主 题: MRCA and bottleneck in an elementary size-varying population model
报告人: Prof. Jean-Francois Delmas (Ecole Nationale des Ponts et Chaussees,France )
时 间: 2011-04-28 上午9：00-10：00
地 点: 理科一号楼1560
We present an elementary model of random size
varying population given by a stationary continuous state branching
process. For this model we compute the joint distribution of: the time
to the most recent common ancestor, the size of the current population
and the size of the population just before the most recent common
ancestor (MRCA). In particular we show a natural mild bottleneck effect
as the size of the population just before the MRCA is stochastically
smaller than the size of the current population. We also compute the
number of old families which corresponds to the number of individuals
involved in the last coalescent event of the genealogical tree. By
studying more precisely the genealogical structure of the population, we
get asymptotics for the number of ancestors just before the current
time. We give explicit computations in the case of the quadratic
branching mechanism. In this case, the size of the population at the
MRCA is, in mean, less by 1/3 than size of the current population
size. We also provide in this case the fluctuations for the renormalized
number of ancestors.
