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The value of a continuous character evolving on a phylogenetic tree is commonly modelled as the location of a particle moving under one-dimensional Brownian motion with constant rate. The Brownian motion model is best suited to characters…
Efforts to reconstruct phylogenetic trees and understand evolutionary processes depend fundamentally on stochastic models of speciation and mutation. The simplest continuous-time model for speciation in phylogenetic trees is the Yule…
Phylogenetic comparative methods are well established tools for using inter-species variation to analyse phenotypic evolution and adaptation. They are generally hampered, however, by predominantly univariate approaches and failure to…
Comparative biologists are often interested in inferring covariation between multiple biological traits sampled across numerous related taxa. To properly study these relationships, we must control for the shared evolutionary history of the…
Phylogenetic comparative methods explore the relationships between quantitative traits adjusting for shared evolutionary history. This adjustment often occurs through a Brownian diffusion process along the branches of the phylogeny that…
We are interested in modelling Darwinian evolution, resulting from the interplay of phenotypic variation and natural selection through ecological interactions. Our models are rooted in the microscopic, stochastic description of a population…
In past decades, Gaussian processes has been widely applied in studying trait evolution using phylogenetic comparative analysis. In particular, two members of Gaussian processes: Brownian motion and Ornstein-Uhlenbeck process, have been…
In this paper, a robust non-parametric measure of statistical dependence, or correlation, between two random variables is presented. The proposed coefficient is a permutation-like statistic that quantifies how much the observed sample S_n :…
We consider a stochastic evolutionary model for a phenotype developing amongst n related species with unknown phylogeny. The unknown tree is modelled by a Yule process conditioned on n contemporary nodes. The trait value is assumed to…
We present an individual-based model of phenotypic trait evolution in two-sex populations, which includes semi-random mating of individuals of the opposite sex, natural death and intra-specific competition. By passing the number of…
Biological data objects often have both of the following features: (i) they are functions rather than single numbers or vectors, and (ii) they are correlated due to phylogenetic relationships. In this paper we give a flexible statistical…
Understanding which phenotypic traits are consistently correlated throughout evolution is a highly pertinent problem in modern evolutionary biology. Here, we propose a multivariate phylogenetic latent liability model for assessing the…
The asymptotic behavior of estimates and information criteria in linear models are studied in the context of hierarchically correlated sampling units. The work is motivated by biological data collected on species where autocorrelation is…
Molecular phenotypes are important links between genomic information and organismic functions, fitness, and evolution. Complex phenotypes, which are also called quantitative traits, often depend on multiple genomic loci. Their evolution…
The branching structure of biological evolution confers statistical dependencies on phenotypic trait values in related organisms. For this reason, comparative macroevolutionary studies usually begin with an inferred phylogeny that describes…
In this article, we review the different models and methods to understand and estimate correlated evolution within the same genome, individual or species. We describe correlated evolution among traits, among genetic components and finally…
Post-genomic research deals with challenging problems in screening genomes of organisms for particular functions or potential for being the targets of genetic engineering for desirable biological features. 'Phenotyping' of wild type and…
Inferring concerted changes among biological traits along an evolutionary history remains an important yet challenging problem. Besides adjusting for spurious correlation induced from the shared history, the task also requires sufficient…
Stochastic models of diffusion with excluded-volume effects are used to model many biological and physical systems at a discrete level. The average properties of the population may be described by a continuum model based on partial…
We introduce a model for the evolution of species triggered by generation of novel features and exhaustive combination with other available traits. Under the assumption that innovations are rare, we obtain a bursty branching process of…