Neutrality tests for sequences with missing data

Missing data are common in DNA sequences obtained through high-throughput sequencing. Furthermore, samples of low quality or problems in the experimental protocol often cause a loss of data even with traditional sequencing technologies. Here we propose modified estimators of variability and neutrality tests that can be naturally applied to sequences with missing data, without the need to remove bases or individuals from the analysis. Modified statistics include the Watterson estimator θ(W), Tajima's D, Fay and Wu's H, and HKA. We develop a general framework to take missing data into account in frequency spectrum-based neutrality tests and we derive the exact expression for the variance of these statistics under the neutral model. The neutrality tests proposed here can also be used as summary statistics to describe the information contained in other classes of data like DNA microarrays.