MEIOSIS .V. MATRIC AND PATH COEFFICIENT SOLUTIONS OF TRI- AND QUADRIVALENTS

Possible classes of spatial ordering between chromosomal components of multivalents and their motion with respect to each other are deduced on the basis of the propositions: (A) that the proximity of centromeres, or similar reference centers, to each other determines which chromosomes are to migrate to opposite poles, irrespective of homology and (B) that segregation from multivalents proceeds as a Markov process consisting of at least three steps taking place during or prior to metaphase I. Segregation matrices constructed from data on the (relative) poles to which chromosomes in a quadrivalent may proceed, taken together with proposition (A), permit deducing possible classes of spatial ordering between elements within multivalents early in meiotic prophase. Transient and ergodic states of centromere ordering are compared to resonance interaction between electrons within single molecules. Outcomes deduced by the method here correspond with many of those proposed in the literature, but some do not. Some of the conclusions are as follows. For trivalents, any one of the three centromeres, or similar reference points, may locate geometrically between the other two early in meiotic prophase and coorient with them both. In some types of quadrivalents the four reference points (centromeres, for example) first separate into cooriented pairs (= presegregation) each of which then segregates independently, or not, of the other pair. In some segregation modes of other quadrivalent types, three of the four centromeres evidently behave as a trivalent, coorienting and segregating independently of the fourth element. It is argued that structures known to be present during later states of meiosis (e.g. chiasmata) cannot, alone, account for observed segregation ratios. © 1968 Martinus Nijhoff.