Using the simulation model for a four gene system on host-pathogen relationship, we studied the principles included in determination of types (cross- and noncross-types) of nonrandom associations between avirulence loci in a pathogen population. Analyses were carried out by giving some changes in host genotype frequencies which bring equilibrium conditions in frequencies of pathogen genotypes. Determination of types [cross-type (C) and noncross-type (N)] of nonrandom association was conducted by complicated but definite principles. When four avirulence genes (a, b, c and d) and four corresponding virulence ones (+
a, +
b, +
c and +
d) and 16 genotypes consisting of four avirulence loci were considered, definite characteristics on determination of types of nonrandom associations appeared depending on the number of susceptibility genes [S
0, S
1, S
2, S
3 and S
4 (subscript is the number of susceptibility genes)]. When, for example, a part of a host genotype S
0 (ABCD) was replaced by another host genotype S
2 (for example, AB++), that is, (S
0→S
2), nonrandom association patterns, NCCCCC, CNCCCC, CCCNCC, CCNCCC, CCCCNC and CCCCCN, were observed for host genotypes AB++, A+C+, +BC+, A++D, +B+D and ++CD belonging to S
2, respectively. NCCCCC is a nonrandom association type for interactions between avirulence loci, a-b, a-c, a-d, b-c, b-d, and c-d, respectively. For determination of the patterns, there were two cases; in some cases a new host genotype (genotype after the replacement; called receptor, for convenience, in the simulations) gave influence, and in other cases, it was the old host genotype (genotype before replacement; donor in the simulations). In the former cases, combinations of a resistance gene and a susceptibility gene induced a cross-type nonrandom association, and combinations between a resistance gene and another resistance gene and between a susceptibility gene and another susceptibility gene induced noncross-type nonrandom association. In contrast, when a host genotype (S
2) was changed to S
0, the pattern became to be reversed, that is, CNNNNN, NCNNNN, NNNCNN, NNCNNN, NNNNCN and NNNNNC, respectively, in the above example.
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