We calculate the probability of a list-gene pair for being connected as the cumulative binomial probability of the list-gene pair being chosen at least once in the process of randomly reconnecting the edges.
The probability under the heterozygous model was calculated as the binomial probability of the observed counts assuming a probability of 0.5 for each allele.
The probability under the homozygous model was calculated as the binomial probability of the observed counts assuming that the less frequent allele was an error with a probability of 0.01 with the more common allele having a probability of 0.99.
We calculate the binomial probability of the number of mutations from amino acid X to Y vs Y to X, given the average ratio between X to Y and Y to X in the whole Sordariomycetes tree.
The normal distribution can be used to approximate the binomial probabilities of B l (i) when M is large: If (tilde {mathbf {a}}_{i}^{(l)} in mathcal {C}^{perp }): hspace*{60pt}B_{l}(i rightarrow mathcal{N}left(mu_{0},{sigma_{0}^{2}}right) (9) If (tilde {mathbf {a}}_{i}^{(l)} notin mathcal {C}^{perp }): hspace*{60pt}B_{l}(i rightarrow mathcal{N}left(mu_{1},{sigma_{1}^{2}}right) (10).
Each state is defined in the HMM by the binomial probability of observing the number of reads aligned to each base from the infected sample, given the total number of reads that align to each base; because the number of reads that map from the infected and naïve samples is not equal, the binomial probably for the unregulated class is not expected to be 0.50 (Table 1; see Methods for details).
The correlation score was measured using -log(P) for correlation and log(P) for anti-correlation, where P is the p-value corresponding to the binomial probability of observing the corresponding frequency shift [ 15].
A cumulative binomial probability of observing the given number of the oligomer or more in each cluster was then computed as follows: F x | n, p = 1 − ∑ i = 0 x − 1 i n p i 1 − p n − i, where x is the number of occurrences of the oligomer, n is the sample size, i.e. sequence length - oligomer size + 1, and p is the probability of observing such an oligomer in the random background sequence.
We statistically evaluated normalization efficiency by calculating the exact binomial probability of obtaining the observed number of counts of a particular gene by chance alone.
For deciding competitiveness, we tested the null hypothesis that the binomial probability of each of the two competing strategies being washed out was equal, i.e. 50 50.
