Which Optimization Approach to

Empirical studies using simulated data sets and those derived from evolution in a test tube have concluded that model-driven approaches like ML and BA give more accurate results than MP when the modeled parameters (i.e., likelihood or probability of nucleotide substitutions) are known, but can be positively misleading when the parameters are unknown (Hillis et al., 1992; Oakley and Cunningham, 2000). MP often provides less resolution (more interior tree nodes reconstructed with ambiguous states), than ML or BA methods, which usually give very precise estimates with high confidence levels even under circumstances in which available data are insufficient to the task. In this regard, MP methods are regarded as more conservative, with lower risk of recovering false positives (Webster and Purvis, 2002).

Most studies on the evolution of neural characters use MP approaches because, unlike molecular sequence data, it is not straightforward how to pose or parametrize models on the evolution of complex phenotypes. Continuously varying aspects of neural features, like the size or shape of structures, have been modeled as simple Brownian motion or random walk processes, under the assumptions that the trait has not experienced selection and that there are no constraints on variance through time (Butler and King, 2004). Whether or not the assumptions of Brownian motion or any other specific model are satisfied by real neural or behavioral data is almost completely unknown.

A general conclusion reached by a number of review studies is that, under most circumstances faced by comparative morphologists, linear parsimony is the most conservative method for reconstructing ancestral trait values (Losos, 1999). Unlike squared-change parsimony, linear parsimony does not average out change over the interior nodes of a tree, but rather permits

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Figure 4 Ambiguous (A) vs. unambiguous (U) optimizations.

Figure 4 Ambiguous (A) vs. unambiguous (U) optimizations.

discontinuous changes along a branch. This has the advantageous effect of not forcing gradual trait evolution on the tree, and also of not forcing unnecessary trait reversals (Figure 3). A methodological advantage of linear over squared-change parsimony is that it permits the reconstruction of ambiguous ancestral character state reconstructions (Figure 4). This is a desirable property in cases where the available data are in fact insufficient to resolve the trait value at a specified internal nodes (Cunningham, 1999). A methodological disadvantage of linear parsimony is that, computationally, it requires a completely resolved tree topology in which all branching events are divided into only two daughter clades. Unfortunately, fully resolved trees are unusual in most studies with many ( >30) species. By contrast, squared-change parsimony can be calculated on a tree with unresolved multicho-tomies (also called polytomies), and therefore often becomes the method of choice by default. One alternative to using squared-change parsimony when faced with an incompletely resolved tree is to use linear parsimony on numerous (100, 1000) arbitrarily resolved trees, and then report statistics (e.g., minimum and maximum) of the trait values obtained. Software for this procedure is available in the freely available Mesquite software package (see 'Relevant Website').

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