referred to as dogs, and constitutes a clade. A member of this family is also called a canid (). There are three subfamily, ...

have larger hearts than felids?'' * Do groups of species that share a

behavioral Behavior (American English) or behaviour (British English) is the range of actions and mannerisms made by individuals, organisms, systems or artificial entities in some environment. These systems can include other systems or organisms as we ...

or ecological feature (e.g.,

social system In sociology, a social system is the patterned network of relationships constituting a coherent whole that exist between individuals, groups, and institutions. It is the formal structure of role and status that can form in a small, stable group. ...

, diet) differ in average phenotype? → ''Example: do carnivores have larger

home range A home range is the area in which an animal lives and moves on a periodic basis. It is related to the concept of an animal's territory which is the area that is actively defended. The concept of a home range was introduced by W. H. Burt in 1943. H ...

s than herbivores?'' * What was the

ancestral An ancestor, also known as a forefather, fore-elder or a forebear, is a parent or ( recursively) the parent of an antecedent (i.e., a grandparent, great-grandparent, great-great-grandparent and so forth). ''Ancestor'' is "any person from w ...

state of a trait? → ''Example: where did endothermy evolve in the lineage that led to mammals?'' → ''Example: where, when, and why did

placenta The placenta is a temporary embryonic and later fetal organ (anatomy), organ that begins embryonic development, developing from the blastocyst shortly after implantation (embryology), implantation. It plays critical roles in facilitating nutrien ...

s and

viviparity Among animals, viviparity is development of the embryo inside the body of the parent. This is opposed to oviparity which is a reproductive mode in which females lay developing eggs that complete their development and hatch externally from the m ...

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

Felsenstein proposed the first general statistical method in 1985 for incorporating phylogenetic information, i.e., the first that could use any arbitrary

topology In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing ho ...

(branching order) and a specified set of branch lengths. The method is now recognized as an

algorithm In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing ...

that implements a special case of what are termed phylogenetic generalized least-squares models. The

logic Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premis ...

of the method is to use phylogenetic information (and an assumed

Brownian motion Brownian motion, or pedesis (from grc, πήδησις "leaping"), is the random motion of particles suspended in a medium (a liquid or a gas). This pattern of motion typically consists of random fluctuations in a particle's position insi ...

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 .g., Cope's rule">Cope's_rule.html" ;"title=".g., Cope's rule">.g., Cope's rulehave 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)

Probably the most commonly used PCM is phylogenetic generalized least squares (PGLS). This approach is used to test whether there is a relationship between two (or more) variables while accounting for the fact that lineage are not independent. The method is a special case of

generalized least squares In statistics, generalized least squares (GLS) is a technique for estimating the unknown parameters in a linear regression model when there is a certain degree of correlation between the residuals in a regression model. In these cases, ordin ...

(GLS) and as such the PGLS estimator is also unbiased,

consistent In classical deductive logic, a consistent theory is one that does not lead to a logical contradiction. The lack of contradiction can be defined in either semantic or syntactic terms. The semantic definition states that a theory is consisten ...

, efficient, and asymptotically normal. In many statistical situations where GLS (or,

ordinary least squares In statistics, ordinary least squares (OLS) is a type of linear least squares method for choosing the unknown parameters in a linear regression model (with fixed level-one effects of a linear function of a set of explanatory variables) by the ...

LS is used residual errors ''ε'' are assumed to be independent and identically distributed random variables that are assumed to be normal :

\varepsilon \mid X\sim \mathcal(0, \sigma^2I_n).

whereas in PGLS the errors are assumed to be distributed as :

\varepsilon \mid X\sim \mathcal(0, \mathbf).

where ''V'' is a matrix of expected variance and covariance of the residuals given an evolutionary model and a phylogenetic tree. Therefore, it is the structure of residuals and not the variables themselves that show

phylogenetic signal Phylogenetic signal is an evolutionary and ecological term, that describes the tendency or the pattern of related biological species to resemble each other more than any other species that is randomly picked from the same phylogenetic tree. C ...

. This has long been a source of confusion in the scientific literature. A number of models have been proposed for the structure of ''V'' such as

Ornstein-Uhlenbeck, and Pagel's λ model. (When a Brownian motion model is used, PGLS is identical to the independent contrasts estimator.). In PGLS, the parameters of the evolutionary model are typically co-estimated with the regression parameters. PGLS can only be applied to questions where the

dependent variable Dependent and independent variables are variables in mathematical modeling, statistical modeling and experimental sciences. Dependent variables receive this name because, in an experiment, their values are studied under the supposition or dema ...

is continuously distributed; however, the phylogenetic tree can also be incorporated into the residual distribution of generalized linear models, making it possible to generalize the approach to a broader set of distributions for the response.

Phylogenetically informed Monte Carlo computer simulations

Martins and Garland proposed in 1991 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") 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