Transmission Bottlenecks in an Expanding Epidemic

Jesse Taylor

There are two competing demographic processes which will influence the
molecular evolution of parasites such as HIV-1. One is the expansion of
the epidemic, as both the number of infected hosts and the total
population size of the parasite increase. The second is the temporary
reduction in within-host population size that is experienced by the
parasite during transmission. While an increasing population size is
expected to lead to an increase in the standing molecular diversity,
mainly through an excess of rare neutral alleles, transmission bottlenecks
will cull the parasite population of some of these rare variants and thus
reduce molecular variation.

I analyze a non-locally branching diffusion process as a model for the
evolution of a single locus under the influence of both an expanding total
population size and intermittent transmission bottlenecks. A renewal
equation is derived for the probability that a neutral allele is
permanently lost from the parasite population and a necessary and
sufficient condition in terms of the branching rate and mechanism, the
within-host population size, and the sampling distributions during
bottlenecks is given for the survival of a family of n alleles.

Last modified: Thu Jan 21 13:55:17 MST 2001