Statistical Methods for Analyzing Drosophila Germline Mutation Rates

Abstract

Most studies of mutation rates implicitly assume that they remain constant throughout development of the germline. However, researchers recently used a novel statistical framework to reveal that mutation rates differ dramatically during sperm development in Drosophila melanogaster. Here a general framework is described for the inference of germline mutation patterns, generated from either mutation screening experiments or DNA sequence polymorphism data, that enables analysis of more than two mutations per family. The inference is made more rigorous and flexible by providing a better approximation of the probabilities of patterns of mutations and an improved coalescent algorithm within a single host with realistic assumptions. The properties of the inference framework, both the estimation and the hypothesis testing, were investigated by simulation. The refined inference framework is shown to provide (1) nearly unbiased maximum-likelihood estimates of mutation rates and (2) robust hypothesis testing using the standard asymptotic distribution of the likelihood-ratio tests. It is readily applicable to data sets in which multiple mutations in the same family are common.

Pattern of Mutation Rates in the Germline of Drosophila melanogaster Males from a Large-Scale Mutation Screening Experiment

“…Using the same notation as Fu (2013), the information conveyed by mutation(s) in a family can be represented by a mutation pattern$\kappa =\langle i,j,k\dots \rangle$in which each element represents a mutation and its value is the number of offspring carrying the mutation, or simply the size of the mutation . After a line obtains a mutation of lethality ≥ d %, a further mutation will likely do nothing or increase the level of lethality, but the effect is usually difficult to distinguish from the first one under our experimental setting.…”

“…The estimate of μ = ( u 1 , … u I ) and statistical tests about them were performed through the maximum likelihood approach developed in Gao et al (2011) and further refined in Fu (2013). The inference makes use of the information about population dynamics, intervals of cell divisions, and coalescent structure of the sample genealogy (Figure 1), but in essence, the inference framework is based on evaluating the likelihood function

Figure 1Population dynamics and an example of the genealogy of four sperm sampled at the time at which maximal 38th cell division has occurred (adapted from Fu 2013).

$L={\displaystyle \prod _f{\displaystyle \prod _{\kappa }{p}_f{\left(\kappa \right)}^{n_f\left(\kappa \right)}}}$where f represents family size, κ is a mutation pattern for a given family size f , n f ( κ ) is the number of occurrences of pattern κ in families of size f , and p f ( κ ) is the probability of mutation pattern κ , which is a function of μ and coefficients that are derived from the dynamics of the germline population.…”

Efficient Estimation of Mutation Rates during Individual Development by Minimization of Chi-Square

“…A recent study [ 1 – 3 ] on the recessive lethal or nearly lethal mutations during the germline development of male Drosophila melanogaster shed some light on this important area of biology. The experimental data reported in Gao et al [ 1 , 3 ] and Fu [ 2 ] were obtained from a large scale mutation accumulation and screening experiment, the basis for which has been refined over the years [ 4 – 6 ]. In general, the germline development of a male Drosophila melanogaster consists of about 36–40 cell divisions, among which the first 14 cell divisions belong to the cleavage stage, the last 5 to spermatogenesis, and those in between to gastrulation and organogenesis.…”

“…In general, the germline development of a male Drosophila melanogaster consists of about 36–40 cell divisions, among which the first 14 cell divisions belong to the cleavage stage, the last 5 to spermatogenesis, and those in between to gastrulation and organogenesis. Gao et al [ 1 , 3 ] and Fu [ 2 ] concluded that the mutation rates in the mature young male Drosophila melanogaster vary significantly during the germline development. In particular, mutation rate for the first cell division is the highest, followed by those during spermatogenesis.…”

“…In particular, mutation rate for the first cell division is the highest, followed by those during spermatogenesis. The framework of statistical inference used in Gao et al [ 1 , 3 ] and Fu [ 2 ] is an approximated maximum likelihood approach, in which, the probability of an observed mutation pattern is approximated and the coefficients necessary for the likelihood computation were obtained through computer simulation based on a newly developed coalescent algorithm [ 1 – 3 , 7 , 8 ] for the germline lineage of male Drosophila melanogaster [ 9 – 11 ].…”