FIG. 8.
(Color online) A single run of the flat-front model with 1000 organisms. At t=0, each site is assigned either allele one or allele two with equal probability. The spatially averaged heterozygosity [defined in the sense of Eq. (C1) but without taking the limit L→∞] for three times measured in generations: t=0, 1024, and 4096. The separation l is the shortest distance between two points around the cylinder, and we take the clockwise direction to be positive. At inoculation, the heterozygosity fluctuates around 1/2 since the two alleles have equal probabilities of occupying any site. The only exception is the site l=0, where the heterozygosity is zero automatically because we only allow a single microorganism per site. After 1024 generations, short-range correlations are clearly visible and after 4096 generations, one can relate the abrupt changes in the slope of H(t,l) to the sizes of the sectors in the population (not shown). The wiggles are eliminated when averaged over many realizations, as shown in Fig. 9. Note that the curve for t=4096τg lies completely below 1/2 because, at this time, the relative fraction of the alleles deviates significantly from the initial 50:50 ratio due to genetic drift.