Related papers: Quasi-Species and Aggregate Dynamics
Natural selection favors the more successful individuals. This is the elementary premise that pervades common models of evolution. Under extreme conditions, however, the process may no longer be probabilistic. Those that meet certain…
We classify and predict the asymptotic dynamics of a class of swarming models. The model consists of a conservation equation in one dimension describing the movement of a population density field. The velocity is found by convolving the…
We study the simple genetic algorithm with a ranking selection mechanism (linear ranking or tournament). We denote by $\ell$ the length of the chromosomes, by $m$ the population size, by $p_C$ the crossover probability and by $p_M$ the…
We investigate the evolutionary rescue of a microbial population in a gradually deteriorating environment, through a combination of analytical calculations and stochastic simulations. We consider a population destined for extinction in the…
Collective sensing is an emergent phenomenon which enables individuals to estimate a hidden property of the environment through the observation of social interactions. Previous work on collective sensing shows that gregarious individuals…
The adaptive evolution of large asexual populations is generally characterized by competition between clones carrying different beneficial mutations. This interference phenomenon slows down the adaptation speed and makes the theoretical…
Owing to the analogies between the problem of wealth redistribution with taxation in a multi-agent society, we introduce and discuss a kinetic model describing the statistical distributions in time of the sizes of groups of biological…
Speciation is fundamental to the huge diversity of life on Earth. Evidence suggests reproductive isolation arises most commonly in allopatry with a higher speciation rate in small populations. Current theory does not address this dependence…
An autocatalytic pattern matching polymer system is studied as an abstract model for chemical ecosystem evolution. Highly ordered populations with particular sequence patterns appear spontaneously out of a vast number of possible states.…
We identify the genetic signature of a selective sweep in a population described by a birth-and-death process with density dependent competition. We study the limit behaviour for large K, where K scales the population size. We focus on two…
To understand the effect of assortative mating on the genetic evolution of a population, we consider a finite population in which each individual has a type, determined by a sequence of n diallelic loci. We assume that the population…
Aggregation-diffusion equations are foundational tools for modelling biological aggregations. Their principal use is to link the collective movement mechanisms of organisms to their emergent space use patterns in a concrete mathematical…
We study the role of recombination, as practiced by genetically-competent bacteria, in speeding up Darwinian evolution. This is done by adding a new process to a previously-studied Markov model of evolution on a smooth fitness landscape;…
It is well known that every finite simple group can be generated by two elements and this leads to a wide range of problems that have been the focus of intensive research in recent years. In this survey article we discuss some of the…
We consider a trait-structured population subject to mutation, birth and competition of logistic type, where the number of coexisting types may fluctuate. Applying a limit of rare mutations to this population while keeping the population…
We analyse numerically the effects of small population size in the initial transient regime of a simple example population dynamics. These effects play an important role for the numerical determination of large deviation functions of…
We study the interplay of population growth and evolutionary dynamics using a stochastic model based on birth and death events. In contrast to the common assumption of an independent population size, evolution can be strongly affected by…
Population expansions trigger many biomedical and ecological transitions, from tumor growth to invasions of non-native species. Although population spreading often selects for more invasive phenotypes, we show that this outcome is far from…
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…
Environmental heterogeneity can drive genetic heterogeneity in expanding populations; mutant strains may emerge that trade overall growth rate for an improved ability to survive in patches that are hostile to the wild type. This…