An extension of the <i>Cx(Co)</i> ^<i>m</i> model of crossover patterning to account for experimental mortality in <i>Drosophila melanogaster</i>

Classic recombination experiments designed to test genetic and environmental treatments do not directly measure crossing-over, instead rates and distribution of meiotic events in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:msub><mml:mi>F</mml:mi> <mml:mn>1</mml:mn></mml:msub> </mml:mrow> </mml:math> meiocytes is inferred from genetic markers in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:msub><mml:mi>F</mml:mi> <mml:mn>2</mml:mn></mml:msub> </mml:mrow> </mml:math> adults. In <i>Drosophila melanogaster</i> 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:msub><mml:mi>F</mml:mi> <mml:mn>2</mml:mn></mml:msub> </mml:mrow> </mml:math> zygotes which cannot be scored for recombination. To address these sources of uncertainty and bias we extend the <i>Cx(Co)</i> ^<i>m</i> 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:msub><mml:mi>F</mml:mi> <mml:mn>2</mml:mn></mml:msub> </mml:mrow> </mml:math> 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% <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:msub><mml:mi>F</mml:mi> <mml:mn>2</mml:mn></mml:msub> </mml:mrow> </mml:math> 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 <i>de facto</i> null hypothesis when comparing <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:msub><mml:mi>F</mml:mi> <mml:mn>2</mml:mn></mml:msub> </mml:mrow> </mml:math> recombinant fractions and provide probabilistic models of the data-generating process to improve characterization of patterns in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:msub><mml:mi>F</mml:mi> <mml:mn>1</mml:mn></mml:msub> </mml:mrow> </mml:math> meiotic events.