Segregation ratios withinSegregation Distorterlines ofDrosophila melanogasterconform to a beta-binomial distribution

Abstract

SummarySegregation Distorter(SD) chromosomes are preferentially recovered fromSD/SD+males due to the dysfunction of sperm bearing theSD+chromosome. The proportion of offspring bearing theSDchromosome is given the symbolk. The nature of the frequency distribution ofkwas examined by comparing observedkdistributions produced by six differentSDchromosomes, each with a different mean, withkdistributions predicted by two different statistical models. The first model was one where thekof all males with a givenSDchromosome were considered to be equal prior to the determination of those gametes which produce viable zygotes. In this model the only source of variation ofkwould be binomial sampling. The results rigorously demonstrated for the first time that the observedkdistributions did not fit the prediction that the only source of variation was binomial sampling. The next model tested was that the prior distribution of segregation ratios conformed to a beta distribution, such that the distribution ofkwould be a beta-binomial distribution. The predicted distributions of this model did not differ significantly from the observed distributions ofkin five of the six cases examined. The sixth case probably failed to fit a beta-binomial distribution due to a major segregating modifier. The demonstration that the prior distribution of segregation ratios ofSDlines can generally be approximated with a beta distribution is crucial for the biometrical analysis of segregation distortion.