Meiotic pairing in autohexaploid Lathyrus: a mathematical model

Abstract

A mathematical meiotic pairing and chiasma model is described for a hexaploid. It estimates, on the basis of observations on chromosome associations at metaphase I of meiosis, the frequencies of initial hexavalent, quadrivalent and bivalent pairing, as well as the frequency of chiasmate association of the two chromosome arms, both after multivalent and after bivalent pairing. These estimates use all nine degrees of freedom available (10 configuration types distinguished). Although potential complications like multiple pairing partner exchange and interstitial chiasma formation are not accommodated by the model, a very close fit is found between the configuration frequencies observed in Lathyrus palustris (2n = 6x = 42) and those reconstructed on the basis of the model. This does not necessarily imply that the model fully represents biological reality, but at least it shows that the arms are significantly different in respect of chiasma formation and that chiasma frequencies may differ between multivalent and bivalent pairing. The hexavalent pairing frequency, as estimated by correcting metaphase frequencies for failure of chiasma formation, was only slightly lower than theoretically expected for an autohexaploid. However, the pairing of the six homologous chromosomes as a quadrivalent + a bivalent was considerably lower than with random pairing. The frequency of pairing as three bivalents was correspondingly higher.