A model of meiotic chromosome association in tetraploids

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Abstract
A model is constructed for chromosome association at meiotic metaphase I in tetraploids. Probabilities are estimated for each pachytene configuration and for subsequent formation of at least one chiasma in each combination of chromosome arms. Long and short arms can differ but are related through an effective arm ratio so as to maintain the same pattern of genomic affinity for both arms. No other a priori assumptions are made about the pattern of genomic affinity, but the same basic assumptions are made as in our preceding model for triploids. The model is statistically overparameterized and therefore has multiple solutions whose range can be found through repeated optimization from different starting points. In some cases the same expected meiotic analysis can arise from quite different genomic structures, which therefore cannot be distinguished on the basis of unmarked chromosomes. Solutions to the model are conveniently expressed in terms of the proportion of metaphase I association due to each pairwise combination of genomes. Interpretation of model solutions is also aided by the use of numerical indices that reflect closeness to 11 particular genomic structures or that reveal properties of the relationship among variables. The model differs from that of Kimber and Alonso in its handling of two chiasmatically bound arms in a randomly pairing homologous group, and frequently as well in its optimized pattern of genomic affinity upon application to 3:1 and 2:1:1 genomic structures. With the aid of the model, genomic affinity is analyzed in 20 individuals, representing hybrids, amphiploids, and species.Key words: polyploidy, genome analysis, preferential pairing, meiotic model.

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