Related papers: Duality and Fixation in $\Xi$-Wright-Fisher proces…
We apply our general method of duality, introduced in [Giardina', Kurchan, Redig, J. Math. Phys. 48, 033301 (2007)], to models of population dynamics. The classical dualities between forward and ancestral processes can be viewed as a change…
The directed preferential attachment model is revisited. A new exact characterization of the limiting in- and out-degree distribution is given by two \emph{independent} pure birth processes that are observed at a common exponentially…
Evolutionary game theory is a mathematical approach to studying how social behaviors evolve. In many recent works, evolutionary competition between strategies is modeled as a stochastic process in a finite population. In this context, two…
The d-dimensional Lambda-Fleming-Viot generator acting on functions g(x), with x being a vector of d allele frequencies, can be written as a Wright-Fisher generator acting on functions g with a modified random linear argument of x induced…
Fixation probabilities are essential for characterizing stochastic evolutionary dynamics, but analytical results remain limited mainly to systems with two competing types. We develop a perturbative framework to compute fixation…
We study a model of selection acting on a diploid population (one in which each individual carries two copies of each gene) living in one spatial dimension. We suppose a particular gene appears in two forms (alleles) $A$ and $a$, and that…
The ancestral selection graph in population genetics was introduced by KroneNeuhauser (1997) as an analogue of the coalescent genealogy of a sample of genes from a neutrally evolving population. The number of particles in this graph,…
Open fermion systems with energy-independent bilinear coupling to a fermionic environment have been shown to obey a general duality relation [Phys. Rev. B 93, 81411 (2016)] which allows for a drastic simplification of time-evolution…
We consider a random forest $\mathcal{F}^*$, defined as a sequence of i.i.d. birth-death (BD) trees, each started at time 0 from a single ancestor, stopped at the first tree having survived up to a fixed time $T$. We denote by…
We pursue the task of developing a finite population counterpart to Eigen's model. We consider the classical Wright-Fisher model describing the evolution of a population of size $m$ of chromosomes of length $\ell$ over an alphabet of…
Both genetic drift and natural selection cause the frequencies of alleles in a population to vary over time. Discriminating between these two evolutionary forces, based on a time series of samples from a population, remains an outstanding…
We consider an extension of the noisy $N$-Branching Random Walk that models the evolution of a population subject to natural selection. We show the existence of a critical value for the noise which separates the limiting genealogical…
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…
Modern developments in population dynamics emphasize the role of the turnover of individuals. In the new approaches stable population size is a dynamic equilibrium between different mortality and fecundity factors instead of an arbitrary…
Starting from the well-known field theory for directed percolation, we describe an evolving population, near extinction, in an environment with its own nontrivial spatio-temporal dynamics. Here, we consider the special case where the…
We study a discrete-time stochastic process that can also be interpreted as a model for a viral evolution. A distinguishing feature of our process is power-law tails due to dynamics that resembles preferential attachment models. In the…
We consider two versions of stochastic population models with mutation and selection. The first approach relies on a multitype branching process; here, individuals reproduce and change type (i.e., mutate) independently of each other,…
We study the fixation and stationary behavior of the Lambda-Wright-Fisher process with parent-independent mutation and finitely many types, a jump-diffusion model for allele frequency dynamics in large populations with potentially large…
Frequency-dependent selection reflects the interaction between different species as they battle for limited resources in their environment. In a stochastic evolutionary game the species relative fitnesses guides the evolutionary dynamics…
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…