To cite freqpcr in publications use:

Sudo M, Osakabe M (2021). “freqpcr: Estimation of Population Allele Frequency Using qPCR ΔΔCq Measures From Bulk Samples.” Molecular Ecology Resources, n/a(n/a), 0–14. doi: 10.1111/1755-0998.13554,,

Corresponding BibTeX entry:

    title = {freqpcr: Estimation of Population Allele Frequency Using
      qPCR ΔΔCq Measures From Bulk Samples},
    author = {Masaaki Sudo and Masahiro Osakabe},
    journal = {Molecular Ecology Resources},
    year = {2021},
    volume = {n/a},
    number = {n/a},
    pages = {0--14},
    keywords = {confidence interval, group testing, maximum-likelihood
      estimation, R language, real-time polymerase chain reaction},
    doi = {10.1111/1755-0998.13554},
    url =
    eprint =
    abstract = {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.},