Improved error bounds for genetic distances from DNA sequences

The genetic distance between two DNA sequences may be measured by the average number of nucleotide substitutions per position that has occurred since the two sequences diverged from a common ancestor. Estimates of this quantity can be derived from Markov models for the substitution process, while the variances are estimated using the delta method and confidence intervals calculated assuming normality. However, when the sampling distribution of the estimator deviates from normality, such intervals will not be accurate. For simple one-parameter models of nucleotide substitution, we propose a transformation of normal confidence intervals, which yields an almost exact approximation to the true confidence intervals of the distance estimators. To calculate confidence intervals for more complicated models, we propose the saddlepoint approximation. A simulation study shows that the saddlepoint-derived confidence intervals are a real improvement over existing methods.