The accuracy of ancestral reconstructions has been investigated by comparisons with known phy-logenies (e.g., viruses, computer simulations; Oakley and Cunningham, 2000). It is well known that all phylogenetically based methods perform poorly when taxon sampling is low and when rates of evolution in the character of interest are unequal among branches of the tree (Garland et al., 1993; Sullivan et al., 1999; Hillis et al., 2003). Further, all methods for studying character evolution on a tree make certain assumptions about the capacity of trees to faithfully record the actual history of character change. These include the assumptions that: phenotypic diversification results largely from specia-tion and that the effects of extinction have not erased the signal, that taxon sampling faithfully represent the history of diversification, and that genealogical history is largely or entirely bifurcating (vs. multi-furcating or converging). Of course, all methods assume we know the 'true' (or 'nearly true') tree topology. In addition, each of the optimization methods makes assumptions about critical parameters, including branch lengths, models of character evolution, absolute rates of evolution, homogeneity (vs. heterogeneity) of evolutionary rates, reversibility (or the lack thereof), and the orderedness (or unordered-ness) of multistate characters.
The accuracy of ancestral trait reconstruction also depends strongly on parameter estimation (e.g., tree topology, branch lengths, and models of trait evolution). ML and BA perform well when model assumptions match real parameters. ML and BA are positively misleading when model assumptions are violated. MP is more conservative, recovering fewer false positives than ML and BA when biological parameters are not known. Squared-change parsimony, ML, and BA minimize large changes, spreading evolution over the internal tree branches. Linear parsimony permits reconstructions at ancestral nodes with no change, and permits ambiguous reconstructions. 'Independent contrasts' assumes that selection operates in the origin but not maintenance of derived traits.
Both conventional and phylogenetic correlations of interspecific character data make assumptions about critical parameters. These assumptions are often of unknown validity, and in some cases are known to be incorrect. Conventional statistics assume that each terminal taxon (tips of the tree) may be treated as independent sample of the relationship under investigation. This means that the character value (phenotype) observed in that taxon evolved independently (without inheritance) from the values in other taxa in the analysis. In an evolutionary context, this is equivalent to assuming that trait values result primarily from stabilizing selection in each species that acts to maintain trait values, rather than from directional selection at the origin of the trait in an ancestral species (Hansen, 1997). In other words, conventional statistics assume traits to be highly labile and without significant phylogenetic inertia. Phylogenetic correlations make converse assumptions, that trait values are due largely or entirely to directional selection at the origin of a feature and that the influence of stabilizing selection is negligible. Phylogenetic correlations also must make particular assumptions about branch lengths and models of trait evolution.
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