Related papers: Quasispecies evolution in general mean-field lands…
The quasi-species equation describes the evolution of the probability that a random individual in a population carries a given genome. Here we map the quasi-species equation for individuals of a self-reproducing population to an ensemble of…
We investigate the evolutionary dynamics of an idealised model for the robust self-assembly of two-dimensional structures called polyominoes. The model includes rules that encode interactions between sets of square tiles that drive the…
We re-examine the evolutionary dynamics of RNA secondary structures under directional selection towards an optimum RNA structure. We find that the punctuated equilibria lead to a very slow approach to the optimum, following on average an…
A microscopic model is developed, within the frame of the theory of quantitative traits, to study both numerically and analytically the combined effect of competition and assortativity on the sympatric speciation process, i.e. speciation in…
Evolutionary trajectories and phenotypic states available to cell populations are ultimately dictated by intermolecular interactions between DNA, RNA, proteins, and other molecular species. Here we study how evolution of gene regulation in…
We study the question of existence of positive steady states of nonlinear evolution equations. We recast the steady state equation in the form of eigenvalue problems for a parametrised family of unbounded linear operators, which are…
Subcritical population processes are attracted to extinction and do not have non-trivial stationary distributions, which prompts the study of quasi-stationary distributions (QSDs) instead. In contrast to what generally happens for…
Recent research has extended methods from the fields of thermodynamics and statistical mechanics into other disciplines. Most notably, one recent work creates a unified theoretical framework to understand evolutionary biology, machine…
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…
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 consider the Nelson model with ultraviolet cutoff, which describes the interaction between non-relativistic particles and a positive or zero mass quantized scalar field. We take the non-relativistic particles to obey Fermi statistics 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…
The quasispecies model introduced by Eigen in 1971 has close connections with the isometry group of the space of binary sequences relative to the Hamming distance metric. Generalizing this observation we introduce an abstract quasispecies…
Evolution is simultaneously driven by a number of processes such as mutation, competition and random sampling. Understanding which of these processes is dominating the collective evolutionary dynamics in dependence on system properties is a…
These lectures contain a brief description of evolutionary models inspired by the statistical mechanics of disordered systems. After an introduction describing the Darwinian paradigm of evolving populations, the deterministic quasispecies…
We study the geometry of the mean fitness surface of replicator systems and its relationship to evolutionary trajectory dynamics. Using the symmetric--antisymmetric decomposition of the fitness landscape matrix, we derive an explicit…
Geographic ranges of communities of species evolve in response to environmental, ecological, and evolutionary forces. Understanding the effects of these forces on species' range dynamics is a major goal of spatial ecology. Previous…
We study the competition between random multiplicative growth and redistribution/migration in the mean-field limit, when the number of sites is very large but finite. We find that for static random growth rates, migration should be strong…
In classical evolutionary theory, genetic variation provides the source of heritable phenotypic variation on which natural selection acts. Against this classical view, several theories have emphasized that developmental variability and…
Coevolving and competing species or game-theoretic strategies exhibit rich and complex dynamics for which a general theoretical framework based on finite populations is still lacking. Recently, an explicit mean-field description in the form…