Related papers: Limiting fitness distributions in evolutionary dyn…
Diffusion theory is a central tool of modern population genetics, yielding simple expressions for fixation probabilities and other quantities that are not easily derived from the underlying Wright-Fisher model. Unfortunately, the textbook…
We consider a continuum version of a previously introduced and numerically studied model of macroevolution (PRL 75, 2055, (1995)) in which agents evolve by an optimization process in a rugged fitness landscape and die due to their…
Selection, the tendency of some traits to become more frequent than others in a population under the influence of some (natural or artificial) agency, is a key component of Darwinian evolution and countless other natural and social…
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…
Biological evolution can be conceptualized as a search process in the space of gene sequences guided by the fitness landscape, a mapping that assigns a measure of reproductive value to each genotype. Here we discuss probabilistic models of…
Analogies between evolutionary dynamics and statistical mechanics, such as Fisher's second-law-like "fundamental theorem of natural selection" and Wright's "fitness landscapes", have had a deep and fruitful influence on the development of…
The appropriate description of fluctuations within the framework of evolutionary game theory is a fundamental unsolved problem in the case of finite populations. The Moran process recently introduced into this context [Nowak et al., Nature…
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…
The nonlocal Fisher equation is a diffusion-reaction equation with a nonlocal quadratic competition, which describes the reaction between distant individuals. This equation arises in evolutionary biological systems, where the arena for the…
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 adapt a fitness function from evolutionary game theory as a mechanism for aggregation and dispersal in a partial differential equation (PDE) model of two interacting populations, described by density functions $u$ and $v$. We consider a…
Competition between biological species in marine environments is affected by the motion of the surrounding fluid. An effective 2D compressibility can arise, for example, from the convergence and divergence of water masses at the depth at…
Understanding the time evolution of fragmented animal populations and their habitats, connected by migration, is a problem of both theoretical and practical interest. This paper presents a method for calculating the time evolution of the…
Adaptation in a fluctuating environment is a process of fueling environmental information to gain fitness. Living systems have gradually developed strategies for adaptation from random and passive diversification of the phenotype to more…
Competitions can occur on an absolute scale, to be faster or more efficient, or they can occur on a relative scale, to "beat" one's competitor in a zero-sum game. Ecological models have focused on absolute competitions, in which optima…
We investigate the evolution of populations of random Boolean networks under selection for robustness of the dynamics with respect to the perturbation of the state of a node. The fitness landscape contains a huge plateau of maximum fitness…
A simple model of macroevolution is proposed exhibiting both the property of punctuated equilibrium and the dynamics of potentialities for different species to evolve towards increasingly higher complexity. It is based on the phenomenon of…
We study evolutionary game dynamics in finite populations. We analyze an evolutionary process, which we call pairwise comparison, for which we adopt the ubiquitous Fermi distribution function from statistical mechanics. The inverse…
Organisms modulate their fitness in heterogeneous environments by dispersing. Prior work shows that there is selection against "unconditional" dispersal in spatially heterogeneous environments. "Unconditional" means individuals disperse at…
The Wright-Fisher model is the most popular population model for describing the behaviour of evolutionary systems with a finite population size. Approximations to the model have commonly been used for the analysis of time-resolved genome…