An extension of the Cx(Co)m model of crossover patterning to account for experimental mortality in Drosophila melanogaster
Classic recombination experiments designed to test genetic and environmental treatments do not directly measure crossing-over, instead rates and distribution of meiotic events in F1 meiocytes is inferred from genetic markers in F2 adults. In Drosophila melanogaster females this procedure introduces a substantial "missing data problem" because 75% of meiotic chromatids segregate to polar body nuclei and another 11% are transmitted to inviable F2 zygotes which cannot be scored for recombination. To address these sources of uncertainty and bias we extend the Cx(Co)m model of the data-generating process by assuming: 1) programmed double strand breaks occur as a Poisson point process, 2) crossover maturation is a stationary renewal process, 3) chromosome segregation is random one-half thinning of this process, 4) fertilization by X-versus Y-bearing sperm is mendelian, and 5) egg-to-adult survival is binomially distributed with a rate parameter determined by F2 marker alleles. To quantify experimental mortality, we performed egg counts in a 6-point X chromosome testcross and marker-free controls on identical genetic backgrounds under standard laboratory conditions. The 19,927 fly dataset reveals 44% F2 experimental mortality, and likelihood ratio tests support a model where 36 of the 44% is due to sex-specific, marker-associated viability defects. Variability in X chromosome genetic lengths with experimental mortality can be simulated and we provide case-control 80% power curves to guide experimental design. We propose that differential mortality should be the de facto null hypothesis when comparing F2 recombinant fractions and provide probabilistic models of the data-generating process to improve characterization of patterns in F1 meiotic events.