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

Abstract

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 , below which heteroplasmy cannot be detected reliably, in order to estimate the mitochondrial mutation rate mu(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 mu(m). This estimate of mu(m) was found to be consistent with earlier estimates from ancient DNA analysis.

Figure 1

Values of ${(Q_{N_x})}_{i,1}$ (written as ${\text{per}}_{N_x}$), the expected number of generations a site heteroplasmy persists, and of ${\text{obs}}_{N_x}(0.23)$, the expected number of generations the site heteroplasmy are observable with threshold θ=0.23 (plotted on a logarithmic scale). Note that ${\text{obs}}_{N_x}(\theta )$ converges to the constant value 2 ln(θ⁻¹−1)=2.417 (dotted line), while ${\text{per}}_{N_x}$ (solid line) grows logarithmically as N_x increases.

Figure 2

The values of per₂₀(i), (a) for i=2, …, 19, and per₄₀(i), (b) for i=2, …, 39, are plotted as dots. The solid lines are the curves 2/i. The shaded regions are outside the detection threshold for θ=0.23 with the observable region (unshaded) between them. We note that in both observed regions the points ${\text{per}}_{N_x}(i)$ fit the curve 2/i closely.