Colloquium
12:30 p.m., Thursday (January 25, 2007)
MATH 105
Kristan Schneider
University of Vienna
A MultilocusMultiallele Analysis of FrequencyDependent Selection Induced by Intraspecific Competition
The study of the mechanisms that maintain genetic variation has a long
history in population genetics. We analyze a multilocusmultiallele
model
of frequency and density dependent selection in a large randomly
mating
population. The number of loci and the number of alleles per locus are
arbitrary. The n loci are assumed to contribute additively to a
quantitative character under stabilizing or directional selection
as well
as under frequencydependent selection caused by intraspecific
competition. We assume the strength of stabilizing selection to be
weak,
whereas the strength of frequency dependence may be arbitrary.
Densitydependence is induced by population regulation. Our main
result is
a characterization of the equilibrium structure and its stability
properties in terms of all parameters. It turns out that no
equilibrium
exists with more than two alleles segregating per locus. We give
necessary
and sufficient conditions on the strength of frequency dependence to
ensure the maintenance of multilocus polymorphism. We also give
explicit
formulas on the number of polymorphic loci maintained at equilibrium.
These results are based on the assumption that selection is
sufficiently
weak compared with recombination, so that linkage equilibrium can be
assumed. If additionally the population size is assumed to be
constant, we
prove that the dynamics of the model form a generalized gradient
system.
Refreshments will be served at 12:15 p.m. (Lounge, MATX 1115).
