On the causes of evolutionary transition:transversion bias

Arlin Stoltzfus; Ryan W. Norris

As explained above, we can define a measure of effect-size with intuitive properties that we designate as AUC, based on an application of ROC analysis that may not be . CC-BY 4.0 International license is made available under a The copyright holder for this preprint (which was not peer-reviewed) is the author/funder. It . https://doi.org/10.1101/027722 doi: bioRxiv preprint obvious. In ROC analysis of a binary classifier, each instance has a binary state (e.g., disease vs. non-disease), and the classifier makes a ranking of instances and predicts the binary state based on a threshold. The ROC curve plots the true-positive rate against the false-negative rate, and the area under this curve is equivalent to the chance that a randomly chosen positive instance is ranked higher than a randomly chosen negative one (Hanley and McNeil 1982) . If we treat the fitness study as the classifier that supplies a ranking for each mutant, and the conservative-radical distinction as the binary state of a mutant, then the AUC is the chance that a mutant of a nominally conservative type has a higher fitness than a randomly chosen mutant of a nominally radical type. The relationship of AUC to the Wilcoxon-Mann-Whitney test is explained by Manley (1982) . Calculating AUC from the test statistic is an algebraic conversion based on the formula AUC = (pairs -WMW_statistic(x, y)) / pairs, where x and y are vectors representing the two samples, and pairs = length(x) * length(y). This formula applies specifically to wilcox.test in the R "stats" package (some other implementations define the test statistic in a different way).