Related papers: Muller's ratchet with overlapping generations
Genetic drift is stochastic fluctuations of alleles frequencies in a population due to sampling effects. We consider a model of drift in an equilibrium population, with high mutation rates: few functional mutations per generation. Such…
We consider a stochastic model of population dynamics where each individual is characterised by a trait in {0,1,...,L} and has a natural reproduction rate, a logistic death rate due to age or competition and a probability of mutation…
We investigate the model of "reversible ratchet" with interacting particles, introduced by us earlier [Europhys. Lett. 84, 50009 (2008)]. We further clarify the effect of efficiency enhancement due to interaction and show that it is of…
Recent interest in human dynamics has stimulated the investigation of the stochastic processes that explain human behaviour in various contexts, such as mobile phone networks and social media. In this paper, we extend the stochastic…
We consider two population models subject to the evolutionary forces of selection and mutation, the Moran model and the $\Lambda$-Wright-Fisher model. In such models the block counting process traces back the number of potential ancestors…
Many mathematical models of evolution assume that all individuals experience the same environment. Here, we study the Moran process in heterogeneous environments. The population is of finite size with two competing types, which are exposed…
The multi-type Moran process is an evolutionary process on a connected graph $G$ in which each vertex has one of $k$ types and, in each step, a vertex $v$ is chosen to reproduce its type to one of its neighbours. The probability of a vertex…
The bit-string model of biological aging is used to simulate the catastrophic senescence of Pacific Salmon. We have shown that reproduction occuring only once and at a fixed age is the only ingredient needed to explain the catastrophic…
A simple analytical framework to study the molecular quasispecies evolution of finite populations is proposed, in which the population is assumed to be a random combination of the constiyuent molecules in each generation,i.e., linkage…
Although mutations drive the evolutionary process, the rates at which the mutations occur are themselves subject to evolutionary forces. Our purpose here is to understand the role of selection and random genetic drift in the evolution of…
Understanding posterior contraction behavior in Bayesian hierarchical models is of fundamental importance, but progress in this question is relatively sparse in comparison to the theory of density estimation. In this paper, we study two…
We consider a multi-colony version of the Wright-Fisher model with seed-bank that was recently introduced by Blath et al. Individuals live in colonies and change type via resampling and mutation. Each colony contains a seed-bank that acts…
We consider the extension of the `Moran effect', where correlated noise generates synchrony between isolated single species populations, to the study of synchrony between populations embedded in multi-species communities. In laboratory…
The evolution of dispersal is a classical question in evolutionary ecology, which has been widely studied with several mathematical models. The main question is to define the fittest dispersal rate for a population in a bounded domain, and,…
Stochastic models of sequential mutation acquisition are widely used to quantify cancer and bacterial evolution. Across manifold scenarios, recurrent research questions are: how many cells are there with $n$ alterations, and how long will…
The coevolutionary dynamics in finite populations currently is investigated in a wide range of disciplines, as chemical catalysis, biological evolution, social and economic systems. The dynamics of those systems can be formulated within the…
We define truncated Mellin moments of parton distributions by restricting the integration range over the Bjorken variable to the experimentally accessible subset x_0 < x < 1 of the allowed kinematic range 0 < x < 1. We derive the evolution…
The goal of this paper is to develop a theory of graphon-valued stochastic processes, and to construct and analyse a natural class of such processes arising from population genetics. We consider finite populations where individuals change…
Motivated by the wide range of known self-replicating systems, some far from genetics, we study a system composed by individuals having an internal dynamics with many possible states that are partially stable, with varying mutation rates.…
We establish a genealogical framework for an existing analytical moment duality between a Wright--Fisher type SDE and a counting process with interaction. To achieve this, we construct a finite-population Moran model featuring interactive…