Related papers: Lambda-lookdown model with selection
Abstract dynamic programming models are used to analyze $\lambda$-policy iteration with randomization algorithms. Particularly, contractive models with infinite policies are considered and it is shown that well-posedness of the…
We exhibit a stochastic discrete time model that has exactly the Eigen model as its deterministic continuous limit. Such model can be divided into two phases: reproduction followed by neutral selection. This result suggests that Eigen model…
Consider a population of fixed size that evolves over time. At each time, the genealogical structure of the population can be described by a coalescent tree whose branches are traced back to the most recent common ancestor of the…
We consider a discrete-time stochastic growth model on the $d$-dimensional lattice with non-negative real numbers as possible values per site. The growth model describes various interesting examples such as oriented site/bond percolation,…
The first chapter concerns monotype population models. We first study general birth and death processes and we give non-explosion and extinction criteria, moment computations and a pathwise representation. We then show how different scales…
We consider the spatial Lambda-Fleming-Viot process model for frequencies of genetic types in a population living in R^d, in the special case in which there are just two types of individual, labelled 0 and 1. At time zero, everyone in 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 review the statistical properties of the genealogies of a few models of evolution. In the asexual case, selection leads to coalescence times which grow logarithmically with the size of the population in contrast with the linear growth of…
We define a Markov process in a forward population model with backward genealogy given by the $\Lambda$-coalescent. This Markov process, called the fixation line, is related to the block counting process through its hitting times. Two…
Non-probability samples become increasingly popular in survey statistics but may suffer from selection biases that limit the generalizability of results to the target population. We consider integrating a non-probability sample with a…
We investigate the infinitely many demes limit of the genealogy of a sample of individuals from a subdivided population subject to sporadic mass extinction events. By exploiting a separation of timescales property of Wright's island model,…
We consider a continuous-time Bienaym\'e-Galton-Watson process with logistic competition in a regime of weak competition, or equivalently of a large carrying capacity. Individuals reproduce at random times independently of each other but…
We study a continuous-time dynamical system that models the evolving distribution of genotypes in an infinite population where genomes may have infinitely many or even a continuum of loci, mutations accumulate along lineages without…
We consider a stochastic model, called the replicator coalescent, describing a system of blocks of $k$ different types which undergo pairwise mergers at rates depending on the block types: with rate $C_{i,j}$ blocks of type $i$ and $j$…
We consider the genealogy of a sample of individuals taken from a spatially structured population when the variance of the offspring distribution is relatively large. The space is structured into discrete sites of a graph G. If the…
Full likelihood inference under Kingman's coalescent is a computationally challenging problem to which importance sampling (IS) and the product of approximate conditionals (PAC) method have been applied successfully. Both methods can be…
This article examines an infinite-dimensional linear control system that describes population models structured by age, size, and spatial position. The control is localized with respect to space, age and size; an estimate of the time…
We consider a class of density-dependent branching processes which generalises exponential, logistic and Gompertz growth. A population begins with a single individual, grows exponentially initially, and then growth may slow down as the…
We introduce the following model for the evolution of a population. At every discrete time $j\geq 0$ exactly one individual is introduced in the population and is assigned a death probability $c_j$ sampled from $C$, a fixed probability…
Traditionally, population models distinguish individuals on the basis of their current state. Given a distribution, a discrete time model then specifies (precisely in deterministic models, probabilistically in stochastic models) the…