Related papers: Evolutionary branching via replicator-mutator equa…
We consider nonlinear mutation selection models, known as replicator-mutator equations in evolutionary biology. They involve a nonlocal mutation kernel and a confining fitness potential. We prove that the long time behaviour of the Cauchy…
We consider a class of nonlocal reaction-diffusion problems, referred to as replicator-mutator equations in evolutionary genetics. By using explicit changes of unknown function, we show that they are equivalent to the heat equation and,…
The replicator-mutator equation is a model for populations of individuals carrying different traits, with a fitness function mediating their ability to replicate, and a stochastic model for mutation. We derive analytical solutions for the…
We analyze a replicator-mutator model arising in the context of directed evolution [23], where the selection term is modulated over time by the mean-fitness. We combine a Cumulant Generating Function approach [13] and a spatio-temporal…
Under constant selection, each trait has a fixed fitness, and small mutation rates allow populations to efficiently exploit the optimal trait. Therefore it is reasonable to expect mutation rates will evolve downwards. However, we find this…
Evolutionary branching is analysed in a stochastic, individual-based population model under mutation and selection. In such models, the common assumption is that individual reproduction and life career are characterised by values of a…
This work completes our previous analysis on models arising in evolutionary genetics. We consider the so-called replicator-mutator equation, when the fitness is quadratic. This equation is a heat equation with a harmonic potential, plus a…
We consider the evolution of populations under the joint action of mutation and differential reproduction, or selection. The population is modelled as a finite-type Markov branching process in continuous time, and the associated…
The replicator-mutator dynamic was originally derived to model the evolution of language, and since the model was derived in such a general manner, it has been applied to the dynamics of social behavior and decision making in multi-agent…
This Letter studies the quasispecies dynamics of a population capable of genetic repair evolving on a time-dependent fitness landscape. We develop a model that considers an asexual population of single-stranded, conservatively replicating…
Deriving evolution equations accounting for both anomalous diffusion and reactions is notoriously difficult, even in the simplest cases. In contrast to normal diffusion, reaction kinetics cannot be incorporated into evolution equations…
We discuss a population of sequences subject to mutations and frequency-dependent selection, where the fitness of a sequence depends on the composition of the entire population. This type of dynamics is crucial to understand the evolution…
In this paper, we discuss the fitness landscape evolution of permanent replicator systems using a hypothesis that the specific time of evolutionary adaptation of the system parameters is much slower than the time of internal evolutionary…
Reaction-diffusion equations are widely used as the governing evolution equations for modeling many physical, chemical, and biological processes. Here we derive reaction-diffusion equations to model transport with reactions on a…
We study quasi-species and closely related evolutionary dynamics like the replicator-mutator equation in high dimensions. In particular, we show that under certain conditions the fitness of almost all quasi-species becomes independent of…
A model for the evolution of a finite population in a rugged fitness landscape is introduced and solved. The population is trapped in an evolutionary loop, alternating periods of stasis to periods in which it performs adaptive walks. The…
We review models of biological evolution in which the population frequency changes deterministically with time. If the population is self-replicating, although the equations for simple prototypes can be linearised, nonlinear equations arise…
The forest of mutations associated to a multitype branching forest is obtained by merging together all vertices of its clusters and by preserving connections between them. We first show that the forest of mutations of any mulitype branching…
The now classical replicator equation describes a wide variety of biological phenomena, including those in theoretical genetics, evolutionary game theory, or in the theories of the origin of life. Among other questions, the permanence of…
Competition between independently arising beneficial mutations is enhanced in spatial populations due to the linear rather than exponential growth of clones. Recent theoretical studies have pointed out that the resulting fitness dynamics is…