Related papers: Karlin-McGregor mutational occupancy problem revis…
Estimating the number $n$ of unseen species from a $k-$sample displaying only $p\leq k$ distinct sampled species has received attention for long. It requires a model of species abundance together with a sampling model. We start with a…
In this paper we propose a Moran model that describes the population dynamics of two types: While the first type has a selective advantage during reproduction, the second type can avoid replacement during reproduction with some positive…
We present a version of the classical Moran model, in which mutations are taken into account; the possibility of mutations was introduced by Moran in his seminal paper, but it is more often overlooked in discussing the Moran model. For this…
Temporal environmental variations are ubiquitous in nature, yet most of the theoretical works in population genetics and evolution assume fixed environment. Here we analyze the effect of variations in carrying capacity on the fate of a…
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,…
Evolution occurs in populations of reproducing individuals. In stochastic descriptions of evolutionary dynamics, such as the Moran process, individuals are chosen randomly for birth and for death. If the same type is chosen for both steps,…
We consider a general, neutral, dynamical model of biodiversity. Individuals have i.i.d. lifetime durations, which are not necessarily exponentially distributed, and each individual gives birth independently at constant rate \lambda. We…
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…
We consider a periodic extension of the classical Kingman non-linear model (Kingman, 1978) for the balance between selection and mutation in a large population. In the original model, the fitness distribution of the population is modeled by…
We first provide some properties of the Mellin transform of nonnegative random variables, such that monotonicity, injectivity and effect of size biasing. Convergence of Mellin transforms is also entirely formalized through convergence in…
Consider a population of $N$ individuals, each of them carrying a type in $\mathbb N_0$. The population evolves according to a Moran dynamics with selection and mutation, where an individual of type $k$ has the same selective advantage over…
Clonal interference, competition between multiple co-occurring beneficial mutations, has a major role in adaptation of asexual populations. We provide a simple individual based stochastic model of clonal interference taking into account a…
The Moran process is a classic stochastic process that models the rise and takeover of novel traits in network-structured populations. In biological terms, a set of mutants, each with fitness $m\in(0,\infty)$ invade a population of…
In this article, a biallelic reversible mutation model with linear and quadratic selection is analyzed. The approach reconnects to one proposed by Kimura ( Possibility of extensive neutral evolution under stabilizing selection with special…
In this paper a new transformation of occupancy models, called merging, is introduced. In particular, it will be studied the effect of merging on a class of occupancy models that was recently introduced in Collet et al (2013). These results…
McNamara and Dall (2011) identified novel relationships between the abundance of a species in different environments, the temporal properties of environmental change, and selection for or against dispersal. Here, the mathematics underlying…
In evolutionary games the fitness of individuals is not constant but depends on the relative abundance of the various strategies in the population. Here we study general games among n strategies in populations of large but finite size. We…
We consider a Moran model with two allelic types, mutation and selection. In this work, we study the behaviour of the proportion of fit individuals when the size of the population tends to infinity, without any rescaling of parameters or…
This paper collects facts about the number of occupied boxes in the classical balls-in-boxes occupancy scheme with infinitely many positive frequencies: equivalently, about the number of species represented in samples from populations with…
Kingman's model describes the evolution of a one-locus haploid population of infinite size and discrete generations under the competition of selection and mutation. A random generalisation has been made in a previous paper which assumes all…