Siegmund duality with applications to the neutral Moran model conditioned on never being absorbed

In this paper, we review recent results of ours concerning branching processes with general lifetimes and neutral mutations, under the infinitely many alleles model, where mutations

This phase is called the quasispecies phase, the master sequences occupy a significant proportion of the population, along with a cloud of mutants consisting of individuals that

Similar results conceming the equations of the temperature critical regions are obtained by comparing the mean field value of the order parameter (the slowest field variable 1~)

Keywords: beta coalescent; Cannings model; Λ-coalescent; exchangeabil- ity; log infinitely divisible distributions; Moran model; multiple collisions 2010 Mathematics

In the following sections, we find additional examples where these duality relations between substochastic kernels can be established: for the well-known Siegmund kernel the

For the ergodic Moran model with mutations, we get interested into the fixation probabilities of a mutant, the growth rate of fluctuations, the first hit- ting time of the

neutral multi-allelic Moran process; Fleming – Viot type particle system; interacting particle system; convergence rate to stationarity; finite continuous-time Markov

One gener- ation backwards in time there will be i − 1 ancestral mating units present if and only if one of the i mating units is removed and all K new-born individuals choose