Nonrandom Association of Avirulence Loci in Four Disease Resistance Gene System. I. Principles of Determination of Nonrandom Association Type and Pattern and Its Confirmation within Host Groups Having the Same Number of Susceptibility Genes.:I. Principles
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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 [S0, S1, S2, S3 and S4 (subscript is the number of susceptibility genes)]. When, for example, a part of a host genotype S0 (ABCD) was replaced by another host genotype S2 (for example, AB++), that is, (S0→S2), 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 S2, 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 (S2) was changed to S0, the pattern became to be reversed, that is, CNNNNN, NCNNNN, NNNCNN, NNCNNN, NNNNCN and NNNNNC, respectively, in the above example.
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