Related papers: Reproduction time statistics and segregation patte…
We investigate a continuous time, probability measure-valued dynamical system that describes the process of mutation-selection balance in a context where the population is infinite, there may be infinitely many loci, and there are weak…
We consider a simple discrete-time Markov chain with values in $[0,\infty)^{Z^d}$. The Markov chain describes various interesting examples such as oriented percolation, directed polymers in random environment, time discretizations of binary…
Biological systems are typically highly open, non-equilibrium systems that are very challenging to understand from a statistical mechanics perspective. While statistical treatments of evolutionary biological systems have a long and rich…
We represent a process of learning by using bit strings, where 1-bits represent the knowledge acquired by individuals. Two ways of learning are considered: individual learning by trial-and-error; and social learning by copying knowledge…
In the face of an infectious disease, a key epidemiological measure is the basic reproduction number, which quantifies the average secondary infections caused by a single case in a susceptible population. In practice, the effective…
We study how environmental stochasticity influences the long-term population size in certain one- and two-species models. The difficulty is that even when one can prove that there is persistence, it is usually impossible to say anything…
To maintain a constant cell size, dividing cells have to coordinate cell cycle events with cell growth. This coordination has for long been supposed to rely on the existence of size thresholds determining cell cycle progression [1]. In…
Understanding the formation and evolution of young star clusters requires quantitative statistical measures of their structure. We investigate the structures of observed and modelled star-forming clusters. By considering the different…
Stochastic discrete-time SIS and SIR models of endemic diseases are introduced and analyzed. For the deterministic, mean-field model, the basic reproductive number $R_0$ determines their global dynamics. If $R_0\le 1$, then the frequency of…
We give a closed form of the discrete-time evolution of a recombination transformation in population genetics. This decomposition allows to define a Markov chain in a natural way. We describe the geometric decay rate to the limit…
We consider stochastic growth models for populations organized in colonies and subject to uniform catastrophes. To assess population viability, we analyze scenarios in which individuals adopt dispersion strategies after catastrophic events.…
We study a class of evolution models, where the breeding process involves an arbitrary exchangeable process, allowing for mutations to appear. The population size $n$ is fixed, hence after breeding, selection is applied. Individuals are…
A general multi-type population model is considered, where individuals live and reproduce according to their age and type, but also under the influence of the size and composition of the entire population. We describe the dynamics of the…
We develop a linear one-sex dynamical model of human population reproduction through marriage. In our model, a woman may marry and divorce multiple times; however, only women who are currently married are assumed to bear children. The…
Generalized Polya urn models have been used to model the establishment dynamics of a small founding population consisting of k different genotypes or strategies. As population sizes get large, these population processes are…
It has been shown that differences in fecundity variance can influence the probability of invasion of a genotype in a population, i.e. a genotype with lower variance in offspring number can be favored in finite populations even if it has a…
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…
Evolutionary graph theory has grown to be an area of intense study. Despite the amount of interest in the field, it seems to have grown separate from other subfields of population genetics and evolution. In the current work I introduce the…
We provide an asymptotic analysis of a nonlinear integro-differential equation describing the evolutionary dynamics of a population which reproduces sexually and which is subject to selection and competition. The sexual reproduction is…
We show that the basic reproduction number of an SIS patch model with standard incidence is either strictly decreasing and strictly convex with respect to the diffusion coefficient of infected subpopulation if the patch reproduction numbers…