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Inferring dependencies between complex biological traits while accounting for evolutionary relationships between specimens is of great scientific interest yet remains infeasible when trait and specimen counts grow large. The…
Many biological characteristics of evolutionary interest are not scalar variables but continuous functions. Here we use phylogenetic Gaussian process regression to model the evolution of simulated function-valued traits. Given…
An ongoing debate in evolutionary biology is whether phenotypic change occurs predominantly around the time of speciation or whether it instead accumulates gradually over time. In this work I propose a general framework incorporating both…
We introduce a simple and extendable coevolution model for the analysis of longitudinal network and nodal attribute data. The model features parameters that describe three phenomena: homophily, contagion and autocorrelation of the network…
Phylogenetics uses alignments of molecular sequence data to learn about evolutionary trees relating species. Along branches, sequence evolution is modelled using a continuous-time Markov process characterised by an instantaneous rate…
Understanding the evolution of binary traits, which affects the birth and survival of species and also the rate of molecular evolution, remains challenging. A typical example is the evolution of mating systems in plant species. In this…
Reconstructing the ancestral state of a group of species helps answer many important questions in evolutionary biology. Therefore, it is crucial to understand when we can estimate the ancestral state accurately. Previous works provide a…
Inferences about the evolution of continuous traits based on reconstruction of ancestral states has often been considered more error-prone than analysis of independent contrasts. Here we show that both methods in fact yield identical…
By introducing the notions of living and dead nodes a new model of random tree evolution with continuous time parameter has been constructed. It is assumed that two random variables, the lifetime and the offspring number of living nodes…
A mechanism of sympatric speciation is presented based on the interaction-induced developmental plasticity of phenotypes. First, phenotypes of individuals with identical genotypes split into a few groups, according to instability in the…
Stochastic models of evolution (Markov random fields on trivalent trees) generally assume that different characters (different runs of the stochastic process) are independent and identically distributed. In this paper we take the first…
Phylogenetic comparative analysis is an approach to inferring evolutionary process from a combination of phylogenetic and phenotypic data. The last few years have seen increasingly sophisticated models employed in the evaluation of more and…
A useful property of independent samples is that their correlation remains the same after applying marginal transforms. This invariance property plays a fundamental role in statistical inference, but does not hold in general for dependent…
We consider an individual based model of phenotypic evolution in hermaphroditic populations which includes random and assortative mating of individuals. By increasing the number of individuals to infinity we obtain a nonlinear transport…
We discuss several connections between discrete and continuous random trees. In the discrete setting, we focus on Galton-Watson trees under various conditionings. In particular, we present a simple approach to Aldous' theorem giving the…
Complex interactions between genes or proteins contribute a substantial part to phenotypic evolution. Here we develop an evolutionarily grounded method for the cross-species analysis of interaction networks by {\em alignment}, which maps…
In a deterministic or random tree, a notion of ancestral diversity can be defined as follows. Sample independently $n$ groups of $k$ leaves and count the number $N_n(k)$ of distinct most recent common ancestors of each of the groups. As $n$…
We introduce a biologically natural, mathematically tractable model of random phylogenetic network to describe evolution in the presence of hybridization. One of the features of this model is that the hybridization rate of the lineages…
We extend our study of a simple model of biological coevolution to its statistical properties. Staring with a complete description in terms of a master equation, we provide its relation to the deterministic evolution equations used in…
Recognition of evolutionary units (species, populations) requires integrating several kinds of data such as genetic or phenotypic markers or spatial information, in order to get a comprehensive view concerning the differentiation of the…