Bayesian analysis of correlated evolution of discrete characters by reversible-jump Markov chain Monte Carlo

We describe a Bayesian method for investigating correlated evolution of discrete binary traits on phylogenetic trees. The method fits a continuous-time Markov model to a pair of traits, seeking the best fitting models that describe their joint evolution on a phylogeny. We employ the methodology of reversible-jump ( RJ) Markov chain Monte Carlo to search among the large number of possible models, some of which conform to independent evolution of the two traits, others to correlated evolution. The RJ Markov chain visits these models in proportion to their posterior probabilities, thereby directly estimating the support for the hypothesis of correlated evolution. In addition, the RJ Markov chain simultaneously estimates the posterior distributions of the rate parameters of the model of trait evolution. These posterior distributions can be used to test among alternative evolutionary scenarios to explain the observed data. All results are integrated over a sample of phylogenetic trees to account for phylogenetic uncertainty. We implement the method in a program called RJ Discrete and illustrate it by analyzing the question of whether mating system and advertisement of estrus by females have coevolved in the Old World monkeys and great apes.

Multivariate quantitative genetics and the Lek Paradox: Genetic variance in male sexually selected traits of Drosophila serrata under field control

Single male sexually selected traits have been found to exhibit substantial genetic variance, even though natural and sexual selection are predicted to deplete genetic variance in these traits. We tested whether genetic variance in multiple male display traits of Drosophila serrata was maintained under field conditions. A breeding design involving 300 field-reared males and their laboratory-reared offspring allowed the estimation of the genetic variance-covariance matrix for six male cuticular hydrocarbons (CHCs) under field conditions. Despite individual CHCs displaying substantial genetic variance under field conditions, the vast majority of genetic variance in CHCs was not closely associated with the direction of sexual selection measured on field phenotypes. Relative concentrations of three CHCs correlated positively with body size in the field, but not under laboratory conditions, suggesting condition-dependent expression of CHCs under field conditions. Therefore condition dependence may not maintain genetic variance in preferred combinations of male CHCs under field conditions, suggesting that the large mutational target supplied by the evolution of condition dependence may not provide a solution to the lek paradox in this species. Sustained sexual selection may be adequate to deplete genetic variance in the direction of selection, perhaps as a consequence of the low rate of favorable mutations expected in multiple trait systems.

Use of the EM algorithm to detect QTL affecting multiple-traits in an across half-sib family analysis

QTL detection experiments in livestock species commonly use the half-sib design. Each male is mated to a number of females, each female producing a limited number of progeny. Analysis consists of attempting to detect associations between phenotype and genotype measured on the progeny. When family sizes are limiting experimenters may wish to incorporate as much information as possible into a single analysis. However, combining information across sires is problematic because of incomplete linkage disequilibrium between the markers and the QTL in the population. This study describes formulae for obtaining MLEs via the expectation maximization (EM) algorithm for use in a multiple-trait, multiple-family analysis. A model specifying a QTL with only two alleles, and a common within sire error variance is assumed. Compared to single-family analyses, power can be improved up to fourfold with multi-family analyses. The accuracy and precision of QTL location estimates are also substantially improved. With small family sizes, the multi-family, multi-trait analyses reduce substantially, but not totally remove, biases in QTL effect estimates. In situations where multiple QTL alleles are segregating the multi-family analysis will average out the effects of the different QTL alleles.

The Roles of Phenotypic Plasticity and Plant-Microbe Interactions in the Evolution of Complex Traits in Boechera stricta

All organisms live in complex habitats that shape the course of their evolution by altering the phenotype expressed by a given genotype (a phenomenon known as phenotypic plasticity) and simultaneously by determining the evolutionary fitness of that phenotype. In some cases, phenotypic evolution may alter the environment experienced by future generations. This dissertation describes how genetic and environmental variation act synergistically to affect the evolution of glucosinolate defensive chemistry and flowering time in Boechera stricta, a wild perennial herb. I focus particularly on plant-associated microbes as a part of the plant’s environment that may alter trait evolution and in turn be affected by the evolution of those traits. In the first chapter I measure glucosinolate production and reproductive fitness of over 1,500 plants grown in common gardens in four diverse natural habitats, to describe how patterns of plasticity and natural selection intersect and may influence glucosinolate evolution. I detected extensive genetic variation for glucosinolate plasticity and determined that plasticity may aid colonization of new habitats by moving phenotypes in the same direction as natural selection. In the second chapter I conduct a greenhouse experiment to test whether naturally-occurring soil microbial communities contributed to the differences in phenotype and selection that I observed in the field experiment. I found that soil microbes cause plasticity of flowering time but not glucosinolate production, and that they may contribute to natural selection on both traits; thus, non-pathogenic plant-associated microbes are an environmental feature that could shape plant evolution. In the third chapter, I combine a multi-year, multi-habitat field experiment with high-throughput amplicon sequencing to determine whether B. stricta-associated microbial communities are shaped by plant genetic variation. I found that plant genotype predicts the diversity and composition of leaf-dwelling bacterial communities, but not root-associated bacterial communities. Furthermore, patterns of host genetic control over associated bacteria were largely site-dependent, indicating an important role for genotype-by-environment interactions in microbiome assembly. Together, my results suggest that soil microbes influence the evolution of plant functional traits and, because they are sensitive to plant genetic variation, this trait evolution may alter the microbial neighborhood of future B. stricta generations. Complex patterns of plasticity, selection, and symbiosis in natural habitats may impact the evolution of glucosinolate profiles in Boechera stricta.

Molecular Systematics and Traits Evolution in Phasmatodea Leach, 1815 (Hexapoda; Insecta)

Phasmatodea Leach, 1815 (Hexapoda; Insecta) is a polyneopteran order which counts approximately 3000 described species, often known for their remarkable forms of mimicry. In this thesis, I provide a comprehensive systematic framework which includes over 180 species never considered in a phylogenetic framework: the latter can facilitate a better understanding of the processes underlying phasmids evolutionary history. The clade represents in fact an incredible testing ground to study trait evolution and its striking disparity of reproductive strategies and wing morphologies have been of great interest to the evolutionary biology community. Phasmids wings represent one of the first and most notable rejection of Dollo’s law and they played a central role in initiating a long- standing debate on the irreversibility of complex traits loss. Macroevolutionary analyses presented here confirm that wings evolution in phasmids is a reversible process even when possible biases - such as systematic uncertainty and trait-dependent diversification rates - are considered. These findings remark how complex traits can evolve in a dynamic, reversible manner and imply that their molecular groundplan can be preserved despite its phenotypical absence. This concept has been further tested with phylogenetic and transcriptomic approaches in two phasmids parthenogenetic lineages and a bisexual congeneric of the European Bacillus species complex. Leveraging a gene co-expression network approach, male gonad associated genes were retrieved in the bisexual species and then their modifications in the parthenogens were charachterized. Pleiotropy appears to constrain gene modifications associated to male reproductive structures after their loss in parthenogens, so that the lost trait molecular groundplan can be largely preserved in both transcription patterns and sequence evolution. Overall, the results presented in this thesis contribute to shape our understanding of the interplay between the phenotypic and molecular levels in trait evolution.

Covariance functions for body weight from birth to maturity in Nellore cows

The objective of this study was to estimate (co)variance functions using random regression models on Legendre polynomials for the analysis of repeated measures of BW from birth to adult age. A total of 82,064 records from 8,145 females were analyzed. Different models were compared. The models included additive direct and maternal effects, and animal and maternal permanent environmental effects as random terms. Contemporary group and dam age at calving (linear and quadratic effect) were included as fixed effects, and orthogonal Legendre polynomials of animal age (cubic regression) were considered as random co-variables. Eight models with polynomials of third to sixth order were used to describe additive direct and maternal effects, and animal and maternal permanent environmental effects. Residual effects were modeled using 1 (i.e., assuming homogeneity of variances across all ages) or 5 age classes. The model with 5 classes was the best to describe the trajectory of residuals along the growth curve. The model including fourth- and sixth-order polynomials for additive direct and animal permanent environmental effects, respectively, and third-order polynomials for maternal genetic and maternal permanent environmental effects were the best. Estimates of (co) variance obtained with the multi-trait and random regression models were similar. Direct heritability estimates obtained with the random regression models followed a trend similar to that obtained with the multi-trait model. The largest estimates of maternal heritability were those of BW taken close to 240 d of age. In general, estimates of correlation between BW from birth to 8 yr of age decreased with increasing distance between ages.

Understanding the concepts of community phylogenetics

Background: Community phylogenetics is an emerging field of research that has made important contributions to understanding community assembly. The rapid development of this field can be attributed to the merging of phylogenetics and community ecology research to provide improved clarity on the processes that govern community structure and composition. Question: What are the major challenges that impede the sound interpretation of the patterns and processes of phylogenetic community assembly? Methods: We use four scenarios to illustrate explicitly how the phylogenetic structure of communities can exist in stable or transient phases, based on the different combinations of phylogenetic relationships and phenotypic traits among co-occurring species. We discuss these phases by implicating a two-way process in the assembly and disintegration of the given ecological community. Conclusions: This paper synthesizes the major concepts of community phylogenetics using habitat filtering and competition processes to elucidate how the understanding of phylogenetic community structure is currently hindered by the dynamics of community assembly and disassembly.

Effects of phylogenetic signal on ancestral state reconstruction.

One of the standard tools used to understand the processes shaping trait evolution along the branches of a phylogenetic tree is the reconstruction of ancestral states (Pagel 1999). The purpose is to estimate the values of the trait of interest for every internal node of a phylogenetic tree based on the trait values of the extant species, a topology and, depending on the method used, branch lengths and a model of trait evolution (Ronquist 2004). This approach has been used in a variety of contexts such as biogeography (e.g., Nepokroeff et al. 2003, Blackburn 2008), ecological niche evolution (e.g., Smith and Beaulieu 2009, Evans et al. 2009) and metabolic pathway evolution (e.g., Gabaldón 2003, Christin et al. 2008). Investigations of the factors affecting the accuracy with which ancestral character states can be reconstructed have focused in particular on the choice of statistical framework (Ekman et al. 2008) and the selection of the best model of evolution (Cunningham et al. 1998, Mooers et al. 1999). However, other potential biases affecting these methods, such as the effect of tree shape (Mooers 2004), taxon sampling (Salisbury and Kim 2001) as well as reconstructing traits involved in species diversification (Goldberg and Igić 2008), have also received specific attention. Most of these studies conclude that ancestral character states reconstruction is still not perfect, and that further developments are necessary to improve its accuracy (e.g., Christin et al. 2010). Here, we examine how different estimations of branch lengths affect the accuracy of ancestral character state reconstruction. In particular, we tested the effect of using time-calibrated versus molecular branch lengths and provide guidelines to select the most appropriate branch lengths to reconstruct the ancestral state of a trait.

Measurement Errors Should Always Be Incorporated in Phylogenetic Comparative Analysis

The evolution of continuous traits is the central component of comparative analyses in phylogenetics, and the comparison of alternative models of trait evolution has greatly improved our understanding of the mechanisms driving phenotypic differentiation. Several factors influence the comparison of models, and we explore the effects of random errors in trait measurement on the accuracy of model selection. We simulate trait data under a Brownian motion model (BM) and introduce different magnitudes of random measurement error. We then evaluate the resulting statistical support for this model against two alternative models: Ornstein-Uhlenbeck (OU) and accelerating/decelerating rates (ACDC). Our analyses show that even small measurement errors (10%) consistently bias model selection towards erroneous rejection of BM in favour of more parameter-rich models (most frequently the OU model). Fortunately, methods that explicitly incorporate measurement errors in phylogenetic analyses considerably improve the accuracy of model selection. Our results call for caution in interpreting the results of model selection in comparative analyses, especially when complex models garner only modest additional support. Importantly, as measurement errors occur in most trait data sets, we suggest that estimation of measurement errors should always be performed during comparative analysis to reduce chances of misidentification of evolutionary processes.

Evidence for adaptive radiation from a phylogenetic study of plant defenses.

One signature of adaptive radiation is a high level of trait change early during the diversification process and a plateau toward the end of the radiation. Although the study of the tempo of evolution has historically been the domain of paleontologists, recently developed phylogenetic tools allow for the rigorous examination of trait evolution in a tremendous diversity of organisms. Enemy-driven adaptive radiation was a key prediction of Ehrlich and Raven's coevolutionary hypothesis [Ehrlich PR, Raven PH (1964) Evolution 18:586-608], yet has remained largely untested. Here we examine patterns of trait evolution in 51 North American milkweed species (Asclepias), using maximum likelihood methods. We study 7 traits of the milkweeds, ranging from seed size and foliar physiological traits to defense traits (cardenolides, latex, and trichomes) previously shown to impact herbivores, including the monarch butterfly. We compare the fit of simple random-walk models of trait evolution to models that incorporate stabilizing selection (Ornstein-Ulenbeck process), as well as time-varying rates of trait evolution. Early bursts of trait evolution were implicated for 2 traits, while stabilizing selection was implicated for several others. We further modeled the relationship between trait change and species diversification while allowing rates of trait evolution to vary during the radiation. Species-rich lineages underwent a proportionately greater decline in latex and cardenolides relative to species-poor lineages, and the rate of trait change was most rapid early in the radiation. An interpretation of this result is that reduced investment in defensive traits accelerated diversification, and disproportionately so, early in the adaptive radiation of milkweeds.

Relating traits to diversification: A simple test

We describe a simple comparative method for determining whether rates of diversification are correlated with continuous traits in species-level phylogenies. This involves comparing traits of species with net speciation rate (number of nodes linking extant species with the root divided by the root to tip evolutionary distance), using a phylogenetically corrected correlation. We use simulations to examine the power of this test. We find that the approach has acceptable power to uncover relationships between speciation and a continuous trait and is robust to background random extinction; however, the power of the approach is reduced when the rate of trait evolution is decreased. The test has low power to relate diversification to traits when extinction rate is correlated with the trait. Clearly, there are inherent limitations in using only data on extant species to infer correlates of extinction; however, this approach is potentially a powerful tool in analyzing correlates of speciation.

Bayesian estimation of ancestral character states on phylogenies

Biologists frequently attempt to infer the character states at ancestral nodes of a phylogeny from the distribution of traits observed in contemporary organisms. Because phylogenies are normally inferences from data, it is desirable to account for the uncertainty in estimates of the tree and its branch lengths when making inferences about ancestral states or other comparative parameters. Here we present a general Bayesian approach for testing comparative hypotheses across statistically justified samples of phylogenies, focusing on the specific issue of reconstructing ancestral states. The method uses Markov chain Monte Carlo techniques for sampling phylogenetic trees and for investigating the parameters of a statistical model of trait evolution. We describe how to combine information about the uncertainty of the phylogeny with uncertainty in the estimate of the ancestral state. Our approach does not constrain the sample of trees only to those that contain the ancestral node or nodes of interest, and we show how to reconstruct ancestral states of uncertain nodes using a most-recent-common-ancestor approach. We illustrate the methods with data on ribonuclease evolution in the Artiodactyla. Software implementing the methods ( BayesMultiState) is available from the authors.

A cautionary note on the use of Ornstein Uhlenbeck models in macroevolutionary studies

Phylogenetic comparative methods are increasingly used to give new insights into the dynamics of trait evolution in deep time. For continuous traits the core of these methods is a suite of models that attempt to capture evolutionary patterns by extending the Brownian constant variance model. However, the properties of these models are often poorly understood, which can lead to the misinterpretation of results. Here we focus on one of these models – the Ornstein Uhlenbeck (OU) model. We show that the OU model is frequently incorrectly favoured over simpler models when using Likelihood ratio tests, and that many studies fitting this model use datasets that are small and prone to this problem. We also show that very small amounts of error in datasets can have profound effects on the inferences derived from OU models. Our results suggest that simulating fitted models and comparing with empirical results is critical when fitting OU and other extensions of the Brownian model. We conclude by making recommendations for best practice in fitting OU models in phylogenetic comparative analyses, and for interpreting the parameters of the OU model.

Genetic parameters and environmental effects on temperament score and reproductive traits of Nellore cattle

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Genotype by environment interaction in Nelore cattle from five Brazilian states

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)