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Developmental bias plays a major role in phenotypic evolution. Some researchers have argued that phenotypes, regulated by development, can only evolve along restricted trajectory under certain scenarios, such as the case for mammalian molar…

We use a classical combinatorial inequality to establish a Markov inequality for multivariate binary Markov processes on trees. We then apply this result, alongside with the FKG inequality, to compare the expected loss of biodiversity under…

We consider the evolution of populations under the joint action of mutation and differential reproduction, or selection. The population is modelled as a finite-type Markov branching process in continuous time, and the associated…

Understanding the processes that give rise to quantitative measurements associated with molecular sequence data remains an important issue in statistical phylogenetics. Examples of such measurements include geographic coordinates in the…

This article introduces a flexible and adaptive nonparametric method for estimating the association between multiple covariates and power spectra of multiple time series. The proposed approach uses a Bayesian sum of trees model to capture…

During bouts of evolutionary diversification, such as adaptive radiations, the emerging species cluster around different locations in phenotype space, How such multimodal patterns in phenotype space can emerge from a single ancestral…

Hierarchical autocorrelation in the error term of linear models arises when sampling units are related to each other according to a tree. The residual covariance is parametrized using the tree-distance between sampling units. When…

In this article we propose a novel method to estimate the frequency distribution of linguistic variables while controlling for statistical non-independence due to shared ancestry. Unlike previous approaches, our technique uses all available…

Many biological characteristics of evolutionary interest are not scalar variables but continuous functions. Given a dataset of function-valued traits generated by evolution, we develop a practical statistical approach to infer ancestral…

Correlations between two variables of a high-dimensional system can be indicative of an underlying interaction, but can also result from indirect effects. Inverse Ising inference is a method to distinguish one from the other. Essentially,…

We consider an aggregation model for two interacting species. The coupling between the species is via their velocities, that incorporate self- and cross-interactions. Our main interest is categorizing the possible steady states of the…

High-dimensional phenotypes hold promise for richer findings in association studies, but testing of several phenotype traits aggravates the grand challenge of association studies, that of multiple testing. Several methods have recently been…

In this paper, we study an integro-differential equation which describes the evolutionary dynamics of a population structured by a phenotypic trait. This population undergoes asexual reproduction, competition, selection, and mutation. We…

The varying-coefficient model is a strong tool for the modelling of interactions in generalized regression. It is easy to apply if both the variables that are modified as well as the effect modifiers are known. However, in general one has a…

In this paper we investigate the geometry of a discrete Bayesian network whose graph is a tree all of whose variables are binary and the only observed variables are those labeling its leaves. We provide the full geometric description of…

This thesis concerns multivariate phylogenetic comparative methods. We investigate two aspects of them. The first is the bias caused by measurement error in regression studies of comparative data. We calculate the formula for the bias and…

The phylogenetic effective sample size is a parameter that has as its goal the quantification of the amount of independent signal in a phylogenetically correlated sample. It was studied for Brownian motion and Ornstein-Uhlenbeck models of…

We derive a Poisson random field model for population site polymorphisms differences within and between two species that share a relatively recent common ancestor. The model can be either equilibrium or time inhomogeneous. We first consider…

An important problem in evolutionary genomics is to investigate whether a certain trait measured on each sample is associated with the sample phylogenetic tree. The phylogenetic tree represents the shared evolutionary history of the samples…

Phylogenetic trees describe the relationships between species in the evolutionary process, and provide information about the rates of diversification. To understand the mechanisms behind macroevolution, we consider a class of multitype…