PHYLOGENY AS AGREEMENT: PARSIMONY DERIVED FROM DISCRETE DATA THEORY

GIANNINI, NP

Buenos Aires

Congreso; 35th Annual Meeting of the Willi Hennig Society; 2016

Discrete-data theory is an area of statistics thatcovers the treatment of categorical data. A basic measure of association between categorical variables is the Chi-square statistic. "Agreement" is a particular case of association; e.g., measuring the degree to which two observers concur in classifying items into thesame pre-established categories. Here I show that parsimony can be derived fromagreement for the simplest case, binary data with no missing entries("binary conditions"), for both maximization of homology andminimization of homoplasy. This is achieved by setting a 2 × 2 agreementtable in which the data matrix (or any of its component characters) is the rowvariable ("observer1") and a parsimoniouslyoptimized tree is designed asthe column variable("observer 2"). In this agreement between data and tree, diagonal (D) cells contain thefrequency of individual 0 and 1 state assignments that remain homologous asoptimized in the tree, and the off-D cells contain 0- and 1-state cases nothomologous across the tree. Optimal trees are those with minimum off-D-cellscount, which is the number of extra steps, and so the empirical quantityfor applying character weightingbased on implied homoplasy.Provided character independence, the retention index is shown to exactly equatethe explained variance of the agreement table. Additional analyses under"binary conditions" suggest that parsimony nodal assignment,character congruence, and degree of support have all a probabilistic basis.