Related papers: Flow-Based Modelling of Population Dynamics with C…
A discrete-time model of reacting evolving fields, transported by a bidimensional chaotic fluid flow, is studied. Our approach is based on the use of a Lagrangian scheme where {\it fluid particles} are advected by a $2d$ symplectic map…
We consider a nonlinear coupled discrete-time model of population dynamics. This model describes the movement of populations within a heterogeneous landscape, where the growth of subpopulations are modelled by (possibly different) bounded…
Phenotypically structured equations arise in population biology to describe the interaction of species with their environment that brings the nutrients. This interaction usually leads to selection of the fittest individuals. Models used in…
Populations evolving under the joint influence of recombination and resampling (traditionally known as genetic drift) are investigated. First, we summarise and adapt a deterministic approach, as valid for infinite populations, which assumes…
We investigate a continuous time, probability measure-valued dynamical system that describes the process of mutation-selection balance in a context where the population is infinite, there may be infinitely many loci, and there are weak…
We introduce a simple model of population dynamics which considers birth and death rates for every individual that depend on the number of particles in its neighborhood. The model shows an inhomogeneous quasistationary pattern with many…
We study the statistical properties of population dynamics evolving in a realistic two-dimensional compressible turbulent velocity field. We show that the interplay between turbulent dynamics and population growth and saturation leads to…
We study the evolutionary dynamics of a phenotypically structured population in a changing environment , where the environmental conditions vary with a linear trend but in an oscillatory manner. Such phenomena can be described by parabolic…
We consider an asexual population evolving on rugged fitness landscapes which are defined on the multi-dimensional genotypic space and have many local optima. We track the most populated genotype as it changes when the population jumps from…
Marine species reproduce and compete while being advected by turbulent flows. It is largely unknown, both theoretically and experimentally, how population dynamics and genetics are changed by the presence of fluid flows. Discrete…
Evolution has fascinated quantitative and physical scientists for decades: how can the random process of mutation, recombination, and duplication of genetic information generate the diversity of life? What determines the rate of evolution?…
Combining discrete and continuous data is an important capability for generative models. We present Discrete Flow Models (DFMs), a new flow-based model of discrete data that provides the missing link in enabling flow-based generative models…
We consider the evolutionary trajectories traced out by an infinite population undergoing mutation-selection dynamics in static, uncorrelated random fitness landscapes. Starting from the population that consists of a single genotype, the…
We introduce a broad class of spatial models to describe how spatially heterogeneous populations live, die, and reproduce. Individuals are represented by points of a point measure, whose birth and death rates can depend both on spatial…
We study the large population limit of the Moran process, assuming weak-selection, and for different scalings. Depending on the particular choice of scalings, we obtain a continuous model that may highlight the genetic-drift (neutral…
In evolutionary dynamics, well-mixed populations are almost always associated with all-to-all interactions; mathematical models are based on complete graphs. In most cases, these models do not predict fixation probabilities in groups of…
We study a nonlinear recombination model from population genetics as a combinatorial version of the Kac-Boltzmann equation from kinetic theory. Following Kac's approach, the nonlinear model is approximated by a mean field linear evolution…
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…
Coevolving and competing species or game-theoretic strategies exhibit rich and complex dynamics for which a general theoretical framework based on finite populations is still lacking. Recently, an explicit mean-field description in the form…
We considered a {multi-block} molecular model of biological evolution, in which fitness is a function of the mean types of alleles located at different parts (blocks) of the genome. We formulated an infinite population model with selection…