Related papers: Understanding clustering in type space using field…
This chapter reviews some aspects of the theory of age-structured models of populations with finite maximum age. We formulate both the renewal equation for the birth rate and the partial differential equation for the age density, and show…
Genetic data are often used to infer demographic history and changes or detect genes under selection. Inferential methods are commonly based on models making various strong assumptions: demography and population structures are supposed…
We examine birth--death processes with state dependent transition probabilities and at least one absorbing boundary. In evolution, this describes selection acting on two different types in a finite population where reproductive events occur…
The cell cycle duration is a variable cellular phenotype that underlies long-term population growth and age structures. By analyzing the stationary solutions of a branching process with heritable cell division times, we demonstrate…
Surnames and nonrecombining alleles are inherited from a single parent in a highly similar way. A simple birth-death model with mutations can accurately describe this process. Exponentially growing and constant populations are investigated,…
An equation describing the evolution of phenotypic distribution is derived using methods developed in statistical physics. The equation is solved by using the singular perturbation method, and assuming that the number of bases in the…
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…
Consider a population where individuals give birth at constant rate during their lifetimes to i.i.d. copies of themselves. Individuals bear clonally inherited types, but (neutral) mutations may happen at the birth events. The smallest…
We consider inhomogeneous branching diffusions on an infinite domain of $\mathbb{R}^d$. The first aim of this article is to derive a general criterium under which the size process (number of particles) and the genealogy of the particle…
A multi-type neutral Cannings population model with mutation and fixed subpopulation sizes is analyzed. Under appropriate conditions, as all subpopulation sizes tend to infinity, the ancestral process, properly time-scaled, converges to a…
We investigate the kinetics of many-species systems with aggregation of similar species clusters and annihilation of opposite species clusters. We find that the interplay between aggregation and annihilation leads to rich kinetic behaviors…
A biologically motivated individual-based framework for evolution in network-structured populations is developed that can accommodate eco-evolutionary dynamics. This framework is used to construct a network birth and death model. The…
We propose a stochastic model for evolution through mutation and natural selection of a population that evolves on a $\bbT_d^+$ tree. We think of this model as a way of describing the evolution fitness landscape of a population. We obtain…
We consider an individual based model of phenotypic evolution in hermaphroditic populations which includes random and assortative mating of individuals. By increasing the number of individuals to infinity we obtain a nonlinear transport…
A Feller's Brownian motion is a diffusion process on the half-line with general boundary behavior at the origin, described by four parameters. A birth-death process, on the other hand, is a continuous-time Markov chain on the nonnegative…
We study the large scale behaviour of a population consisting of two types which evolve in dimension d = 1, 2 according to a spatial Lambda- Fleming-Viot process subject to random time-independent selection. If one of the two types is rare…
Starting from the well-known field theory for directed percolation, we describe an evolving population, near extinction, in an environment with its own nontrivial spatio-temporal dynamics. Here, we consider the special case where the…
Density dependence is important in the ecology and evolution of microbial and cancer cells. Typically, we can only measure net growth rates, but the underlying density-dependent mechanisms that give rise to the observed dynamics can…
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…
We study the evolution of the network properties of a populated network embedded in a genotype space characterised by either a low or a high number of potential links, with particular emphasis on the connectivity and clustering. Evolution…