Lecture_7

Lecture_7 - Models of morphological evolution Fredrik...

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Models of morphological evolution Fredrik Ronquist September 21, 2005 In this lecture, we will be covering models of morphological evolution. These fall into two different classes: those that model morphology in terms of discrete states and those that treat morphology as quantitative characters. Both are applicable to other types of data; for instance, the discrete-state models can be applied to restriction site data and other data of a presence/absence nature, and the quantitative character models can be used as approximations of allele frequency evolution (see previous lecture). 1 Morphology as discrete states In many cases, morphological variation falls naturally into discrete states. Typical examples include the presence or absence of major features like wings and feathers. Although it is currently standard practice to use parsimony methods, like Fitch optimization, to infer phylogenies from such discrete- state morphological data, we can also apply discrete-state continuous-time Markov models like the ones we have seen previously for molecular sequence data. A few minor complications arise but they are all possible to address. 1.1 The binary model For a morphological character with two states (0 and 1) we can simply use a Markov model with the instantaneous rate matrix (unscaled) Q = { q ij } = ± - 1 1 - ² 1
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BSC5936-Fall 2005-PB,FR Computational Evolutionary Biology This is obviously an analogue of the Jukes-Cantor model of DNA evolution. Lewis (2002) recently referred to this model as the M2 model ; it has been in use for morphological and other types of discrete data at least since the 80’s. In principle, the M2 model can be easily extended to multi-state characters, but the issue of state ordering comes up. Recall that parsimony methods distinguish between ordered and unordered multi-state characters (Fig. 1). In the simplest case, we assume that all changes between states are possible (Fig. 1a); the alternative is to order the states in a linear series such that, in a three-state character, changes between the two end states have to go through the intermediate state (Fig. 1b). In a stochastic model, we would simply set the instantaneous rate of the impossible changes to zero and use a uniform rate for the other events. Thus, the stochastic model for a three-state unordered character, we can refer to it as the M3u model, is: Q = { q ij } = - 1 1 1 - 1 1 1 - The equivalent for the three-state ordered character, the M3o model, is: Q = { q ij } = - 1 0 1 - 1 0 1 - Figure 1: Stochastic models for unordered (a) and ordered (b) morphological characters. Note the similarity between the M3o model and the codon models we discussed earlier. As with 2
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BSC5936-Fall 2005-PB,FR Computational Evolutionary Biology the latter models, the zero entries in the instantaneous rate matrix of the M3o model do not result in transitions between the end states being impossible but they do force those transitions
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Lecture_7 - Models of morphological evolution Fredrik...

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