My Current research is a
model of antagonistic Coevolution in a Metapopulation. This is a 1 locus, 2
allele, discrete time, haploid system for both the host and parasite. Spatial
parameters alpha and beta in each niche modify the density dependent effects
for host and parasite. Migration rates connect the niches currently in an
island model spatial structure.
This
research is an extension of Levene’s model of spatial heterogeneity preserving
genetic variation in populations by having genotypes fit to one environment or
the other. In this model, genetic variation is preserved if asynchronous cycles
arise between niches with alpha/beta, migration rates, and number of niches
affecting the dynamics.
Local
adaptation is also explored though at present the model seems incapable of
producing any lasting local adaptation at the system level.
Heteroclinic
cycles can be produced under various conditions. A single niche always
produces these cycles as well as homogeneous systems of demes. Setting the migration rate to
100% also produces heteroclinic cycles regardless of a heterogeneous system
of niches.
Analytical
results suggested that changes in the model's behavior
might change in a 2 niche system as host (parasite) migration rates cross
2*alpha1*alpha2 (2*beta1*beta2) or as host (parasite) migration rates cross alpha
(beta) but this does not appear to be the case.