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United States Department of Agriculture

Agricultural Research Service

Title: Modeling Gene Frequency Dynamics

Author
item Leonard, Kurt

Submitted to: British Society of Plant Pathology Presidential Meeting
Publication Type: Abstract Only
Publication Acceptance Date: December 12, 1995
Publication Date: N/A

Technical Abstract: Race-specific resistance to plant pathogens often exists in highly polymorphic gene-for-gene relationships. Patterns of variation for resistance and virulence in wild systems are consistent with stable rather than transient polymorphisms. I analyzed stability of gene-for-gene polymorphisms in a mathematical model for natural plant-parasite systems. Fitnesses of the avirulent, W(A-), and virulent, W(V-), pathogen genotypes on susceptible and resistant hosts are: W(A,S) = 1, W(V,S) = 1 - k, W(A,R) = 1 - t, and W(V,R) = 1 - k + a, respectively, where k is cost of virulence t is effectiveness of resistance, and a = 0 (hard selection) or a = k (competition) for two versions of the model. Fitnesses of susceptible, W(S-), and resistant, W(R-), host genotypes attacked by avirulent and virulent parasites are: W(S,A) = 1 - sW(A,S), W(R,A) = 1 - c - sW(A,R), W(S,V) = 1 - sW(V,S), and W(R,V) = 1 - c - sW(V,R), where c is cost of resistance and s is loss of host fitness due to disease. Stability of polymorphisms requires a high cost of resistance in the hard selection version of the model, but in the competition version stability is possible even with no cost of resistance. A finite cost of unnecessary virulence is required to prevent fixation of resistance and virulence in both versions of the model. Allowing limited parasite migration between two niches with dissimilar disease severity increases the range of parameter combinations that allow stable polymorphisms and speeds the approach of gene frequencies to equilibrium. Polymorphisms were most stable with 3-5% exchange of parasite populations between niches. With parasite migration, frequencies of resistance and virulence approached equilibrium within a few hundred host generations.

Last Modified: 4/16/2014
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