We model the evolutionary dynamics of mitochondrial mutations in the cytoplasm of a single cell by a Wright Fisher process (Wright, 1931), in which the number of mitochondria in a subsequent generation is a binomial sample of the mitochondria in the previous generation.
This integral has a closed-form solution with f (p t | x 0, N N e ) being a beta distribution and the binomial sampling of f (x t | p t ).
The function V x) is the variance in allele frequency after one generation of binomial sampling of N alleles [ 27].
The 'platform noise' of DArT assays, estimated by comparing two identical aliquots of a DNA mixture, was significantly lower than the 'pooling noise' reflecting the binomial sampling variance of the bulking process.
With the assumption that segregating alleles are at equilibrium and conditioned on observing a segregating allele using binomial sampling, the probability of sampling a deleterious allele more than once among 44 chromosomes is around 2.1% (the probability of sampling nonsingletons divided by the probability of sampling a segregating allele at least once).
If we wish to replace N by sample size n, the binomial sampling error of n has to be accounted in the calculation of the variance.
We then considered multiple herds under binomial sampling with the primary goal of estimating the prevalence distribution and the proportion of infected herds.
First, we compared the observed proportion of significant genes in each GO term to an expected number, which is the binomial sampling probability of sampling an equal or larger number of genes in each category given the number of significant genes in the genome.
To reduce the random binomial sampling noise of two alleles introduced by sequencing, the smoothed G test (G′ test) (Magwene et al. 2011) was performed at each SNP marker position with a sliding window of 9 Mb (∼36 cM as determined in Results section) and the tri-cube weight function (Cleveland 1979).
The validity of assuming a negative binomial sampling distribution for the consumption data was checked by comparing cumulative left probabilities for each datum, computed from its corresponding predictive distribution, with the negative binomial distribution (QQ plot).
