Related papers: Coalescent results for diploid exchangeable popula…
Coalescent models of evolution account for incomplete lineage sorting by specifying a species tree parameter which determines a distribution on gene trees. It has been shown that the unrooted topology of the species tree parameter of the…
We present a sequential Monte Carlo sampler for coalescent based Bayesian hierarchical clustering. The model is appropriate for multivariate non-\iid data and our approach offers a substantial reduction in computational cost when compared…
The genealogy at a single locus of a constant size $N$ population in equilibrium is given by the well-known Kingman's coalescent. When considering multiple loci under recombination, the ancestral recombination graph encodes the genealogies…
Expansions are provided for the moments of the number of collisions $X_n$ in the $\beta(2,b)$-coalescent restricted to the set $\{1,...,n\}$. We verify that $X_n/\mathbb{E}X_n$ converges almost surely to one and that $X_n$, properly…
We establish convergence to the Kingman coalescent for a class of age-structured population models with time-constant population size. Time is discrete with unit called a year. Offspring numbers in a year may depend on mother's age.
A well-established model for the genealogy of a large population in equilibrium is Kingman's coalescent. For the population together with its genealogy evolving in time, this gives rise to a time-stationary tree-valued process. We study the…
We introduce and analyze a novel type of coalescent processes called cross-multiplicative coalescent that models a system with two types of particles, $A$ and $B$. The bonds are formed only between the pairs of particles of opposite types…
Study sample sizes in human genetics are growing rapidly, and in due course it will become routine to analyze samples with hundreds of thousands if not millions of individuals. In addition to posing computational challenges, such large…
The Yule model and the coalescent model are two neutral stochastic models for generating trees in phylogenetics and population genetics, respectively. Although these models are quite different, they lead to identical distributions…
We consider a dynamic metapopulation involving one large population of size N surrounded by colonies of size \varepsilon_NN, usually called peripheral isolates in ecology, where N\to\infty and \varepsilon_N\to 0 in such a way that…
The multi-species coalescent provides an elegant theoretical framework for estimating species trees and species demographics from genetic markers. Practical applications of the multi-species coalescent model are, however, limited by the…
The two-parent reproduction model of Derrida and Peliti is simulated on a rugged fitness landscape. Fixed fitness values for each possible genotype are assigned randomly, with all fit individuals having the same probability of reproduction.…
We define a new class of $\Xi$-coalescents characterized by a possibly infinite measure over the non negative integers. We call them symmetric coalescents since they are the unique family of exchangeable coalescents satisfying a symmetry…
A long genomic segment inherited by a pair of individuals from a single, recent common ancestor is said to be identical-by-descent (IBD). Shared IBD segments have numerous applications in genetics, from demographic inference to phasing,…
This paper develops mathematical models describing the evolutionary dynamics of both asexually and sexually reproducing populations of diploid unicellular organisms. We consider two forms of genome organization. In one case, we assume that…
A two-parameter family of exchangeable partitions with a simple updating rule is introduced. The partition is identified with a randomized version of a standard symmetric Dirichlet species-sampling model with finitely many types. A…
Galaxy populations at different cosmic epochs are often linked together by comoving cumulative number density in observational studies. Many theoretical works, however, have shown that the number densities of tracked galaxy populations…
We propose a class of evolutionary models that involves an arbitrary exchangeable process as the breeding process and different selection schemes. In those models, a new genome is born according to the breeding process, and then a genome is…
We present a quantitative, multi-scale coarse-grained model of DNA coated colloids. The parameters of this model are transferable and are solely based on experimental data. As a test case, we focus on nano-sized colloids carrying…
Consider a population evolving as a discrete-time supercritical multi-type Galton--Watson process. Suppose we run the process for $T$ generations, then sample $k$ individuals uniformly at generation $T$ and trace their genealogy backwards…