Related papers: Stochastic evolution and multifractal classificati…
Phylogenetic networks extend phylogenetic trees to allow for modeling reticulate evolutionary processes such as hybridization. They take the shape of a rooted, directed, acyclic graph, and when parameterized with evolutionary parameters,…
Modelling stochastic systems has many important applications. Normal form coordinate transforms are a powerful way to untangle interesting long term macroscale dynamics from detailed microscale dynamics. We explore such coordinate…
We propose a new procedure to monitor and forecast the onset of transitions in high dimensional complex systems. We describe our procedure by an application to the Tangled Nature model of evolutionary ecology. The quasi-stable…
In this paper we introduce the phylogenetic scan test (PhyloScan) for investigating cross-group differences in microbiome compositions using the Dirichlet-tree multinomial (DTM) model. DTM models the microbiome data through a cascade of…
Models of random phylogenetic networks have been used since the inception of the field, but the introduction and rigorous study of mathematically tractable models is a much more recent topic that has gained momentum in the last 5 years.…
A number of methods have been developed to infer differential rates of species diversification through time and among clades using time-calibrated phylogenetic trees. However, we lack a general framework that can delineate and quantify…
As an alternative to parsimony analyses, stochastic models have been proposed (Lewis, 2001), (Nylander, et al., 2004) for morphological characters, so that maximum likelihood or Bayesian analyses may be used for phylogenetic inference. A…
Populations of isogenic embryonic stem cells or clonal bacteria often exhibit extensive phenotypic heterogeneity which arises from stochastic intrinsic dynamics of cells. The internal state of the cell can be transmitted epigenetically in…
We survey results on the description of stochastically evolving genealogies of populations and marked genealogies of multitype populations or spatial populations via tree-valued Markov processes on (marked) ultrametric measure spaces. In…
Implementing Bayesian variable selection for linear Gaussian regression models for analysing high dimensional data sets is of current interest in many fields. In order to make such analysis operational, we propose a new sampling algorithm…
In the idealized Morgan model of crossover, we study the probability distributions of shared DNA (identical by descent) between individuals having a wide range of relationships (not just lineal descendants), especially cases for which…
In this paper we study the dynamics of stochastic microorganism flocculation models. Given the strong influence of environmental and seasonal fluctuations that are present in these models, we propose a stochastic model that includes…
The functions of proteins and RNAs are determined by a myriad of interactions between their constituent residues, but most quantitative models of how molecular phenotype depends on genotype must approximate this by simple additive effects.…
We study the probabilities of evolution based on random mutations and natural selection. We conclude that evolution to multicellular eukaryots, or even prokaryots, is unlikely to be the result of only random mutations. Complex organisms…
Biological living systems in general exhibit complex and diverse dynamics. The latter, in particular, is essential, since diversification increases the odds of survival of an organism while reducing the risk of extinction of the population.…
Comparisons of single-cell RNA sequencing (scRNA-seq) data across species can reveal links between cellular gene expression and the evolution of cell functions, features, and phenotypes. These comparisons invoke evolutionary histories, as…
Probability modelling for DNA sequence evolution is well established and provides a rich framework for understanding genetic variation between samples of individuals from one or more populations. We show that both classical and more recent…
This thesis develops and expands upon known techniques of mathematical physics relevant to the analysis of the popular Markov model of phylogenetic trees required in biology to reconstruct the evolutionary relationships of taxonomic units…
We take up the challenge of designing realistic computational models of large interacting cell populations. The goal is essentially to bring Gillespie's celebrated stochastic methodology to the level of an interacting population of cells.…
Plant breeding programs use data obtained from multi-environment selection experiments to produce improved varieties with the ultimate aim of maintaining high levels of genetic gain. Selection accuracy can be improved with the use of…