Related papers: Can evolution paths be explained by chance alone?
We consider an exactly solvable model of branching random walk with random selection, which describes the evolution of a population with $N$ individuals on the real line. At each time step, every individual reproduces independently, and its…
We introduce a model to study the impact of catastrophes on evolutionary paths. If we do not allow catastrophes the number of changes in the maximum fitness of a population grows logarithmically with respect to time. Allowing catastrophes…
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…
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…
How fast does a population evolve from one fitness peak to another? We study the dynamics of evolving, asexually reproducing populations in which a certain number of mutations jointly confer a fitness advantage. We consider the time until a…
We consider the evolutionary trajectories traced out by an infinite population undergoing mutation-selection dynamics in static, uncorrelated random fitness landscapes. Starting from the population that consists of a single genotype, the…
Traditionally evolution is seen as a process where from a pool of possible variations of a population (e.g. biological species or industrial goods) a few variations get selected which survive and proliferate, whereas the others vanish.…
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…
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 revisit the model by Wiser, Ribeck, and Lenski (Science \textbf{342} (2013), 1364--1367), which describes how the mean fitness increases over time due to beneficial mutations in Lenski's long-term evolution experiment. We develop the…
We consider a branching particle system where each particle moves as an independent Brownian motion and breeds at a rate proportional to its distance from the origin raised to the power $p$, for $p\in[0,2)$. The asymptotic behaviour of the…
The recent availability of large databases allows to study macroscopic properties of many complex systems. However, inferring a model from a fit of empirical data without any knowledge of the dynamics might lead to erroneous interpretations…
We study a model of stochastic evolutionary game dynamics in which the probabilities that agents choose suboptimal actions are dependent on payoff consequences. We prove a sample path large deviation principle, characterizing the rate of…
On rugged fitness landscapes where sign epistasis is common, adaptation can often involve either individually beneficial "uphill" mutations or more complex mutational trajectories involving fitness valleys or plateaus. The dynamics of the…
Predicting evolution of expanding populations is critical to control biological threats such as invasive species and cancer metastasis. Expansion is primarily driven by reproduction and dispersal, but nature abounds with examples of…
The expansion of a population into new habitat is a transient process that leaves its footprints in the genetic composition of the expanding population. How the structure of the environment shapes the population front and the evolutionary…
A simple model of species origin resulted from dynamic features of a population, solely, is developed. The model is based on the evolution optimality in space distribution, and the selection is gone over the mobility. Some biological issues…
Biological evolution depends on the passing down to subsequent generations of genetic information encoding beneficial traits, and on the removal of unfit individuals by a selection mechanism. However, selection acts on phenotypes, and is…
We are interested in the study of models describing the evolution of a polymorphic population with mutation and selection in the specific scales of the biological framework of adaptive dynamics. The population size is assumed to be large…
We consider an asexually reproducing population on a finite type space whose evolution is driven by exponential birth, death and competition rates, as well as the possibility of mutation at a birth event. On the individual-based level this…