Power of the Concentrated Changes Test for Correlated Evolution

Abstract

The concentrated changes test (CCT) calculates the probability that changes in a binary character are distributed randomly on the branches of a cladogram. This test is used to examine hypotheses of correlated evolution, especially cases where changes in the state of one character influence changes in the state of another character. The test may be sensitive to the addition of branches that lack either trait of interest (white branches). To examine the effects of the proportion of white branches and of tree topology on the CCT probability, we conducted a simulation analysis using a series of randomly generated 100-taxon trees, in addition to a nearly perfectly balanced (symmetrical) and a completely imbalanced (asymmetrical) 100-taxon tree. Using two models of evolution (gains only, or gains and losses), we evolved character pairs randomly onto these trees to simulate cases where (1) characters evolve independently (i.e., no correlation among the traits) or (2) all changes in the dependent character occur on branches containing the independent trait (i.e., a strong correlation among the traits). This allowed us to evaluate the sensitivity of the CCT to type I and type II errors, respectively. In the simulations, the CCT did not appear to be overly sensitive to the inclusion of white branches (low likelihood of type I error with both CCT probabilities < 0.05 and < 0.01). However, the CCT was susceptible to type II error when the proportion of white branches was < 20%. The test was also sensitive to tree shape and was positively correlated to Colless's tree imbalance statistic I. Finally, the CCT responded differently for simulations where only gains were allowed and those where both gains and losses were permitted. These results indicate that the CCT is unlikely to detect a correlation between characters when no such correlation exists. However, when a trait can be gained but not lost, the CCT is conservative and may fail to detect true correlations among traits (increased type II error). Determination of the sampling universe (the taxa included in the comparative analysis) can strongly influence the probability of making such type II errors. We suggest guidelines to circumvent these limitations.

Phylogenetic Logistic Regression for Binary Dependent Variables

“…Nonetheless, our goal was a model for logistic regression that could accommodate either continuously valued or discrete independent variables and an arbitrary number of them. This is the main difference between our method and not only Pagel (1994) but also other methods for binary traits (Maddison 1990;Ridley and Grafen 1996;Grafen and Ridley 1997;Pagel 1997;Schluter et al 1997;Cunningham et al 1998;Lorch and Eadie 1999;Schultz and Churchill 1999;Lindenfors et al 2003;Pagel and Meade 2006).…”

“…The independent variables can be continuous and/or discrete, even when there is only a single independent variable. This sets our method apart from existing methods for analyzing binary dependent variables that do not allow for continuous-valued predictors (Maddison 1990;Pagel 1994;Ridley and Grafen 1996;Grafen and Ridley 1997;Pagel 1997;Schluter et al 1997;Cunningham et al 1998;Lorch and Eadie 1999;Schultz and Churchill 1999;Perez-Barberia et al 2002;Lindenfors et al 2003;Pagel and Meade 2006). Our approach involves generalized linear models (GLMs) that can be used to analyze data from the exponential family of statistical distributions, including Gaussian (normal), Poisson, and binomial distributions (McCullagh and Nelder 1989).…”

Loss of male secondary sexual structures in allopatry in the Neotropical butterfly genus Arcas (Lycaenidae: Theclinae: Eumaeini)

“…For example, the lack of a hindwing scent pouch in A. delphia and A. tuneta is due to one evolutionary loss on the cladogram. Further, a concentrated changes test for correlated evolution (e.g., Maddison 1990, Lorch & Eadie 1999) is inapplicable because sympatry/allopatry is not a phylogenetic character. As an alternative, given the inferred tree structure and information on the sympatry or allopatry for each pair of species (in the species accounts), we determine how our results compared with those from a sample of 200 trees produced using the random shuffle of terminal taxa option of Mesquite software (Madison & Madison 2011) for the ingroup species.…”

Comparative methods for studying primate adaptation and allometry

“…A recent computer simulation study has shown that the concentrated changes test has acceptable Type I error rates, 62 but the method has other shortcomings. For example, it requires a bifurcating tree and does not incorporate branch length information (see Sillén-Tullberg 63 and Werdelin and Tullberg 64 ).…”