Comparison of mode estimation methods and application in molecular clock analysis

BACKGROUND: Distributions of time estimates in molecular clock studies are sometimes skewed or contain outliers. In those cases, the mode is a better estimator of the overall time of divergence than the mean or median. However, different methods are available for estimating the mode. We compared these methods in simulations to determine their strengths and weaknesses and further assessed their performance when applied to real data sets from a molecular clock study. RESULTS: We found that the half-range mode and robust parametric mode methods have a lower bias than other mode methods under a diversity of conditions. However, the half-range mode suffers from a relatively high variance and the robust parametric mode is more susceptible to bias by outliers. We determined that bootstrapping reduces the variance of both mode estimators. Application of the different methods to real data sets yielded results that were concordant with the simulations. CONCLUSION: Because the half-range mode is a simple and fast method, and produced less bias overall in our simulations, we recommend the bootstrapped version of it as a general-purpose mode estimator and suggest a bootstrap method for obtaining the standard error and 95% confidence interval of the mode.