freqpcr: Estimation of population allele frequency using qPCR ΔΔCq measures from bulk samples

PCR techniques, both quantitative (qPCR) and nonquantitative, have been used to estimate the frequency of a specific allele in a population. However, the labour required to sample numerous individuals and subsequently handle each sample renders the quantification of rare mutations (e.g., pesticide resistance gene mutations at the early stages of resistance development) challenging. Meanwhile, pooling DNA from multiple individuals as a "bulk sample" combined with qPCR may reduce handling costs. The qPCR output for a bulk sample, however, contains uncertainty owing to variations in DNA yields from each individual, in addition to measurement errors. In this study, we have developed a statistical model to estimate the frequency of the specific allele and its confidence interval when the sample allele frequencies are obtained in the form of ΔΔCq in the qPCR analyses on multiple bulk samples collected from a population. We assumed a gamma distribution as the individual DNA yield and developed an R package for parameter estimation, which was verified using real DNA samples from acaricide-resistant spider mites, as well as a numerical simulation. Our model resulted in unbiased point estimates of the allele frequency compared with simple averaging of the ΔΔCq values. The confidence intervals suggest that dividing the bulk samples into more parts will improve precision if the total number of individuals is equal; however, if the cost of PCR analysis is higher than that of sampling, increasing the total number and pooling them into a few bulk samples may also yield comparable precision.