Under our triplet method, we aim to estimate the true rate of nucleotide substitution, p ij , between sequences s i and s j with an unobserved error δ ij . With respect to outgroup sequence k, an unbiased estimate is where the factor corrects for bias resulting from the time sampling error structure (see Appendix for derivation). We superscript to denote its weak dependence on outgroup sequence k. Dependence is weak as the path of evolution from t k to α is shared between the paths from sequence k to both sequence i and sequence j and hence largely cancels out in Equation 1. We make this transparent in the following derivation. For brevity, we consider only unobservable true values, ignoring error terms. Let u be the location on the triplet in Figure 1 corresponding to time α and let p xy be the true rate along the path connecting locations x and y. Then, as distance is rate multiplied by time, we have