Related papers: Single gene dynamics under controlled mating
We propose a stochastic model for evolution. Births and deaths of species occur with constant probabilities. Each new species is associated with a fitness sampled from the uniform distribution on [0,1]. Every time there is a death event…
I discuss the so-called stochastic individual based model of adaptive dynamics and in particular how different scaling limits can be obtained by taking limits of large populations, small mutation rate, and small effect of single mutations…
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…
The central goal of a dynamical theory of evolution is to abstract the mean evolutionary trajectory in the trait space by considering ecological processes at the level of the individual. In this work, we develop such a theory for a new…
We present a model for the dynamics of a population of bacteria with a continuum of traits, who compete for resources and exchange horizontally (transfer) an otherwise vertically inherited trait with possible mutations. Competition…
The purpose of this Note is twofold: First, we introduce the general formalism of evolutionary genetics dynamics involving fitnesses, under both the deterministic and stochastic setups, and chiefly in discrete-time. In the process, we…
Biological living systems in general exhibit complex and diverse dynamics. The latter, in particular, is essential, since diversification increases the odds of survival of an organism while reducing the risk of extinction of the population.…
Continuum models for the spatial dynamics of growing cell populations have been widely used to investigate the mechanisms underpinning tissue development and tumour invasion. These models consist of nonlinear partial differential equations…
We study the stochastic evolution of four species in cyclic competition in a well mixed environment. In systems composed of a finite number $N$ of particles these simple interaction rules result in a rich variety of extinction scenarios,…
We review and extend results for mutation, selection, genetic drift, and migration in a one-dimensional continuous population. The population is described by a continuous limit of the stepping stone model, which leads to the stochastic…
Multitype branching processes are ideal for studying the population dynamics of stem cell populations undergoing mutation accumulation over the years following transplant. In such stochastic models, several quantities are of clinical…
We propose a hybrid dynamical system approach to model the evolution of a pathogen that experiences different selective pressures according to a stochastic process. In every environment, the evolution of the pathogen is described by a…
Bootstrapping was designed to randomly resample data from a fixed sample using Monte Carlo techniques. However, the original sample itself defines a discrete distribution. Convolutional methods are well suited for discrete distributions,…
We explore the complex dynamical behavior of two simple predator-prey models of biological coevolution that on the ecological level account for interspecific and intraspecific competition, as well as adaptive foraging behavior. The…
In this paper I describe a cellular automaton model of a multi-species ecosystem, suitable for the study of emergent properties of macroevolution. Unlike majority of ecological models, the number of coexisting species is not fixed. Starting…
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 explore the complex dynamical behavior of simple predator-prey models of biological coevolution that account for interspecific and intraspecific competition for resources, as well as adaptive foraging behavior. In long kinetic Monte…
In this paper we explore the eco-evolutionary dynamics of a predator-prey model, where the prey population is structured according to a certain life history trait. The trait distribution within the prey population is the result of interplay…
Single species population models and discrete stochastic gene frequency models are two standards of mathematical biology important for the evolution of populations. An agent based model is presented which reproduces these models and then…
We perform individual-based Monte Carlo simulations in a community consisting of two predator species competing for a single prey species, with the purpose of studying biodiversity stabilization in this simple model system. Predators are…