Related papers: Neutral Aggregation in Finite Length Genotype spac…
A massive dataset often consists of a growing number of (potentially) heterogeneous sub-populations. This paper is concerned about testing various forms of heterogeneity arising from massive data. In a general nonparametric framework, a set…
We consider an asexual population under strong selection-weak mutation conditions evolving on rugged fitness landscapes with many local fitness peaks. Unlike the previous studies in which the initial fitness of the population is assumed to…
In large populations, multiple beneficial mutations may be simultaneously spreading. In asexual populations, these mutations must either arise on the same background or compete against each other. In sexual populations, recombination can…
In this paper, we review recent results of ours concerning branching processes with general lifetimes and neutral mutations, under the infinitely many alleles model, where mutations can occur either at birth of individuals or at a constant…
In the first paper of this series, we included the effects of population genetics in the agent-based Monte Carlo code HERITAGE under the hypothesis of neutral phenotypic effects. It implied that mutations (genetic changes) had only neutral…
We consider a neutral dynamical model of biological diversity, where individuals live and reproduce independently. They have i.i.d. lifetime durations (which are not necessarily exponentially distributed) and give birth (singly) at constant…
We introduce a modified spatial $\Lambda$-Fleming-Viot process to model the ancestry of individuals in a population occupying a continuous spatial habitat divided into two areas by a sharp discontinuity of the dispersal rate and effective…
A fundamental problem in the fields of population genetics, evolution, and community ecology, is the fate of a single mutant, or invader, introduced in a finite population of wild types. For a fixed-size community of $N$ individuals, with…
The prediction of phenotypic traits using high-density genomic data has many applications such as the selection of plants and animals of commercial interest; and it is expected to play an increasing role in medical diagnostics. Statistical…
In evolutionary dynamics, a key measure of a mutant trait's success is the probability that it takes over the population given some initial mutant-appearance distribution. This "fixation probability" is difficult to compute in general, as…
Fundamental properties of macroscopic gene-mating dynamic evolutionary systems are investigated. We focus on a single locus, any number of alleles in a two-gender dioecious population, for a large class of systems within population…
We show that training of generative adversarial network (GAN) may not have good generalization properties; e.g., training may appear successful but the trained distribution may be far from target distribution in standard metrics. However,…
Game theoretic tools are utilized to analyze a one-locus continuous selection model of sex-specific meiotic drive by considering nonequivalence of the viabilities of reciprocal heterozygotes that might be noticed at an imprinted locus. The…
Aggregation-diffusion equations are foundational tools for modelling biological aggregations. Their principal use is to link the collective movement mechanisms of organisms to their emergent space use patterns in a concrete mathematical…
In the analysis of complex traits, genetic effects are frequently modelled as either fixed or random effects. Such assumptions serve as a foundation of defining heritability and relatedness using genome-wide single nucleotide polymorphism…
Environmental changes greatly influence the evolution of populations. Here, we study the dynamics of a population of two strains, one growing slightly faster than the other, competing for resources in a time-varying binary environment…
We present an individual-based model for two interacting populations diffusing on lattices in which a strong natural selection develops spontaneously. The models combine traditional local predator-prey dynamics with random walks.…
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,…
Understanding the forces shaping ecological communities is crucially important to basic science and conservation. In recent years, considerable progress was made in explaining communities using simple and general models, with neutral theory…
Our goal is to study the genetic composition of a population in which each individual has 2 parents, who contribute equally to the genome of their ospring. We use a biparental Moran model, which is characterized by its xed number N of…