Related papers: Power-Law Tails in a Fitness-Driven Model for Biol…
We introduce the following model for the evolution of a population. At every discrete time $j\geq 0$ exactly one individual is introduced in the population and is assigned a death probability $c_j$ sampled from $C$, a fixed probability…
We study biological evolution on a random fitness landscape where correlations are introduced through a linear fitness gradient of strength $c$. When selection is strong and mutations rare the dynamics is a directed uphill walk that…
In the present work, via computational simulation we study the statistical distribution of people versus number of steps acquired by them in a learning process, considering Darwin classical theory of evolution, i.e. competition, learning…
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.…
An individual-based model of stochastic branching is proposed and studied, in which point particles drift in $\bar{\mathds{R}}_{+}:=[0,+\infty)$ towards the origin (edge) with unit speed, where each of them splits into two particles that…
Near the beginning of the century, Wright and Fisher devised an elegant, mathematically tractable model of gene reproduction and replacement that laid the foundation for contemporary population genetics. The Wright-Fisher model and its…
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…
Resource are often not uniformly distributed within a population. Spatial variations of concentration of a resource, change the fitness of competing strategies locally. The notion of fitness varying with respect to both genotype and…
We aim to understand the evolution of the genetic composition of cancer cell populations. To achieve this, we consider an individual-based model representing a cell population where cells divide, die and mutate along the edges of a finite…
Within the framework of population genetics we consider the evolution of an asexual haploid population under the effect of a rapidly varying natural selection (microevolution). We focus on the case in which the environment exerting…
We introduce a toy model of the "rat race" in which individuals try to better themselves relative to the rest of the population. An individual is characterized by a real-valued fitness and each advances at a constant rate by an amount that…
This article is a presentation of specific recent results describing scaling limits of individual-based models. Thanks to them, we wish to relate the time-scales typical of demographic dynamics and natural selection to the parameters of the…
In a recent study of certain merging-splitting models of animal-group size (Degond et al., J. Nonl. Sci. 27 (2017) 379), it was shown that an initial size distribution with infinite first moment leads to convergence to zero in weak sense,…
In this paper we study the iterated birth process of which we examine the first-passage time distributions and the hitting probabilities. Furthermore, linear birth processes, linear and sublinear death processes at Poisson times are…
We present a generalization of the Yule model for macroevolution in which, for the appearance of genera, we consider point processes with the order statistics property, while for the growth of species we use nonlinear time-fractional pure…
We consider a population with two types of individuals, distinguished by the resources required for reproduction: type-$0$ (small) individuals need a fractional resource unit of size $\vartheta \in (0,1)$, while type-$1$ (large) individuals…
Frequency dependent selection and demographic fluctuations play important roles in evolutionary and ecological processes. Under frequency dependent selection, the average fitness of the population may increase or decrease based on…
We develop a ``unified'' model that describes both ``micro'' and ``macro'' evolutions within a single theoretical framework. The eco-system is described as a dynamic network; the population dynamics at each node of this network describes…
Existing theoretical models of evolution focus on the relative fitness advantages of different mutants in a population while the dynamic behavior of the population size is mostly left unconsidered. We here present a generic stochastic model…
We consider an approximating sequence of interacting population models with branching, mutation and competition. Each individual is characterized by its trait and the traits of its ancestors. Birth- and death-events happen at exponential…