Statistical analysis of nondisjunction assays in Drosophila

Many advances in the understanding of meiosis have been made by measuring how often errors in chromosome segregation occur. This process of nondisjunction can be studied by counting experimental progeny, but direct measurement of nondisjunction rates is complicated by not all classes of nondisjunctional progeny being viable. For X chromosome nondisjunction in Drosophila female meiosis, all of the normal progeny survive, while nondisjunctional eggs produce viable progeny only if fertilized by sperm that carry the appropriate sex chromosome. The rate of nondisjunction has traditionally been estimated by assuming a binomial process and doubling the number of observed nondisjunctional progeny, to account for the inviable classes. However, the correct way to derive statistics (such as confidence intervals or hypothesis testing) by this approach is far from clear. Instead, we use the multinomial-Poisson hierarchy model and demonstrate that the old estimator is in fact the maximum-likelihood estimator (MLE). Under more general assumptions, we derive asymptotic normality of this estimator and construct confidence interval and hypothesis testing formulae. Confidence intervals under this framework are always larger than under the binomial framework, and application to published data shows that use of the multinomial approach can avoid an apparent type 1 error made by use of the binomial assumption. The current study provides guidance for researchers designing genetic experiments on nondisjunction and improves several methods for the analysis of genetic data.