The cytonuclear effects of facultative apomixis - II. Definitions and dynamics of disequilibria in tetraploid populations

We develop a cytonuclear framework for tetraploid populations in which a di allelic nuclear marker exhibits tetrasomic inheritance. This system require s two separate parameterizations, with six cytonuclear disequilibria ( nonr andom associations) in tetraploid individuals and four in their diploid gam etes. Double reduction during meiosis adds further complexity by causing ga metic output to vary with the distance of the nuclear locus from the centro mere. We derive and analyze dynamical solutions for the disequilibria under generalized mixed mating, with any combination of apomixis, selfing, and o utcrossing, with and without double reduction. As in comparable diploid sys tems, all disequilibria ultimately decay to zero, unless nuclear and cytopl asmic alleles are nonrandomly associated and outcrossing is absent, in whic h case permanent associations result. Selfing and apomixis retard the decay of disequilibria (or approach to equilibrium), and often to the same exten t. In contrast, double reduction can accelerate the loss of tetraploid cyto nuclear associations, but only negligibly in hybrid zones, and this loss is never faster than in diploids, Only in the absence of allelic associations or outcrossing is the asymptotic approach to equilibrium differentially af fected by apomixis and selfing or slower under tetrasomic than disomic inhe ritance. To facilitate empirical applications, we also examine tetraploid h ybrid zone dynamics and offer practical guidelines for experimental design and data analysis, showing how the consequences of the mating system alone provide a valuable baseline for drawing evolutionary inferences from the ob served patterns of cytonuclear associations. (C) 2000 Academic Press.