Measuring homoplasy I: comprehensive measures of maximum and minimum cost under parsimony across discrete cost matrix character types

Here, we propose, prove mathematically and discuss maximum and minimum measures of maximum parsimony evolution across 12 discrete phylogenetic character types, classified across 4467 morphological and molecular datasets. Covered character types are: constant, binary symmetric, multistate unordered (non-additive) symmetric, multistate linear ordered symmetric, multistate non-linear ordered symmetric, binary irreversible, multistate irreversible, binary Dollo, multistate Dollo, multistate custom symmetric, binary custom asymmetric and multistate custom asymmetric characters. We summarize published solutions and provide and prove a range of new formulae for the algebraic calculation of minimum (m), maximum (g) and maximum possible (gmax) character cost for applicable character types. Algorithms for exhaustive calculation of m, g and gmax applicable to all classified character types (within computational limits on the numbers of taxa and states) are also provided. The general algorithmic solution for minimum steps (m) is identical to a minimum spanning tree on the state graph or minimum weight spanning arborescence on the state digraph. Algorithmic solutions for character g and gmax are based on matrix mathematics equivalent to optimization on the star tree, respectively for given state frequencies and all possible state frequencies meeting specified numbers of taxa and states. We show that maximizing possible cost (gmax) with given transition costs can be equivalent to maximizing, across all possible state frequency combinations, the lowest implied cost of state transitions if any one state is ancestral on the star tree, via the solution of systems of linear equations. The methods we present, implemented in the Claddis R package, extend to a comprehensive range, the fundamental character types for which homoplasy may be measured under parsimony using m, g and gmax, including extra cost (h), consistency index (ci), retention index (ri) or indices based thereon.

Fossilization can mislead analyses of phenotypic disparity

Analyses of morphological disparity can incorporate living and fossil taxa to facilitate the exploration of how phenotypic variation changes through time. However, taphonomic processes introduce non-random patterns of data loss in fossil data and their impact on perceptions of disparity is unclear. To address this, we characterize how measures of disparity change when simulated and empirical data are degraded through random and structured data loss. We demonstrate that both types of data loss can distort the disparity of clades, and that the magnitude and direction of these changes varies between the most commonly employed distance metrics and disparity indices. The inclusion of extant taxa and exceptionally preserved fossils mitigates these distortions and clarifies the full extent of the data lost, most of which would otherwise go uncharacterized. This facilitates the use of ancestral state estimation and evolutionary simulations to further control for the effects of data loss. Where the addition of such reference taxa is not possible, we urge caution in the extrapolation of general patterns in disparity from datasets that characterize subsets of phenotype, which may represent no more than the traits that they sample.

Molecular phylogenies map to biogeography better than morphological ones

Phylogenetic relationships are inferred principally from two classes of data: morphological and molecular. Currently, most phylogenies of extant taxa are inferred from molecules and when morphological and molecular trees conflict the latter are often preferred. Although supported by simulations, the superiority of molecular trees has rarely been assessed empirically. Here we test phylogenetic accuracy using two independent data sources: biogeographic distributions and fossil first occurrences. For 48 pairs of morphological and molecular trees we show that, on average, molecular trees provide a better fit to biogeographic data than their morphological counterparts and that biogeographic congruence increases over research time. We find no significant differences in stratigraphic congruence between morphological and molecular trees. These results have implications for understanding the distribution of homoplasy in morphological data sets, the utility of morphology as a test of molecular hypotheses and the implications of analysing fossil groups for which molecular data are unavailable.

Using biogeographical and phylogenetic data, it is shown that molecular trees fit species geographical data better than trees inferred from morphology, and that these differences are not simply due to better tree resolution.