Related papers: Evolutionary branching in a stochastic population …
We study a universal object for the genealogy of a sample in populations with mutations: the critical birth-death process with Poissonian mutations, conditioned on its population size at a fixed time horizon. We show how this process arises…
We study the adaptation dynamics of an initially maladapted asexual population with genotypes represented by binary sequences of length $L$. The population evolves in a maximally rugged fitness landscape with a large number of local optima.…
We propose a modelling framework to analyse the stochastic behaviour of heterogeneous, multi-scale cellular populations. We illustrate our methodology with a particular example in which we study a population with an oxygen-regulated…
Infinite population models are important tools for studying population dynamics of evolutionary algorithms. They describe how the distributions of populations change between consecutive generations. In general, infinite population models…
We are interested in modeling the Darwinian evolution resulting from the interplay of phenotypic variation and natural selection through ecological interactions, in the specific scales of the biological framework of adaptive dynamics.…
In this paper, we consider a stochastic ratio-dependent predator-prey model. We firstly prove the existence, uniqueness and positivity of the solutions. Then, the boundedness of moments of population are studied. Finally, we show the…
We are interested in the impact of natural selection in a prey-predator community. We introduce an individual-based model of the community that takes into account both prey and predator phenotypes. Our aim is to understand the phenotypic…
The recent interest in human dynamics has led researchers to investigate the stochastic processes that explain human behaviour in various contexts. Here we propose a generative model to capture the dynamics of survival analysis,…
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,…
Is evolution always gradual or can it make leaps? We examine a mathematical model of an evolutionary process on a fitness landscape and obtain analytic solutions for the probability of multi-mutation leaps, that is, several mutations…
The growth of a population divided among spatial sites, with migration between the sites, is sometimes modelled by a product of random matrices, with each diagonal elements representing the growth rate in a given time period, and…
We consider the Moran model of population genetics with two types, mutation, and selection, and investigate the line of descent of a randomly-sampled individual from a contemporary population. We trace this ancestral line back into the…
Random walks on multidimensional nonlinear landscapes are of interest in many areas of science and engineering. In particular, properties of adaptive trajectories on fitness landscapes determine population fates and thus play a central role…
We represent a process of learning by using bit strings, where 1-bits represent the knowledge acquired by individuals. Two ways of learning are considered: individual learning by trial-and-error; and social learning by copying knowledge…
We present a general framework to describe the evolutionary dynamics of an arbitrary number of types in finite populations based on stochastic differential equations (SDE). For large, but finite populations this allows to include…
The spreading of evolutionary novelties across populations is the central element of adaptation. Unless population are well-mixed (like bacteria in a shaken test tube), the spreading dynamics not only depends on fitness differences but also…
Random walks and related spatial stochastic models have been used in a range of application areas including animal and plant ecology, infectious disease epidemiology, developmental biology, wound healing, and oncology. Classical random walk…
Establishing a quantitative connection between the population growth rate and the generation times of single cells is a prerequisite for understanding evolutionary dynamics of microbes. However, existing theories fail to account for the…
To learn about the past from a sample of genomic sequences, one needs to understand how evolutionary processes shape genetic diversity. Most population genetic inference is based on frameworks assuming adaptive evolution is rare. But if…
Discrete time, spatially extended models play an important role in ecology, modelling population dynamics of species ranging from micro-organisms to birds. An important question is how 'bottom up', individual-based models can be…