Bias-corrected paralinear and LogDet distances and tests of molecular clocks and phylogenies under nonstationary nucleotide frequencies

The statistical properties of the paralinear and LogDet distances under nonstationary nucleotide frequencies were studied. First, we developed formulas for correcting the estimation biases of the paralinear and LogDet distances, i.e., the bias-corrected distance is estimated by (d) over cap(c) = (d) over cap - 2var((d) over cap), where (d) over cap and var((d) over cap) are the estimated distance and sampling variance, respectively. The performances of these formulas and the formulas for sampling variances were examined by computer simulation. Second, we developed a method for estimating the variance-covariance matrix of paralinear distances, so that statistical tests of DNA phylogenies can be conducted in the nonstationary case. Third, a new LogDet-based method for testing the molecular clock hypothesis was developed under nonstationary nucleotide frequencies.