A viral sampling design for testing the molecular clock and for estimating evolutionary rates and divergence times

Motivation: The high pace of viral sequence change means that variation in the times at which sequences are sampled can have a profound effect both on the ability to detect trends over time in evolutionary rates and on the power to reject the Molecular Clock Hypothesis (MCH). Trends in viral evolutionary rates are of particular interest because their detection may allow connections to be established between a patient's treatment or condition and the process of evolution. Variation in sequence isolation times also impacts the uncertainty associated with estimates of divergence times and evolutionary rates. Variation in isolation times can be intentionally adjusted to increase the power of hypothesis tests and to reduce the uncertainty of evolutionary parameter estimates, but this fact has received little previous attention. Results: We provide approximations for the power to reject the MCH when the alternative is that rates change in a linear fashion over time and when the alternative is that rates differ randomly among branches. In addition, we approximate the standard deviation of estimated evolutionary rates and divergence times. We illustrate how these approximations can be exploited to determine which viral sample to sequence when samples representing different dates are available.