Related papers: Nonlinear deterministic equations in biological ev…
There are many natural, physical, and biological systems that exhibit multiple time scales. For example, the dynamics of a population of ticks can be described in continuous time during their individual life cycle yet discrete time is used…
In many models of genotypic evolution, the vector of genotype populations satisfies a system of linear ordinary differential equations. This system of equations models a competition between differential replication rates (fitness) and…
The nonlinear recombination equation from population genetics has a long history and is notoriously difficult to solve, both in continuous and in discrete time. This is particularly so if one aims at full generality, thus also including…
Evolution occurs in populations of reproducing individuals. The structure of a biological population affects which traits evolve. Understanding evolutionary game dynamics in structured populations is difficult. Precise results have been…
Which factors govern the evolution of mutation rates and emergence of species? Here, we address this question using a first principles model of life where population dynamics of asexual organisms is coupled to molecular properties and…
We describe a continuous-time modelling framework for biological population dynamics that accounts for demographic noise. In the spirit of the methodology used by statistical physicists, transitions between the states of the system are…
Stochastic models, based on random processes, may lead to power law distributions, which provide long range correlations. The observation of power law behavior and the presence of long range correlations in biological systems has been…
In large asexual populations, multiple beneficial mutations arise in the population, compete, interfere with each other, and accumulate on the same genome, before any of them fix. The resulting dynamics, although studied by many authors, is…
In this paper the spatial-temporal dynamics of the members of interacting populations is described by nonlinear partial differential equations. We consider the migration as a diffusion process influenced by the changing values of the birth…
We propose a class of evolutionary models that involves an arbitrary exchangeable process as the breeding process and different selection schemes. In those models, a new genome is born according to the breeding process, and then a genome is…
Since steep declines in a population's size also typically alter its composition, population bottlenecks are considered highly important for evolution. However, despite such significance, the mechanisms governing the impact of a given…
Existence of nontrivial nonnegative equilibrium solutions for age structured population models with nonlinear diffusion is investigated. Introducing a parameter measuring the intensity of the fertility, global bifurcation is shown of a…
Changing base composition during the evolution of biological sequences can mislead some of the phylogenetic inference techniques in current use. However, detecting whether such a process has occurred may be difficult, since convergent…
We introduce and analyse an individual-based evolutionary model, in which a population of genetically diverse organisms compete with each other for limited resources. Through theoretical analysis and stochastic simulations, we show that the…
In a complex community, species continuously adapt to each other. On rare occasions, the adaptation of a species can lead to the extinction of others, and even its own. "Adaptive dynamics" is the standard mathematical framework to describe…
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…
We consider an individual based model of phenotypic evolution in hermaphroditic populations which includes random and assortative mating of individuals. By increasing the number of individuals to infinity we obtain a nonlinear transport…
We study a class of evolution models, where the breeding process involves an arbitrary exchangeable process, allowing for mutations to appear. The population size $n$ is fixed, hence after breeding, selection is applied. Individuals are…
We suggest the method for group classification of evolution equations admitting nonlocal symmetries which are associated with a given evolution equation possessing nontrivial Lie symmetry. We apply this method to second-order evolution…
We investigate the evolutionary dynamics of a population structured in phenotype, subjected to trait dependent selection with a linearly moving optimum and an asexual mode of reproduction. Our model consists of a non-local and non-linear…