Resolving the correlation of a phylogenetic character and a non-evolving variable

GIANNINI, NP; GOLOBOFF, PA

San Miguel de Tucuman

Congreso; Willi Hennig Meeting; 2008

Willi Hennig Society

<!-- /* Style Definitions */ p.MsoNormal, li.MsoNormal, div.MsoNormal {mso-style-parent:""; margin:0in; margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:12.0pt; font-family:"Times New Roman"; mso-fareast-font-family:"Times New Roman"; mso-ansi-language:ES-AR;} @page Section1 {size:8.5in 11.0in; margin:1.0in 1.25in 1.0in 1.25in; mso-header-margin:.5in; mso-footer-margin:.5in; mso-paper-source:0;} div.Section1 {page:Section1;} --> Species are related by phylogeny and this poses a statistical problem of non-independence in data gathered from terminals. A diverse family of phylogenetic comparative methods deal with various aspects of the problem, chiefly in the context of correlation / regression of two characters on a tree. This is a commonly encountered problem across all Biology. One instance would be the response of basal metabolic rate to changes in body size. In this case, both characters clearly evolve in any lineage of interest. However, other biologically interesting problems involve characters whose variation cannot be transferred to descendants via genomic transmission. Some demographic parameters and geographic location (e.g., latitude) are examples of variables that do not evolve. We argue that when two such variables are measured in terminals, then a randomized version of correlation / regression is a valid analytical option. Here we deal with a more complicated situation, the correlation of one evolving character (e.g., body size) with one non-evolving variable. For the evolving character, phylogenetic dependence among terminals is rampant. Therefore the tree structure should be taken into account, and by this we mean a very specific concept: both the branching pattern and the total amount of evolution should be taken into account. By contrast, for the non-evolving character, the tree structure is irrelevant, so considering this difference is crucial to develop a test. We propose a rather simple solution. We calculate an observed correlation coefficient r between the two variables, x and y, the first being an evolving character and the second a non-evolving variable, conserving the original pairing of data. Then we optimize x on the tree and collect the changes between nodes (whose sum equals total steps on the tree), sampling a reasonable number of reconstructions. Next we randomly assign the changes (not the ancestral assignments) of a given reconstruction in the nodes of the tree, and recalculate each terminal´s value by summing the changes from root to tip. Thus, terminals acquire new values while preserving the exact same amount of evolution on the tree. The new set of x-values is correlated with the original y-values. In this way, a distribution of random r is generated (e.g., 5000 times) and the observed r is compared with that distribution, obtaining a randomized significance test for r. We discuss unexpected properties of this procedure, called here dual phylogenetic correlation.