Journal of Statistics: Advances in Theory and ApplicationsAuthor'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).
