Related papers: Bistability in two-locus models with selection, mu…
We considered a {multi-block} molecular model of biological evolution, in which fitness is a function of the mean types of alleles located at different parts (blocks) of the genome. We formulated an infinite population model with selection…
In this work, we characterize the solution of a system of elliptic integro-differential equations describing a phenotypically structured population subject to mutation, selection and migration between two habitats. Assuming that the effects…
Genetic switch systems with mutual repression of two transcription factors are studied using deterministic methods (rate equations) and stochastic methods (the master equation and Monte Carlo simulations). These systems exhibit bistability,…
We consider a biological population in which a beneficial mutation is undergoing a selective sweep when a second beneficial mutation arises at a linked locus and we investigate the probability that both mutations will eventually fix in the…
We have analyzed the relations between the mutational pressure, recombination and selection pressure in the bit-string model with sexual reproduction. For specific sets of these parameters we have found three phase transitions with one…
We use fitness graphs, or directed cube graphs, for analyzing evolutionary reversibility. The main application is antimicrobial drug resistance. Reversible drug resistance has been observed both clinically and experimentally. If drug…
This contribution is concerned with mathematical models for the dynamics of the genetic composition of populations evolving under recombination. Recombination is the genetic mechanism by which two parent individuals create the mixed type of…
When polygenic traits are under stabilizing selection, many different combinations of alleles allow close adaptation to the optimum. If alleles have equal effects, all combinations that result in the same deviation from the optimum are…
The relationship between genotype and phenotype plays a crucial role in determining the function and robustness of biological systems. Here the evolution progresses through the change in genotype, whereas the selection is based on the…
Self-arrangement of individuals into spatial patterns often accompanies and promotes species diversity in ecological systems. Here, we investigate pattern formation arising from cyclic dominance of three species, operating near a…
We study the probability of fixation in a stochastic two-species competition model. By identifying a naturally occurring fast timescale, we derive an approximation to the associated backward Kolmogorov equation that allows us to obtain an…
Epistasis describes the phenomenon that mutations at different loci do not have independent effects with regard to certain phenotypes. Understanding the global epistatic landscape is vital for many genetic and evolutionary theories. Current…
This is an introductory review of deterministic mutation-selection models for asexual populations (i.e., quasispecies theory) and related topics. First, the basic concepts of fitness, mutations, and sequence space are introduced. Different…
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…
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 show that higher order epistasis has a substantial impact on evolutionary dynamics by analyzing peaks in the fitness landscapes. There are 193,270,310 fitness graphs, or cube orientations, for 4-locus systems, distributed on 511, 863…
The relationship between the shape of a fitness landscape and the underlying gene interactions, or epistasis, has been extensively studied in the two-locus case. Gene interactions among multiple loci are usually reduced to two-way…
Evolutionary adaptation is the process that increases the fit of a population to the fitness landscape it inhabits. As a consequence, evolutionary dynamics is shaped, constrained, and channeled, by that fitness landscape. Much work has been…
We study the evolution of a population in a two-locus genotype space, in which the negative effects of two single mutations are overcompensated in a high fitness double mutant. We discuss how the interplay of finite population size, $N$,…
Epistasis occurs when the effect of a mutation depends on its carrier's genetic background. Despite increasing evidence that epistasis for fitness is common, its role during evolution is contentious. Fitness landscapes, mappings of genotype…