An optimization-based method to estimate and test character correlation for continuous characters

GOLOBOFF, PABLO A.; GIANNINI, NORBERTO P.

Oaxaca, México

Congreso; The 25th Annual Meeting of the Willi Hennig Society; 2006

Willi Hennig Society

A common problem in evolutionary and ecological studies is whether one character responds to change in another. Using species as sampling units introduces dependence because of common ancestry; so called "phylogenetic comparative methods" attempt to address this problem, but none of the techniques proposed is based on optimization, except for Maddison´s (1991) "concentrated changes" method for binary characters. Here, we explore the problem of regressing two continuous characters x and y, with y dependent on x, as optimized on a given phylogeny. A method to estimate the slope (or correlation coefficient) of such relationship, and its statistical significance, is proposed. The need to consider that a response in the dependent variable may be delayed, relative to change in the independent variable, is demonstrated. We propose a way to take this delay into account when forming the data pairs for the regression analysis. For a given set of most parsimonious reconstructions for both characters, the procedure tracks character changes in an upward pass (i.e. considering the sequence with which the characters are hypothesized to have evolved). For the significance of the regression slope, we used permutation, considering ambiguities in optimizations so as to make the test as conservative as possible. For the observed data, a range of slopes can be obtained (by comparing every possible reconstruction of one character with every possible reconstruction of the other, or at least a sample of reconstructions). For each of the permuted data sets, a similar range of slopes can be obtained. Significance is calculated as the proportion of permuted slope ranges that overlap with the observed slope range. Given our procedure for taking into account delays, it is possible to have cases where changes on a character, y, significantly depend on changes on another character, x, while changes in character x show no significant dependence from changes in character y. This procedure is implemented with a TNT script. Examples are analyzed, and general implications discussed.