An exact version of Hunt's ancestor-descendant directional random walk parameterization
- 1University of South-Eastern Norway
Abstract
Hunt's ancestor-descendant parameterization for fitting of 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 adjacent trait differences share a trait mean value and its sampling error, and ignorance of this fact may give large errors in the estimated step size. 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. This results in a tridiagonal covariance matrix instead of Hunt s diagonal matrix, and the estimated step sizes, and thus prediction slopes, in cases where the estimated step variance is zero will then be identical to those found by weighted least squares estimation.
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BibTeX
@misc{ergon2026exact,
title = {{An exact version of Hunt's ancestor-descendant directional random walk parameterization}},
author = {R. Ergon},
howpublished = {bioRxiv},
year = {2026},
month = aug,
doi = {10.64898/2026.08.21.746177},
url = {https://www.biorxiv.org/content/10.64898/2026.08.21.746177v2},
note = {CC BY},
}
RIS
TY - UNPB
TI - An exact version of Hunt's ancestor-descendant directional random walk parameterization
AU - R. Ergon
PY - 2026
DA - 2026/08/21
PB - bioRxiv
DO - 10.64898/2026.08.21.746177
UR - https://www.biorxiv.org/content/10.64898/2026.08.21.746177v2
AB - Hunt's ancestor-descendant parameterization for fitting of 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 adjacent trait differences share a trait mean value and its sampling error, and ignorance of this fact may give large errors in the estimated step size. 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. This results in a tridiagonal covariance matrix instead of Hunt s diagonal matrix, and the estimated step sizes, and thus prediction slopes, in cases where the estimated step variance is zero will then be identical to those found by weighted least squares estimation.
ER -