Confidence intervals of evolutionary distances between sequences and comparison with usual approaches including the bootstrap method

Abstract

Two methods are commonly employed for evaluating the extent of the uncertainty of evolutionary distances between sequences: either some estimator of the variance of the distance estimator, or the bootstrap method. However, both approaches can be misleading, particularly when the evolutionary distance is small. We propose using another statistical method which does not have the same defect: interval estimation. We show how confidence intervals may be constructed for the Jukes and Cantor (1969) and Kimura two-parameter (1980) estimators. We compare the exact confidence intervals thus obtained with the approximate intervals derived by the two previous methods, using artificial and biological data. The results show that the usual methods clearly underestimate the variability when the substitution rate is low and when sequences are short. Moreover, our analysis suggests that similar results may be expected for other evolutionary distance estimators.