Figure 1

Dynamics of the frequencies of a resistance ( RES ) allele in two demes linked by migration. The model is of a gene-for-gene interaction between a host RES gene and a parasite avirulence (AVR) gene. The costs to the host of having the RES allele (u) or the parasite the virulence (avr) allele (b) are 0.05 in both demes. The cost to a plant of being diseased (s) is 0.1 in deme 1 (red) and 0.3 in deme 2 (blue). First, the model was run without migration between the demes for 1000 generations; the oscillations in the two demes had different frequencies and spiralled outwards from the interior equilibrium point. After 2000 generations, migration was introduced with a fraction 0.03 of the population being dispersed between the two demes; the oscillations in the two demes became synchronised and damped one another, thus stabilising polymorphism. After a further 2000 generations, migration was eliminated again, resulting once again in expanding, asynchronous oscillations in the two demes.