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In forensic DNA calculations of relatedness of individuals and in DNA mixture analyses, two sources of uncertainty are present concerning the allele frequencies used for evaluating genotype probabilities when evaluating likelihoods. They…
The most general exclusion single species reaction-diffusion models with nearest-neighbor interactions one a one dimensional lattice are investigated, for which the evolution of full intervals are closed. Using a generating function method,…
Here we describe how some important scaling laws observed in the distribution of languages on Earth can emerge from a simple computer simulation. The proposed language dynamics includes processes of selective geographic colonization,…
Diffusion models are a class of probabilistic generative models that have been widely used as a prior for image processing tasks like text conditional generation and inpainting. We demonstrate that these models can be adapted to make…
Despite the remarkable empirical success of score-based diffusion models, their statistical guarantees remain underdeveloped. Existing analyses often provide pessimistic convergence rates that do not reflect the intrinsic low-dimensional…
The key findings of classical population genetics are derived using a framework based on information theory using the entropies of the allele frequency distribution as a basis. The common results for drift, mutation, selection, and gene…
The ancestral selection graph in population genetics was introduced by KroneNeuhauser (1997) as an analogue of the coalescent genealogy of a sample of genes from a neutrally evolving population. The number of particles in this graph,…
We investigate through numerical simulations the effect of selection on two summary statistics for nucleotide variation in a sample of two genes from a population of N asexually reproducing haploid individuals. One is the mean time since…
The bifurcation theory of ordinary differential equations (ODEs), and its application to deterministic population models, are by now well established. In this article, we begin to develop a complementary theory for diffusion-like…
Wright-Fisher diffusions and their dual ancestral graphs occupy a central role in the study of allele frequency change and genealogical structure, and they provide expressions, explicit in some special cases but generally implicit, for the…
We investigate random searches under stochastic position resetting at rate $r$, in a bounded 1D environment with space-dependent diffusivity $D(x)$. For arbitrary shapes of $D(x)$ and prescriptions of the associated multiplicative…
We explore a model of metapopulation genetics which is based on a more ecologically motivated approach than is frequently used in population genetics. The size of the population is regulated by competition between individuals, rather than…
The sample frequency spectrum (SFS) of DNA sequences from a collection of individuals is a summary statistic which is commonly used for parametric inference in population genetics. Despite the popularity of SFS-based inference methods,…
Diffusion in an evolving environment is studied by continuos-time Monte Carlo simulations. Diffusion is modelled by continuos-time random walkers on a lattice, in a dynamic environment provided by bubbles between two one-dimensional…
Gene duplications are one of major primary driving forces for evolutionary novelty. We took population genetics models of genes duplicate to study how evolutionary forces acting during the fixation of mutant allele at duplicate loci. We…
How should dispersal strategies be chosen to increase the likelihood of survival of a species? We obtain the answer for the spatially extended versions of three well-known models of two competing species with unequal diffusivities. Though…
By considering diffusion on De Bruijn graphs, we study in details the dynamics of the histories in the Minority Game, a model of competition between adaptative agents. Such graphs describe the structure of temporal evolution of $M$ bits…
The effects of a stochastic reset, to its initial configuration, is studied in the exactly solvable one-dimensional coagulation-diffusion process. A finite resetting rate leads to a modified non-equilibrium stationary state. If in addition…
We study the stochastic dynamics of evolutionary games, and focus on the so-called `stochastic slowdown' effect, previously observed in (Altrock et. al, 2010) for simple evolutionary dynamics. Slowdown here refers to the fact that a…
Modern biomedicine is challenged to predict the effects of genetic variation. Systematic functional assays of point mutants of proteins have provided valuable empirical information, but vast regions of sequence space remain unexplored.…