Evolutionary (phylogenetic) methods



Ginger Jui


The physiological traits of plants are of major interest for the analysis of trait evolution. Broadly, evolutionary analyses test questions about the timing and sequence of trait evolution and the association between traits, or between traits and the environment. Other statistics describe how traits are distributed between related species or across a phylogeny. As such, the evolution of plant physiology helps to describe and explain major patterns in ecology and evolution, such as the latitudinal biodiversity gradient, the rise and fall of major plant groups and the processes underlying rapid and adaptive radiations.

Systematics and Applied Phylogenetics

Ecologically important traits, such as leaf functional traits or life history strategies, vary to some degree across related species. Statistical analyses ranging from simple correlations to phylogenetically informed methods are used to test for associations between traits or other factors. These methods commonly assume that the adaptive significance of a trait may be inferred by correlating functional traits with ecological or environmental characteristics. Other strategies for inferring adaptive significance include correlating the rate of trait change with speciation dynamics and fitting the observed distribution of traits across organisms to some theoretical model of trait evolution.

All questions of trait evolution depend upon a hypothesis of relatedness between species. The field of systematics provides methods for building phylogenies, reconstructing the number and sequence of evolutionary events and explicitly mapping these events along a phylogeny. These methods can be used to test questions such as whether C3 or C4 photosynthesis was the ancestral state for a group and the number of transitions between C3 and C4 photosynthesis.

Molecular Phylogenies

A typical workflow for constructing a molecular phylogeny would be to acquire DNA sequences (either by sequencing or downloading from GenBank), align the sequences and then build the phylogeny using a computer program. Sequence alignment can be automated using a variety of computer programs. Clustal is a popular alignment program for DNA or protein sequences and is available for download at http://www.clustal.org/. The most popular computer programs for phylogeny inference include PAUP* and Phylip (implementing parsimony, distance and maximum likelihood methods), RAxML (maximum likelihood) and MrBayes (Bayesian methods).

Many comparative methods require chronograms, or phylogenies with branch lengths proportional to time. Most phylogenies recovered using the programs above have branch lengths proportional to the expected number of nucleotide changes between speciation events. In most cases, a relaxed molecular clock assumption must be applied to estimate the branch lengths proportional to time between speciation events. BEAST http://beast.bio.ed.ac.uk/Main_Page and r8s https://help.rc.ufl.edu/doc/R8S are two widely used, freely available programs for estimating divergence times using relaxed molecular clock assumptions. BEAST is also used for phylogenic inference. Absolute time calibration can be conducted in these programs using dated fossils or vicariance events or using known rates of molecular evolution.

Comparative Phylogenetic Analysis

The comparative analysis of trait evolution most commonly seeks to test for (a) a relation between traits, or traits and environments, (b) reconstruct ancestral traits, (c) determine the rate of phenotypic change and (d) test for an effect of phylogenetic history on phenotypic change (Martins and Hansen, 1997). An excellent introduction to the analysis of trait evolution is The Comparative Method in Evolutionary Biology (Harvey and Pagel, 1991). This text introduces the statistical phylogenetic approach to comparative analysis.

The Bodega Phylogenetics Workshop hosts an up-to-date wiki on phylogenetic analysis http://treethinkers.org/. The wiki includes excellent how-to guides for phylogenetic inference, diversification analysis, ancestral state reconstruction and analysis of character evolution, including all the software packages mentioned in this summary. In addition to free-standing software, a number of packages for comparative phylogenetic analysis are available in the R Statistical Computing environment http://www.r-project.org/. These packages are summarized in the CRAN phylogenetics taskview: http://cran.r-project.org/web/views/Phylogenetics.html.

For a comprehensive reference, Inferring Phylogenies (Felsenstein, 2004) provides a technical guide to the methods used for sequence alignment, phylogeny inference and other major topics in the field.

Models of Trait Evolution

Plant traits can provide insight into how evolution proceeds under different historical scenarios, such as adaptive radiations, coevolution and climate change. The goal of testing models of trait evolution may be to detect general macroevolutionary patterns, to test mechanistic models of trait evolution, or test for correlated evolution between traits and/or environments.

Many qualitative models have beeen proposed for the patterns and processes of trait evolution, but a more limited number have been framed as statistical models of evolution. All the models described below have been implemented for testing in a maximum likelihood framework. These are freely available for use as statistical packages in R or as free-standing software.

The branch lengths of a phylogenetic tree can be thought of as a hypothesis of how phenotypic evolution proceeds through time. For example, a simple hypothesis might predict that the amount of trait evolution observed between two species is proportional to the time since they split from their common ancestor. This hypothesis predicts that recently diverged species are more phenotypically similar than deeply diverged species. A Brownian motion model has been proposed as a statistical statement of this hypothesis.

Brownian Motion

Under Brownian motion, trait evolution proceeds as a random walk through trait space. After a speciation event, the daughter species then each go on their separate random walks. The expected phenotypic difference between the daughters grows proportional to the time since they shared a common ancestor (i.e. the sum of the branch lengths between the two taxa). Mechanistically, this model could be interpreted as neutral drift evolution or evolution towards randomly fluctuating selective optima.

Brownian motion has been proposed as a null model of evolution for testing hypotheses of trait evolution. Blomberg’s K statistic (Blomberg et al. 2003) is used to to test whether an observed distribution of traits exhibits more or less divergence than expected for traits evolving under Brownian motion. Values of K range from 0 to infinity, with K=1 indicating Brownian motion evolution. K > 1 indicates that close relatives are more similar than expected and K < 1 indicates more divergence between taxa than expected under a Brownian model. Most values of K observed in the literature are less than one.

Ornstein-Uhlenbeck/Hansen Models

Ornstein-Uhlenbeck (OU) models describe the evolution of traits under stabilizing selection. OU models modify the Brownian motion model to include one or more selective optima that assert an attractive force on random walk trait evolution. Attraction to the optimum increases as one wanders farther away from it. When the strength of this attraction is zero, the Ornstein-Uhlenbeck model is identical to a Brownian motion model. The OU model can be tested using the R packages GEIGER and OUCH.

Branch Length Transformation Models

Different models of evolution may be specified by changing the branch lengths of the phylogeny. Mark Pagel has proposed three branch length transformation models, delta, kappa, and lambda (Pagel, 1999), named after the parameter used to transform branch lengths. The values of the parameters that best fit the data can be estimated by maximum likelihood methods in the R package GEIGER. The expected distribution of traits under each of these models can be simulated on the transformed tree using Brownian motion evolution.

Pagel’s delta transformation is a model of increasing or decreasing rates of trait change through time. Values of delta < 1 transform branch lengths to be increasingly shorter towards the tips, describing a model in which trait change occurs rapidly early in the history of a clade and then slows through time. Models with delta > 1 describe an increasing rate of character evolution through time, while delta = 0 is identical to a Brownian motion model.

The kappa transformation model raises branch lengths to the power kappa. A punctuational model is specified when kappa = 0 and all branch lengths are equal. Again, the model reduces to Brownian when kappa = 1. Values of kappa between 0 and 1 tend to shorten long branch lengths more than short ones, describing a model of saturating evolution. In this interpretation, most trait change occurs after speciation and the rate of trait change declines through a species duration.

In the lambda transformation, internal branch lengths are multiplied by the lambda parameter, which specifies the degree of phylogenetic signal in the data. When lambda = 0, a star phylogeny results with all tips radiating from a basal node, describing a model where traits evolve independent of the phylogeny. The influence of the phylogeny increases with values of lambda between 0 and 1. When lambda = 1, the model is again identical to the Brownian motion model.

Trait Dependent Evolution

Trait-dependent diversification models have been developed for binary and multistate characters (BiSSE and MuSSE). These model describes the evolution of a categorical character along a phylogenetic tree where the speciation and extinction rate depends on the character state of the lineage. The models may be tested using both maximum likelihood and Bayesian methods. Both methods are available in the R package diversitree http://www.zoology.ubc.ca/prog/diversitree/ and BiSSE is available in Mesquite http://mesquiteproject.org/. A BiSSE-like method may also be available for continuous traits, by contacting the developer of the diversitree package. A simple test for relating continuous traits to diversification has also been proposed by Freckleton et al. 2008.

Literature References

Blomberg, S., T. Garland, and A. Ives. 2003. Testing for phylogenetic signal in comparative data: Behavioral traits are more labile. Evolution, 57:717-745.

Felsenstein, J. 2004. Inferring phylogenies. Sinauer Associates, Sunderland, Mass..

Freckleton, R. P., A. B. Phillimore, and M. Pagel. 2008. Relating traits to diversi cation: A simple test. American Naturalist, 172:102-115.

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.

Pagel, M. 1999. Inferring the historical patterns of biological evolution. Nature, 401(6756):877-884.

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