A general treatment of chromosome synapsis in even-numbered polyploids.

Relationships between frequencies of fully paired pachytene configurations are examined for even-numbered polyploids, up to decaploids and beyond. Sequential association is assumed at any given number of equidistant synaptic sites showing uniform propensities for partner exchange. Only with two sites per chromosome, can each configuration represent an equal proportion of the nucleus. In the limit as the number of sites tends to infinity and the intervals between them tend to zero, pachytene multivalent frequency is seen to be a function of bivalent frequency, the minimum number of changes in pairing partner and ploidy. Each type of multivalent may represent the entire nucleus only in the lowest ploidy which can support it, thereafter becoming rare. Sets of homologous multivalents are never likely to be common and large multivalents are expected to be scarce, unless representing maximal configurations. Only bivalents can prevail at every even-numbered ploidy level. At constant bivalent frequency, the transition from discrete to continuous pairing favours the largest type of multivalent. These deductions provide a basis for investigations of the mechanics of chromosome synapsis and may lead to a comprehensive theory of genome analysis.