update SiteModel/gammaCategoryCount

_pages/hmc/SiteModel/gammaCategoryCount.md

@@ -19,8 +19,15 @@ A generally used number of categories is 4 when gamma rate heterogeneity is desi
 When running the gamma rate heterogeneity model, keep an eye out on the estimate of the shape parameter: if it is large (>16) this indicates there is almost no rate heterogeneity in the data, and using the model just wastes computation.
 
 
+A recent paper by Ferretti et al (2024) points out that the discretised gamma model with 4 categories can show biases in root age estimates, due to the gamma model not being able to capture the rates in the tail accurately.
+I found that increasing to 8 categories resolved the problem for their set-up.
+When finding small shape parameter estimates, it may be useful to rerun the analysis with more categories and check whether age estimates are sensitive t the category count.
+
+
 ## References
 
+Ferretti L, Golubchik T, Di Lauro F, Ghafari M, Villabona-Arenas J, Atkins KE, Fraser C, Hall MD. Biased estimates of phylogenetic branch lengths resulting from the discretised Gamma model of site rate heterogeneity. bioRxiv. 2024:2024-08. <a href="https://doi.org/10.1101/2024.08.01.606208">do:10.1101/2024.08.01.606208</a>
+
 Shapiro B, Rambaut A, Drummond AJ. Choosing appropriate substitution models for the phylogenetic analysis of protein-coding sequences. Molecular biology and evolution. 2006 Jan 1;23(1):7-9. <a href="http://doi.org/10.1093/molbev/msj021">doi:10.1093/molbev/msj021</a>.
 
 Yang Z. Maximum likelihood phylogenetic estimation from DNA sequences with variable rates over sites: approximate methods. Journal of Molecular evolution. 1994 Sep;39(3):306-14. <a href="http://doi.org/10.1007/BF00160154">doi:10.1007/BF00160154</a>.