Related papers: Gene-Mating Dynamic Evolution Theory I: Fundamenta…
Adaptive dynamics so far has been put on a rigorous footing only for clonal inheritance. We extend this to sexually reproducing diploids, although admittedly still under the restriction of an unstructured population with Lotka-Volterra-like…
Populations evolving under the joint influence of recombination and resampling (traditionally known as genetic drift) are investigated. First, we summarise and adapt a deterministic approach, as valid for infinite populations, which assumes…
We show that the Tangled Nature model can be interpreted as a general formulation of the quasi-species model by Eigen et al. in a frequency dependent fitness landscape. We present a detailed theoretical derivation of the mutation threshold,…
We introduce and analyze a purely competitive dynamics for the evolution of an infinite population subject to a 3-strategy game. We argue that this dynamics represents a characterization of how certain systems, both natural and artificial,…
Classical population genetics a priori assigns fitness to alleles without considering molecular or functional properties of proteins that these alleles encode. Here we study population dynamics in a model where fitness can be inferred from…
A simplified form of the time dependent evolutionary dynamics of a quasispecies model with a rugged fitness landscape is solved via a mapping onto a random flux model whose asymptotic behavior can be described in terms of a random walk. The…
We deal with the study of the evolution of the allelic frequencies, at a single locus, for a population distributed continuously over a bounded habitat. We consider evolution which occurs under the joint action of selection and arbitrary…
In considering evolution of transcribed regions, regulatory modules, and other genomic loci of interest, we are often faced with a situation in which the number of allelic states greatly exceeds the population size. In this limit, the…
We consider a model for Darwinian evolution in an asexual population with a large but non-constant populations size characterized by a natural birth rate, a logistic death rate modelling competition and a probability of mutation at each…
Many socio-economic and biological processes can be modeled as systems of interacting individuals. The behaviour of such systems can be often described within game-theoretic models. In these lecture notes, we introduce fundamental concepts…
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…
In this paper we study the discrete-time dynamical systems associated with gonosomal algebras used as algebraic model in the sex-linked genes inheritance. We show that the class of gonosomal algebras is disjoint from the other…
This survey focuses on the most important aspects of the mathematical theory of population genetic models of selection and migration between discrete niches. Such models are most appropriate if the dispersal distance is short compared to…
This paper is concerned with the global dynamics of a hybrid parabolic-hyperbolic model describing populations with distinct dispersal and sedentary stages. We first establish the global well-posedness of solutions, prove a comparison…
Spatially resolved genetic data is increasingly used to reconstruct the migrational history of species. To assist such inference, we study, by means of simulations and analytical methods, the dynamics of neutral gene frequencies in a…
Single species population models and discrete stochastic gene frequency models are two standards of mathematical biology important for the evolution of populations. An agent based model is presented which reproduces these models and then…
In subdivided populations, migration acts together with selection and genetic drift and determines their evolution. Building up on a recently proposed method, which hinges on the emergence of a time scale separation between local and global…
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…
Near the beginning of the century, Wright and Fisher devised an elegant, mathematically tractable model of gene reproduction and replacement that laid the foundation for contemporary population genetics. The Wright-Fisher model and its…
Existing theoretical models of evolution focus on the relative fitness advantages of different mutants in a population while the dynamic behavior of the population size is mostly left unconsidered. We here present a generic stochastic model…