Related papers: Mutation, selection, and ancestry in branching mod…
We consider two versions of stochastic population models with mutation and selection. The first approach relies on a multitype branching process; here, individuals reproduce and change type (i.e., mutate) independently of each other,…
Evolutionary branching is analysed in a stochastic, individual-based population model under mutation and selection. In such models, the common assumption is that individual reproduction and life career are characterised by values of a…
We show how concepts from statistical physics, such as order parameter, thermodynamic limit, and quantum phase transition, translate into biological concepts in mutation-selection models for sequence evolution and can be used there. The…
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 consider a branching model in discrete time where each individual has a trait in some general state space. Both the reproduction law and the trait inherited by the offsprings may depend on the trait of the mother and the environment. We…
We study a universal object for the genealogy of a sample in populations with mutations: the critical birth-death process with Poissonian mutations, conditioned on its population size at a fixed time horizon. We show how this process arises…
The forest of mutations associated to a multitype branching forest is obtained by merging together all vertices of its clusters and by preserving connections between them. We first show that the forest of mutations of any mulitype branching…
In this work we model the dynamics of a population that evolves as a continuous time branching process with a trait structure and ecological interactions in form of mutations and competition between individuals. We generalize existing…
A discrete time branching process where the offspring distribution is generation-dependent, and the number of reproductive individuals is controlled by a random mechanism is considered. This model is a Markov chain but, in general, the…
We are interested in modelling Darwinian evolution, resulting from the interplay of phenotypic variation and natural selection through ecological interactions. Our models are rooted in the microscopic, stochastic description of a population…
We consider the discrete-time migration-recombination equation, a deterministic, nonlinear dynamical system that describes the evolution of the genetic type distribution of a population evolving under migration and recombination in a law of…
We are interested in the study of models describing the evolution of a polymorphic population with mutation and selection in the specific scales of the biological framework of adaptive dynamics. The population size is assumed to be large…
We reconsider the deterministic haploid mutation-selection equation with two types. This is an ordinary differential equation that describes the type distribution (forward in time) in a population of infinite size. This paper establishes…
We consider the Moran model of population genetics with two types, mutation, and selection, and investigate the line of descent of a randomly-sampled individual from a contemporary population. We trace this ancestral line back into the…
A probability model is presented for the dynamics of mutation-selection balance in a haploid infinite-population infinite-sites setting sufficiently general to cover mutation-driven changes in full age-specific demographic schedules. The…
We study the continuous-time evolution of the recombination equation of population genetics. This evolution is given by a differential equation that acts on a product probability space, and its solution can be described by a Markov chain on…
In this paper, we review recent results of ours concerning branching processes with general lifetimes and neutral mutations, under the infinitely many alleles model, where mutations can occur either at birth of individuals or at a constant…
We develop a continuous mathematical model of population dynamics that describes the sequential emergence of new genotypes under limited resources. The framework models genotype density as a nonlinear flow in mutation space, combining…
We investigate two stochastic models of a growing population subject to selection and mutation. In our models each individual carries a fitness which determines its mean offspring number. Many of these offspring inherit their parent's…
A population genetics model based on a multitype branching process, or equivalently a Galton-Watson branching process for multiple alleles, is pre- sented. The diffusion limit forward Kolmogorov equation is derived for the case of neutral…