Related papers: Phylogenetic confidence intervals for the optimal …
The Ornstein-Uhlenbeck (OU) process plays a major role in the analysis of the evolution of phenotypic traits along phylogenies. The standard OU process includes drift and stabilizing selection and assumes that species evolve independently.…
Discovering evolutionary traits that are heritable across species on the tree of life (also referred to as a phylogenetic tree) is of great interest to biologists to understand how organisms diversify and evolve. However, the measurement of…
Phylogenetic comparative methods for real-valued traits usually make use of stochastic process whose trajectories are continuous. This is despite biological intuition that evolution is rather punctuated than gradual. On the other hand,…
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…
This paper focuses on the maximum speed at which biological evolution can occur. I derive inequalities that limit the rate of evolutionary processes driven by natural selection, mutations, or genetic drift. These \emph{rate limits} link the…
An explicit bound is given for the Kolmogorov distance between a mixture of normal distributions and a normal distribution with properly chosen parameter values. A random variable X has a mixture of normal distributions if its conditional…
Predicting the adaptation of populations to a changing environment is crucial to assess the impact of human activities on biodiversity. Many theoretical studies have tackled this issue by modeling the evolution of quantitative traits…
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…
Understanding how stochastic and non-linear deterministic processes interact is a major challenge in population dynamics theory. After a short review, we introduce a stochastic individual-centered particle model to describe the evolution in…
In a phylogenetic tree, we often don't have information about the time a speciation event (inner node) occured. Under a neutral model for speciation, I develop fast algorithms for calculating the probability that an inner node i is the k-th…
We consider the problem of estimating the expected value of information (the knowledge gradient) for Bayesian learning problems where the belief model is nonlinear in the parameters. Our goal is to maximize some metric, while simultaneously…
Dynamic programming approaches have long been applied to fit models of univariate and multivariate trait evolution on phylogenetic trees for discrete and continuous traits, and more recently adapted to phylogenetic networks with…
The rates-across-sites assumption in phylogenetic inference posits that the rate matrix governing the Markovian evolution of a character on an edge of the putative phylogenetic tree is the product of a character-specific scale factor and a…
This work develops formal statistical inference procedures for machine learning ensemble methods. Ensemble methods based on bootstrapping, such as bagging and random forests, have improved the predictive accuracy of individual trees, but…
Many biological systems regulate phenotypic heterogeneity as a fitness-maximising strategy in uncertain and dynamic environments. Analysis of such strategies is typically confined both to a discrete set of environmental conditions, and to a…
Species evolution is essentially a random process of interaction between biological populations and their environments. As a result, some physical parameters in evolution models are subject to statistical fluctuations. In this paper, two…
In this paper I address the question - how large is a phylogenetic sample I propose a definition of a phylogenetic effective sample size for Brownian motion and Ornstein-Uhlenbeck processes - the regression effective sample size. I discuss…
Modern biological techniques enable very dense genetic sampling of unfolding evolutionary histories, and thus frequently sample some genotypes multiple times. This motivates strategies to incorporate genotype abundance information in…
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…
Recent work on mutation-selection models has revealed that, under specific assumptions on the fitness function and the mutation rates, asymptotic estimates for the leading eigenvalue of the mutation-reproduction matrix may be obtained…