Clote
Le Jeudi 29 Novembre 2001 à 14h30
au LRI, Salle 101
(Dept of Computer Science and Dept of Biology, Boston College)
Mitochondrial Eve and population bottlenecks
Résumé/Abstract :
In 1987 Cann, Stoneking and Wilson postulated that all
currently existing humans have a common female ancestor,
the so-called `Mitochondrial Eve', who lived in Africa
around 200,000 years ago. Several years before this,
Avise et al. had shown by computer simulation that if
a population bottleneck occurs for a sufficiently long
time, then most likely all members of the population
will be mitochondrially monomorphic. Specifically, by
simulating a Poisson process, Avise et al. cited 4n
as an upper bound on the expected number of generations for
the entire future progeny of a constant-size population of
n females to share the same mtDNA. Since the branching
process simulations of Avise et al. necessarily lead to
population extinction, we model neutral selection during a
population bottleneck by a Markov chain with hypergeometric
(and binomial) transition probabilities, and provide the
first rigorous upper bound for mean stopping time for
Markov chains with absorbing states which satisfy a certain
``mean condition'' (related to martingales) and
``weak variation condition''.
For population size n and k founding lineages,
we prove a mean stopping time of O(n loglog k), which,
if k is constant with respect to n, yields O(n).
Our result has applications to the mitochondrial Eve hypothesis
as well as to a problem of Fisher-Wright concerning
expected time for gene fixation. We introduce an efficient, interative
algorithm for precisely computing the mean stopping time and give
some simulation results.
This is joint work with Samuel R. Buss, UCSD.