1 Integrative Biology 200A "PRINCIPLES OF PHYLOGENETICS" Spring 2012 University of California, Berkeley B.D. Mishler Feb. 16, 2012. Phylogenetic Trees I: Reconstruction; Models, Algorithms & Assumptions A. Trees -- what are they, really, and what can go wrong? Here are some important initial questions for discussion: What are phylogenetic trees, really? What do you see when you look closely at a branch? -- the fractal nature of phylogeny (is there a smallest level?) What is the relationship between characters and trees? Characters and OTUs? Characters and levels? The tree of life is inherently fractal, which complicates the search for answers to these questions. Look closely at one lineage of a phylogeny and it dissolves into many separate lineages, and so on down to a very fine scale. Thus the nature of both OTU's ("operational taxonomic units," the "twigs" of the tree in any particular analysis) and characters (hypotheses of homology, markers that serve as evidence for the past existence of a lineage) change as one goes up and down this fractal scale. Furthermore, there is a tight interrelationship between OTUs and character states, since they are reciprocally recognized during the character analysis process. B. Two approaches to tree-building What is the basic goal of tree building? How good is the fit between "reality" and a phylogenetic model designed to represent reality? These questions have many different answers depending on the background of the investigator, but there are two major schools of thought: 1. The "reconstruction" school of thought. The Hennigian phylogenetic systematics tradition, derived from comparative anatomy and morphology, focuses on the implications of individual homologies. This tradition tends to conceive of the inference process as one of reconstructing history following deductive-analytic procedures. The goal is seen as coming up with the best supported hypothesis to explain a unique past event. -- the data matrix as itself a refined result of character analysis -- each character is an independent hypothesis of taxic and transformation homology -- test these independent hypotheses against each other, look for the best-fitting joint hypothesis2 -- straight parsimony as a "solution" to the data matrix. -- only the fewest and least controversial assumptions should be used: characters are heritable and independent, and that changes in state are relatively slow as compared to branching events in a lineage. -- when these hold, reconstructions for a character showing one change on one branch will be more likely than reconstructions showing two or more changes in that character on different branches. -- Statistical considerations primarily enter the process during the phase called "character analysis," that is when the data matrix is being assembled. Based on expectations of "good" phylogenetic markers (characters), procedures have been developed that involve assessing the likely independence and evolutionary conservatism of potential characters using experimental and statistical manipulations. -- This school of thought tends not to see the tree building process per se to involve statistical inference. Since each column in the data matrix is regarded as an independently justified hypothesis about phylogenetic grouping, an individual piece of evidence for the existence of a monophyletic group (a putative taxic homology), the parsimony method used to produce a cladogram from a matrix is then viewed as a solution of that matrix, an analytic transformation of the information contained therein from one form to another, just as in the solution of a set of linear equations. No inductive, statistical inference has been made at that step, only a deductive, mathematical one. -- In summary: a rigorously produced data matrix has already been evaluated carefully for potential homology of each feature when being assembled. Everything interesting has already been encoded in the matrix; what is needed is a simple transformation of that matrix into a tree without any pretended "value added." Straight, evenly-weighted parsimony is to be preferred, because it is a robust method (insensitive to variation over a broad range of possible biasing factors) and because it is based on a simple, interpretable, and generally applicable model. 2. The "estimation" school of thought The population genetic tradition, derived from studies of the fate of genes in populations, tends to see phylogenetic inference as a statistical estimation problem. The goal is seen to be choosing a set of trees out of a statistical universe of possible trees, while putting confidence limits on the choice. -- task is to pick the single tree out of the statistical universe of possible trees that is the most likely given the data set. --relationship between probability and likelihood (see figure next page)3 A maximum likelihood approach to phylogenetic estimation attempts to evaluate the probability of observing a particular set of data, given an underlying phylogenetic tree (assuming an evolutionary model). Among competing phylogenetic trees, the most believable (likeliest) tree is one that makes the observed data most probable. -- to make such a connection between data and trees, it is necessary to have auxiliary assumptions about such parameters as the rate of character change, the length of branches, the number of possible character-states, and relative probabilities of change from one state to another. Hence, there is controversy. -- the primary debate has involved these assumptions: how much is necessary or desirable or possible to assume about evolution before a phylogeny can be established? Sober (1988) has shown convincingly that some evolutionary assumptions are necessary to justify any method of inference, but he (and the field in general) remains unclear about exactly what the minimum assumptions are or should be. Keep in mind also that parsimony and likelihood are fundamentally related methods -- a spectrum of character-based methods rather than two distinct methods. [More in future lectures] The procedure (more details in later lecture!) -- You need three things: Data, a Model, and a Likelihood Function. -- The Data is our normal matrix, where each column is a vector. -- The Model has three parts: 1. a topology 2.
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