Related papers: More rigorous results on the Kauffman-Levin model …
It has recently been suggested that the fundamental haploid-diploid cycle of eukaryotic sex exploits a rudimentary form of the Baldwin effect. Thereafter the other associated phenomena can be explained as evolution tuning the amount and…
The idea of adaptive walks on fitness landscapes as a means of studying evolutionary processes on large time scales is extended to fitness landscapes that are slowly changing over time. The influence of ruggedness and of the amount of…
We consider a fixed size population that undergoes an evolutionary adaptation in the weak mutuation rate limit, which we model as a biased Langevin process in the genotype space. We show analytically and numerically that, if the fitness…
Evolution is the process of optimal adaptation of biological populations to their living environments. This is expressed via the concept of fitness, defined as relative reproductive success. However, it has been pointed out that this…
Recent work on mutation-selection models has revealed that, under specific assumptions on the fitness function and the mutation rates, asymptotic estimates for the leading eigenvalue of the mutation-reproduction matrix may be obtained…
This paper is concerned with the evolution of haploid organisms that reproduce asexually. In a seminal piece of work, Eigen and coauthors proposed the quasispecies model in an attempt to understand such an evolutionary process. Their work…
We consider an asexual biological population of constant size $N$ evolving in discrete time under the influence of selection and mutation. Beneficial mutations appear at rate $U$ and their selective effects $s$ are drawn from a distribution…
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…
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.…
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 consider a nonlocal Fisher-KPP equation that models a population structured in space and in phenotype. The population lives in a heterogeneous periodic environment: the diffusion coefficient, the mutation coefficient and the fitness of…
The potentially beneficial interaction between learning and evolution, the Baldwin effect, has long been established. This paper considers their interaction within a coevolutionary scenario, ie, where the adaptations of one species…
We consider a population of genotype sequences evolving on a rugged fitness landscape with many local fitness peaks. The population walks uphill until it encounters a local fitness maximum. We find that the statistical properties of the…
The spin market model [S. Bornholdt, Int.J.Mod.Phys. C 12 (2001) 667] is extended into co-evolutionary version, where strategies of interacting and competitive traders are represented by local and global couplings between the nodes of…
We reformulate the eigenvalue problem for the selection--mutation equilibrium distribution in the case of a haploid asexually reproduced population in the form of an equation for an unknown probability generating function of this…
One essential ingredient of evolutionary theory is the concept of fitness as a measure for a species' success in its living conditions. Here, we quantify the effect of environmental fluctuations onto fitness by analytical calculations on a…
We explore some aspects of the relationship between biological evolution processes and the mathematical theory of records. For Eigen's quasispecies model with an uncorrelated fitness landscape, we show that the evolutionary trajectories…
We suggest a natural approach that leads to a modification of classical quasispecies models and incorporates the possibility of population extinction in addition to growth. The resulting modified models are called open. Their essential…
This article gives a brief introduction to the mathematical modeling of large-scale biological evolution and extinction. We give three examples of simple models in this field: the coevolutionary avalanche model of Bak and Sneppen, the…
When mutations are rampant, quasispecies theory or Eigen's model predicts that the fittest type in a population may not dominate. Beyond a critical mutation rate, the population may even be delocalized completely from the peak of the…