Abstract
A long-standing goal in the field of polyploid biology has been the derivation of mathematical models of gamete mode formation. These models form the basis of statistical inference and evolutionary theory. Here, we present 3-locus models of gamete mode formation in autotetraploids without and with preferential cross-over formation. The three loci are assumed to occur on one arm of the same chromosome. For preferential cross-over formation, one of the three loci affects the tendency for sets of sister chromatids to pair and therefore affects rates of recombination. The models are derived such that the process of double reduction is a function of rates of synaptic partner switches and recombination, as opposed to being independent of these processes. We assume potentially one synaptic partner switch per meiosis. We also assume the coefficient of coincidence is one, such that cross-over events are independent, given a set of cross-over rates. Illustrative cases are examined demonstrating differences in the gamete mode probabilities without and with preferential cross-over formation. Lastly, we explore the accuracy of maximum likelihood estimates of the probability of synaptic partner switches and preferential cross-over formation when the locus controlling preference is at a proximal, middle, or distal location on the chromosome arm. All Supplementary Information is available at https://github.com/ckgriswold/3-locus-autotetraploid-meiosis .