An exact version of Hunt’s ancestor-descendant directional random walk model

Hunt’s ancestor-descendant (AD) method for fitting evolutionary models to empirical paleontological sequences assumes independent log-likelihoods for the transitions between populations (Hunt, 2006). This is not quite correct, as he also pointed out in his paper. The reason is that trait differences in adjacent transitions are correlated, and ignorance of this fact may give large errors in the estimated parameter and Akaike Information Criterion (AIC) values. Here, the problem is solved by use of the N − 1 – dimensional normal density for a random vector, where N is the number of samples. The exact AD model has a tridiagonal trait covariance matrix instead of Hunt’s diagonal matrix, and the estimated prediction slopes in cases where the estimated random component is zero will then be identical to those found by weighted least squares estimation.