Previous estimates of mitochondrial DNA mutation level variance did not account for sampling error: comparing the mtDNA genetic bottleneck in mice and humans

Abstract

In cases of inherited pathogenic mitochondrial DNA (mtDNA) mutations, a mother and her offspring generally have large and seemingly random differences in the amount of mutated mtDNA that they carry. Comparisons of measured mtDNA mutation level variance values have become an important issue in determining the mechanisms that cause these large random shifts in mutation level. These variance measurements have been made with samples of quite modest size, which should be a source of concern because higher-order statistics, such as variance, are poorly estimated from small sample sizes. We have developed an analysis of the standard error of variance from a sample of size n, and we have defined error bars for variance measurements based on this standard error. We calculate variance error bars for several published sets of measurements of mtDNA mutation level variance and show how the addition of the error bars alters the interpretation of these experimental results. We compare variance measurements from human clinical data and from mouse models and show that the mutation level variance is clearly higher in the human data than it is in the mouse models at both the primary oocyte and offspring stages of inheritance. We discuss how the standard error of variance can be used in the design of experiments measuring mtDNA mutation level variance. Our results show that variance measurements based on fewer than 20 measurements are generally unreliable and ideally more than 50 measurements are required to reliably compare variances with less than a 2-fold difference.

Figure 1

Measurements of the Mean and Variance from Samples Drawn from a Normal Distribution (A) The normal distribution used with mean = 0.5 and variance = 0.01. (B) Mean values as a function of the sample size n ranging from 3 to 100. The error bars were set to twice the standard error of the mean as calculated from Equation 1. (C) Values of variance as a function of the sample size n. The error bars were set to twice the standard error of the variance for a normal distribution as calculated from Equation 6. The 95% confidence intervals were determined from the mean and variance values from 10,000 samples of size n.

Figure 2

Measurements of the Mean and Variance from Samples Drawn from a Kimura Distribution with Moderate Mean Value (A) The Kimura distribution ϕ(p) used with mean p₀ = 0.5 and b = 0.9. (B) Mean values as a function of the sample size n ranging from 3 to 100. The error bars were set to twice the standard error of the mean as calculated from Equation 1. (C) Values of variance as a function of the sample size n. The error bars were set to twice the standard error of the variance for a Kimura distribution as calculated from Equations 11 and 2. The 95% confidence intervals were determined from the mean and variance values from 10,000 independent samples of size n.

Figure 3

Measurements of the Mean and Variance from Samples Drawn from a Kimura Distribution with an Extreme Mean Value (A) The Kimura distribution ϕ(p) used with mean p₀ = 0.1 and b = 0.9. (B) Mean values as a function of the sample size n ranging from 3 to 100. The error bars were set to twice the standard error of the mean as calculated from Equation 1. (C) Values of variance as a function of the sample size n. The error bars were set to twice the standard error of the variance for a Kimura distribution as calculated from Equations 11 and 2. The 95% confidence intervals were determined from the mean and variance values from 10,000 samples of size n.

Figure 4

Application of the Standard Error of Variance to Data from Human and Mouse Models (A) Heteroplasmic mouse model data from Jenuth et al. (circles) at four stages of mtDNA inheritance: primordial germ cells (PGC), primary oocytes, mature oocytes, and offspring. Human data (stars) from Brown et al. for primary oocytes and from numerous sources for offspring data are compared to the mouse data. (B) mtDNA mutation level variance with error bars measured in 21 mouse lineages. All error bars are twice the standard error calculated from a Kimura distribution. Variance values are normalized by dividing by p₀(1 − p₀).

Figure 5

mtDNA Mutation Level Variance with Error Bars in a Mouse Model of the Postnatal Development of Oocytes The data are taken from Wai et al. and all error bars are twice the standard error of variance calculated from a Kimura model. Variance values are normalized by dividing by p₀(1 − p₀).

Figure 6

Levene Test p Values for Comparisons of Two Data Sets with Different Variances but Equal Mean Mutation Levels of 0.5 Both data sets were drawn randomly from a Kimura distribution. The distribution for the first data set was set to have b = 0.9 while the value of b for the second distribution was lowered according to Equation 10 to give the stated variance difference. p values were calculated with the standard Levene test. The horizontal line indicates a p value of 0.05. Differences in variance are as follows: (A) 10-fold; (B) 5-fold; (C) 2-fold; (D) 50% increase; (E) equal variance.

Figure 7

Levene Test p Values for Comparisons of Two Data Sets with Different Variances but Equal Mean Mutation Levels of 0.1 Other details are the same as in Figure 6.

Figure 8

Dependence of the Standard Error of Variance Divided by the Variance on the Mean mtDNA Mutation Level p₀ and on the Sample Size n (A) Dependence on the sample size n for three values of the mean mutation level. (B) Dependence on the mean mutation level for a range of sample sizes. All standard error values are calculated for a Kimura distribution from Equations 11 and 2. All curves were calculated from Equations 11 and 2 with a value of b = 0.9. That b value was chosen as a simple value that was close to the b value calculated from the one human oocyte data set.