Related papers: The Wright-Fisher model with efficiency
Following some recent works, we investigate the problem of optimising the total population size for logistic diffusive models with respect to resources distributions. Using the spatially heterogeneous Fisher-KPP equation, we obtain a…
We consider a population evolving under mutation and selection. The genotype of an individual is a word of length $\ell$ over a finite alphabet. Mutations occur during reproduction, independently on each locus; the fitness depends on the…
A two-types, discrete-time population model with finite, constant size is constructed, allowing for a general form of frequency-dependent selection and skewed offspring distribution. Selection is defined based on the idea that individuals…
We study a stochastic spatial model of biological competition in which two species have the same birth and death rates, but different diffusion constants. In the absence of this difference, the model can be considered as an off-lattice…
Wright-Fisher diffusions and their dual ancestral graphs occupy a central role in the study of allele frequency change and genealogical structure, and they provide expressions, explicit in some special cases but generally implicit, for the…
We study stochastic evolutionary game dynamics in a population of finite size. Individuals in the population are divided into two dynamically evolving groups. The structure of the population is formally described by a Wright-Fisher type…
The interplay between energy efficiency and evolutionary mechanisms is addressed. One important question is how evolutionary mechanisms can select for the optimised usage of energy in situations where it does not lead to immediate…
Genetic information and environmental factors determine the path of an individuals life and therefore, the evolution of its entire species. We have succeeded in proposing and studying a model that captures this idea. In our model, a…
We consider a stochastic model describing a constant size $N$ population that may be seen as a directed polymer in random medium with $N$ sites in the transverse direction. The population dynamics is governed by a noisy traveling wave…
The problem of natural selection in dispersal-structured populations consisting of individuals characterized by different diffusion coefficients is studied. The competition between the organisms is taken into account through the assumption…
In the context of population genetics, active information can be extended to measure the change of information of a given event (e.g., fixation of an allele) from a neutral model in which only genetic drift is taken into account to a…
Dispersal is an important strategy that allows organisms to locate and exploit favorable habitats. The question arises: given competition in a spatially heterogeneous landscape, what is the optimal rate of dispersal? Continuous population…
This paper is concerned with exploring the microscopic basis for the discrete versions of the standard replicator equation and the adjusted replicator equation. To this end, we introduce frequency-dependent selection -- as a result of…
The entropy rates of the Wright-Fisher process, the Moran process, and generalizations are computed and used to compare these processes and their dependence on standard evolutionary parameters. Entropy rates are measures of the variation…
Demographic models built from genetic data play important roles in illuminating prehistorical events and serving as null models in genome scans for selection. We introduce an inference method based on the joint frequency spectrum of genetic…
Darwinian evolution can be modeled in general terms as a flow in the space of fitness (i.e. reproductive rate) distributions. In the diffusion approximation, Tsimring et al. have showed that this flow admits "fitness wave" solutions:…
We consider a Wright-Fisher diffusion (x(t)) whose current state cannot be observed directly. Instead, at times t1 < t2 < . . ., the observations y(ti) are such that, given the process (x(t)), the random variables (y(ti)) are independent…
We consider the Wright-Fisher model for a population of $N$ individuals, each identified with a sequence of a finite number of sites, and single-crossover recombination between them. We trace back the ancestry of single individuals from the…
Traditionally, population models distinguish individuals on the basis of their current state. Given a distribution, a discrete time model then specifies (precisely in deterministic models, probabilistically in stochastic models) the…
When competing species grow into new territory, the population is dominated by descendants of successful ancestors at the expansion front. Successful ancestry depends on both the reproductive advantage (fitness), as well as ability and…