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. Analytical representations for the response trait variables, as well as their optima among a group of related species, are derived. Due to the models' lack of tractable likelihood, a procedure that implements the Approximate Bayesian Computation (ABC) technique is applied for statistical inference. Simulation results show that the new models perform well where the posterior means of the parameters are close to the true parameters. Empirical analysis supports the new models when analyzing the trait relationship among kangaroo species.

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. Another possible explanation is that parasites and pathogens have enemies themselves and that victim species persist because parasites and pathogens are regulated from the top down and thus generally have only modest demographic impacts on victim populations. Here we explore a third possibility: that victim species are not as evolutionarily impotent as conventional wisdom holds, but instead have unique evolutionary advantages that help to level the playing field. We use quantitative genetic analysis and individual-based simulations to show that victims can achieve such an advantage when coevolution involves multiple traits in both the host and the parasite.

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. In this paper, we investigate the relationship between the expected log likelihood of a candidate model, and the expected KL divergence in the context of phylogenetic tree estimation. We find that given the tree topology, AIC is an unbiased estimator of the expected KL divergence. However, when the tree topology is unknown, AIC tends to underestimate the expected KL divergence for phylogenetic models. Simulation results suggest that the degree of underestimation varies across phylogenetic models so that even for large sample sizes, the bias of AIC can result in selecting a wrong model. As the choice of phylogenetic models is essential for statistical phylogenetic inference, it is important to improve the accuracy of model selection criteria in the context of phylogenetics.

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. In response to the analytical challenges of count-dependent variables in phylogenetically related species, we have developed a novel phylogenetic negative binomial regression model that allows for overdispersion, a limitation present in the phylogenetic Poisson regression model in the literature. This model overcomes limitations of conventional GLMs, which overlook the inherent dependence arising from shared lineage. Instead, our proposed model acknowledges this factor and uses the generalized estimating equation (GEE) framework for precise parameter estimation. The effectiveness of the proposed model was corroborated by a rigorous simulation study, which, despite the need for careful convergence monitoring, demonstrated its reasonable efficacy. The empirical application of the model to lizard egg-laying count and mammalian litter size data further highlighted its practical relevance. In particular, our results identified negative correlations between increases in egg mass, litter size, ovulation rate, and gestation length with respective yearly counts, while a positive correlation was observed with species lifespan. This study underscores the importance of our proposed model in providing nuanced and accurate analyses of count-dependent variables in related species, highlighting the often overlooked impact of shared ancestry. The model represents a critical advance in research methodologies, opening new avenues for interpretation of related species data in the field.

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. The highlights of the method include: 1.The implementation of the popular Cox-Ingersol-Ross process for modeling rate evolution within the package to prevent rates from becoming negative and thus is potentially a useful extension to study adaptive trait evolution in randomly evolved environment.2.The established trait simulator approach along with approximate Bayesian computation procedure provides a feasible statistical inference without model likelihood.3.The procedure proposed for trait simulator along phylogenetic tree can be applied to all established models of trait evolution in literature, thus providing users an alternative option to analyze their data.

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 n taxa can be algebraically transformed into an n by n squared symmetric phylogenetic covariance matrix C where each element c ij in C represents the affinity between extant species i and extant species j. This matrix C is used internally in several comparative methods: for example, it is often inverted to compute the likelihood of the data under a model. However, if the matrix is ill-conditioned (ie, if κ , defined by the ratio of the maximum eigenvalue of C to the minimum eigenvalue of C , is too high), this inversion may not be stable, and thus neither will be the calculation of the likelihood or parameter estimates that are based on optimizing the likelihood. We investigate this potential issue and propose several methods to attempt to remedy this issue.

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. ANALYSIS METHOD: I used the Akaike information criterion to compare PCMs, and then fit PCMs to bivariate data sets through REML analysis. Correlation estimates between two traits and bootstrapped confidence intervals of correlations from each model were also compared. CONCLUSIONS: For phylogenies of less than one hundred taxa, the Independent Contrast method and the independent, non-phylogenetic models provide the best fit.For bivariate analysis, correlations from different PCMs are qualitatively similar so that actual correlations from real data seem to be robust to the PCM chosen for the analysis. Therefore, researchers might apply the PCM they believe best describes the evolutionary mechanisms underlying their data.

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. Here, we expand the OU model of adaptive evolution to include models that variously relax the assumption of a constant rate and strength of selection. In its most general form, the methods described here can assign each selective regime a separate trait optimum, a rate of stochastic motion parameter, and a parameter for the strength of selection. We use simulations to show that our models can detect meaningful differences in the evolutionary process, especially with larger sample sizes. We also illustrate our method using an empirical example of genome size evolution within a large flowering plant clade.