Modelling mitochondrial site polymorphisms to infer the number of segregating units and mutation rate

We present a mathematical model of mitochondrial inheritance evolving under neutral evolution to interpret the heteroplasmies observed at some sites. A comparison of the levels of heteroplasmies transmitted from mother to her offspring allows us to estimate the number N_x of inherited mitochondrial genomes (segregating units). The model demonstrates the necessity of accounting for both the multiplicity of an unknown number N_x, and the threshold θ, below which heteroplasmy cannot be detected reliably, in order to estimate the mitochondrial mutation rate μ_m in the maternal line of descent. Our model is applicable to pedigree studies of any eukaryotic species where site heteroplasmies are observed in regions of the mitochondria, provided neutrality can be assumed. The model is illustrated with an analysis of site heteroplasmies in the first hypervariable region of mitochondrial sequence data sampled from Adélie penguin families, providing an estimate N_x and μ_m. This estimate of μ_m was found to be consistent with earlier estimates from ancient DNA analysis.