NUCLEAR-CYTOPLASMIC MALE-STERILITY - SINGLE-POINT EQUILIBRIA VERSUS LIMIT-CYCLES

The evolutionary dynamics of nuclear-cytoplasmic male sterility in a gynodioecious, self-incompatible species was examined through computer simulations of a deterministic model. In the model, two cytoplasmic types were assumed, each interacting with a specific, nuclear locus with one restorer and one sterility allele. A plant was male sterile when it was homozygous for the sterility allele at the locus corresponding to the cytoplasmic type it carried. Two additional fitness effects, which are the minimum required for maintenance of the nuclear-cytoplasmic polymorphism, were considered: (1) the female fitness component of females relative to that of hermaphrodites, x, and (2) the cost of restoration, that is, the fitness of plants carrying a restorer gene together with the cytoplasmic type that is not restored by that allele. The parameter related to the cost of restoration, a, was assumed to act on male fertility. Two different types of stable nuclear-cytoplasmic polymorphism were obtained: the well-known single-point equilibria and limit cycles. We show how the occurrence of limit cycles as well as their shape depend on values of x and a. Limit cycles are not a peculiarity of the model used; they also occur when some of the assumptions are relaxed. Models were tested with a acting on female fertility and with recessiveness of the x and a effects of the restorer alleles. All models used were deterministic, but it can be inferred from the mechanism underlying limit cycles that finite populations can, in principle, also show cyclelike behavior, provided that some seed migration between populations occurs. The limit-cycle phenomenon may explain the negative correlation between the two cytoplasmic male-sterility types found in Plantago lanceolata and, more generally, any interpopulation variation in male-sterile frequencies, without invoking any ecological cause.