Dynamics of the B-chromosome polymorphism in rye. I. simulated populations

Abstract

A computer model has been developed to simulate the transmission characteristics of the B chromosomes in rye, and to provide a basis on which to identify, and to understand, the main factors responsible for determining the equilibrium B-frequency levels in open pollinating populations. The model has been devised by expressing the behaviour of the Bs, at various phases of the life cycle, in terms of mathematical equations. These equations contain parameters which determine the behaviour of the Bs at meiosis, pollen grain (and egg cell) mitosis and during the development of gametes and sporophytes. By exploring a range of values for the parameters it has been possible to ascertain that variation in the amount of meiotic elimination of Bs, as well as in their direction rate during nondisjunction in the pollen grain and egg cell, influence the final B-frequency equilibrium. Variation in the rate of nondisjunction on the other hand, affects the number of generations required to attain equilibrium more than the final equilibrium itself. Selection against gametes and plants containing Bs, even at levels which are higher than can reasonably be expected to occur naturally, cannot prevent the accumulation of Bs within populations, provided that high rates of directed nondisjunction are also occurring. The results are discussed in relation to the B chromosome polymorphism in natural populations of rye.