Author's: THIERRY E. HUILLET
Pages: [85] - [154]
Received Date: March 22, 2012
Submitted by:
When the reproduction law of a discrete branching process preserving
the total size N of a population is ‘balanced’, scaling
limits of the forward and backward in time processes are known to be
the Wright-Fisher diffusion and the Kingman coalescent.
When the reproduction law is ‘unbalanced’, depending on extreme
reproduction events occurring either occasionally or systematically,
then various forward and backward jump processes, either in continuous
time or in discrete time arise as scaling limits in the large N
limit. This is in sharp contrast with diffusion limits, whose sample
paths are continuous. We study some aspects of these limiting jump
processes both forward and backward, especially the discrete-time
ones. In the forward in time approach, because the absorbing
boundaries are not hit in finite time, the analysis of the models
together with the conclusions, which can be drawn deviate
significantly from the ones available in the diffusion context.
mutational and evolutionary processes (theory), population dynamics (theory), phylogeny (theory).