Phylogenetic comparative methods (PCMs) use information on the historical relationships of lineages (

phylogenies A phylogenetic tree (also phylogeny or evolutionary tree Felsenstein J. (2004). ''Inferring Phylogenies'' Sinauer Associates: Sunderland, MA.) is a branching diagram or a tree showing the evolutionary relationships among various biological spec ...

) 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 naturalist, geologist, and biologist, widely known for his contributions to evolutionary biology. His proposition that all species of life have descended fr ...

used differences and similarities between species as a major source of evidence in '' The Origin of Species''. 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 In biology, adaptation has three related meanings. Firstly, it is the dynamic evolutionary process of natural selection that fits organisms to their environment, enhancing their evolutionary fitness. Secondly, it is a state reached by the po ...

; 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 in ...

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

) 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. Home Range 49 Mammals 1

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

allometric Allometry is the study of the relationship of body size to shape, anatomy, physiology and finally behaviour, first outlined by Otto Snell in 1892, by D'Arcy Thompson in 1917 in ''On Growth and Form'' and by Julian Huxley in 1932. Overview Allom ...

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, t ...

of organisms differ with respect to some phenotypic trait? → ''Example: do

canids Canidae (; from Latin, ''canis'', " dog") is a 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 subfamilies found within th ...

have larger hearts than

felids Felidae () is the family of mammals in the order Carnivora colloquially referred to as cats, and constitutes a clade. A member of this family is also called a felid (). The term "cat" refers both to felids in general and specifically to th ...

?'' * 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 wel ...

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. A ...

diet Diet may refer to: Food * Diet (nutrition), the sum of the food consumed by an organism or group * Dieting, the deliberate selection of food to control body weight or nutrient intake ** Diet food, foods that aid in creating a diet for weight loss ...

) differ in average phenotype? → ''Example: do carnivores have larger home ranges 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 whom ...

state of a trait? → ''Example: where did

endothermy An endotherm (from Greek ἔνδον ''endon'' "within" and θέρμη ''thermē'' "heat") is an organism that maintains its body at a metabolically favorable temperature, largely by the use of heat released by its internal bodily functions inste ...

evolve in the lineage that led to mammals?'' → ''Example: where, when, and why did placentas 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 (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 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 ins ...

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 Inferences are steps in reasoning, moving from premises to logical consequences; etymologically, the word '' infer'' means to "carry forward". Inference is theoretically traditionally divided into deduction and induction, a distinction that in ...

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 Evolution is change in the heritable characteristics of biological populations over successive generations. These characteristics are the expressions of genes, which are passed on from parent to offspring during reproduction. Variation ...

.g.,_Cope's_rule.html" ;"title="Cope's_rule.html" ;"title=".g., Cope's rule">.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 (GLS) and as such the PGLS estimator is also

unbiased Bias is a disproportionate weight ''in favor of'' or ''against'' an idea or thing, usually in a way that is closed-minded, prejudicial, or unfair. Biases can be innate or learned. People may develop biases for or against an individual, a group, ...

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 consistent i ...

, efficient, and asymptotically normal. In many statistical situations where GLS (or, ordinary least squares 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. Char ...

. 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 demand ...

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