A Novel Phylogenetic Negative Binomial Regression Model for Count-Dependent Variables.

Regression models are extensively used to explore the relationship between a dependent variable and its covariates. These models work well when the dependent variable is categorical and the data are supposedly independent, as is the case with generalized linear models (GLMs). However, trait data from related species do not operate under these conditions due to their shared common ancestry, leading to dependence that can be illustrated through a phylogenetic tree.

Phylogenetic Curved Optimal Regression for Adaptive Trait Evolution.

Regression analysis using line equations has been broadly applied in studying the evolutionary relationship between the response trait and its covariates. However, the characteristics among closely related species in nature present abundant diversities where the nonlinear relationship between traits have been frequently observed. By treating the evolution of quantitative traits along a phylogenetic tree as a set of continuous stochastic variables, statistical models for describing the dynamics of the optimum of the response trait and its covariates are built herein.

Building an adaptive trait simulator package to infer parametric diffusion model along phylogenetic tree.

The development of an adaptive trait simulator package for inferring trait evolution along a phylogenetic tree is shown. Stochastic processes of the continuous type are broadly applied to modeling trait evolution when the evolutionary relationship among species and traits of study interest are present. By including several popular stochastic processes, evolutionary information embedded in a dataset can be revealed.

On the Matrix Condition of Phylogenetic Tree.

Phylogenetic comparative analyses use trees of evolutionary relationships between species to understand their evolution and ecology. A phylogenetic tree of taxa can be algebraically transformed into an by squared symmetric phylogenetic covariance matrix where each element in represents the affinity between extant species and extant species . This matrix is used internally in several comparative methods: for example, it is often inverted to compute the likelihood of the data under a model.

Investigating the performance of AIC in selecting phylogenetic models.

The popular likelihood-based model selection criterion, Akaike's Information Criterion (AIC), is a breakthrough mathematical result derived from information theory. AIC is an approximation to Kullback-Leibler (KL) divergence with the derivation relying on the assumption that the likelihood function has finite second derivatives. However, for phylogenetic estimation, given that tree space is discrete with respect to tree topology, the assumption of a continuous likelihood function with finite second derivatives is violated.

Assessing the Goodness of Fit of Phylogenetic Comparative Methods: A Meta-Analysis and Simulation Study.

Background: Phylogenetic comparative methods (PCMs) have been applied widely in analyzing data from related species but their fit to data is rarely assessed.

Question: Can one determine whether any particular comparative method is typically more appropriate than others by examining comparative data sets?

Data: I conducted a meta-analysis of 122 phylogenetic data sets found by searching all papers in JEB, Blackwell Synergy and JSTOR published in 2002-2005 for the purpose of assessing the fit of PCMs. The number of species in these data sets ranged from 9 to 117.

Modeling stabilizing selection: expanding the Ornstein-Uhlenbeck model of adaptive evolution.

Comparative methods used to study patterns of evolutionary change in a continuous trait on a phylogeny range from Brownian motion processes to models where the trait is assumed to evolve according to an Ornstein-Uhlenbeck (OU) process. Although these models have proved useful in a variety of contexts, they still do not cover all the scenarios biologists want to examine. For models based on the OU process, model complexity is restricted in current implementations by assuming that the rate of stochastic motion and the strength of selection do not vary among selective regimes.

Coevolution in multidimensional trait space favours escape from parasites and pathogens.

Almost all species are subject to continuous attack by parasites and pathogens. Because parasites and pathogens tend to have shorter generation times and often experience stronger selection due to interaction than their victims do, it is frequently argued that they should evolve more rapidly and thus maintain an advantage in the evolutionary race between defence and counter-defence. This prediction generates an apparent paradox: how do victim species survive and even thrive in the face of a continuous onslaught of more rapidly evolving enemies? One potential explanation is that defence is physiologically, mechanically or behaviourally easier than attack, so that evolution is less constrained for victims than for parasites or pathogens.