Preferential pairing estimates from multivalent frequencies in tetraploids

Mathematical models are presented for estimating preferential pairing and chiasma parameters in amphidiploids and autotetraploids on the basis of diakinesis or metaphase I configuration frequencies and are compared with other approaches of estimating affinity. With a preferential pairing factor p, estimated from quadrivalent and trivalent frequencies, and estimated chiasmate association factors for the two arms in quadrivalents (a(qu) and b(qu) for arms A and B, respectively) and in bivalents (a(bi) and b(bi)) a perfect fit between observed and predicted configuration frequencies can often be obtained in amphidiploids of several plant species, including Solanaceae and Gramineae. Since several proven autotetraploids give very similar apparent preferential pairing estimates, the biological significance of such parameters as preferential pairing and affinity factors is considered limited. The same is true for pairing parameters estimated by optimizing fit of configuration frequencies expected on the basis of theoretical models to observed data.