Related papers: Hatchery-induced transition of the effective size …
Let $W_1,\ldots,W_N$ be a sample of $\mathrm{Pareto}(\alpha)$ random variables normalized by their sum, such that $\sum_i W_i=1$. The $W_i$ may represent the weights of valleys in a spin glass (if $0<\alpha<1$), or the frequency of…
In many biological processes, the size of a population changes stochastically with time, and recent work in the context of cancer and bacterial growth have focused on the situation when the mean population size grows exponentially. Here,…
This paper is concerned with exploring the microscopic basis for the discrete versions of the standard replicator equation and the adjusted replicator equation. To this end, we introduce frequency-dependent selection -- as a result of…
Recruitment is calculated by summing random offspring-numbers entering the population, where the number of summands (i.e. spawning population size) is also a random process. A priori, it is not clear that individual reproductive variability…
A strong demographic Allee effect in which the expected population growth rate is negative below a certain critical population size can cause high extinction probabilities in small introduced populations. However, many species are…
The drift-barrier hypothesis states that random genetic drift constrains the refinement of a phenotype under natural selection. The influence of effective population size and the genome-wide deleterious mutation rate were studied…
A phenomenon that strongly influences the demography of small introduced populations and thereby potentially their genetic diversity is the Allee effect, a reduction in population growth rates at small population sizes. We take a stochastic…
Star-shaped branching patterns of genealogies are common in marine species. High-fecundity marine populations are characterized by low ratios of effective to actual population size, which reflect high variance in reproductive success among…
The entropy rates of the Wright-Fisher process, the Moran process, and generalizations are computed and used to compare these processes and their dependence on standard evolutionary parameters. Entropy rates are measures of the variation…
We investigate the behaviour of the genealogy of a Wright-Fisher population model under the influence of a strong seed-bank effect. More precisely, we consider a simple seed-bank age distribution with two atoms, leading to either classical…
Large populations may contain numerous simultaneously segregating polymorphisms subject to natural selection. Since selection acts on individuals whose fitness depends on many loci, different loci affect each other's dynamics. This leads to…
We study the population genetics of two neutral alleles under reversible mutation in the \Lambda-processes, a population model that features a skewed offspring distribution. We describe the shape of the equilibrium allele frequency…
Although interventional studies demonstrate that preventing malaria during pregnancy can reduce the low birth weight (i.e., child's birth weight $<$ 2,500 grams) rate, it remains unknown whether natural changes in parasite transmission and…
Near the beginning of the century, Wright and Fisher devised an elegant, mathematically tractable model of gene reproduction and replacement that laid the foundation for contemporary population genetics. The Wright-Fisher model and its…
We consider a population with two types of individuals, distinguished by the resources required for reproduction: type-$0$ (small) individuals need a fractional resource unit of size $\vartheta \in (0,1)$, while type-$1$ (large) individuals…
The expected level of linkage disequilibrium (LD) in a finite ideal population at equilibrium is of relevance for many applications in population and quantitative genetics. Several recursion formulae have been proposed during the last…
Metapopulation theory for a long time has assumed dispersal to be symmetric, i.e. patches are connected through migrants dispersing bi-directionally without a preferred direction. However, for natural populations symmetry is often broken,…
The recently introduced two-parameter Poisson-Dirichlet diffusion extends the infinitely-many-neutral-alleles model, related to Kingman's distribution and to Fleming-Viot processes. The role of the additional parameter has been shown to…
I study a population model in which the reproduction rate lambda is inherited with mutation, favoring fast reproducers in the short term, but conflicting with a process that eliminates agglomerations of individuals. The model is a variant…
Random discrete distributions, say $F,$ known as species sampling models, represent a rich class of models for classification and clustering, in Bayesian statistics and machine learning. They also arise in various areas of probability and…