2010/12/29 by Peter J. Waddell, Xi Li Tan, Waddell, Peter J. +4
Biochemistry, Genetics and Molecular Biology · Earth and Planetary Sciences · #Evolution and Paleontology Studies #FOS: Biological sciences #Genetic diversity and population structure #Genomics (q-bio.GN) #Genomics and Phylogenetic Studies #Populations and Evolution (q-bio.PE)
paper · pdf · doi:10.48550/arxiv.1012.5882
openalex publication_date 2010/12/29 · openalex created_date 2022/09/15 · openalex updated_date 2026/07/28
The method of flexi-Weighted Least Squares on evolutionary trees uses simple\npolynomial or exponential functions of the evolutionary distance in place of\nmodel-based variances. This has the advantage that unexpected deviations from\nadditivity can be modeled in a more flexible way. At present, only polynomial\nweights have been used. However, a general family of exponential weights is\ndesirable to compare with polynomial weights and to potentially exploit recent\ninsights into fast least squares edge length estimation on trees. Here describe\nfamilies of weights that are multiplicative on trees, along with measures of\nfit of data to tree. It is shown that polynomial, but also multiplicative\nweights can approximate model-based variance of evolutionary distances well.\nBoth models are fitted to evolutionary data from yeast genomes and while the\npolynomial weights model fits better, the exponential weights model can fit a\nlot better than ordinary least squares. Iterated least squares is evaluated and\nis seen to converge quickly and with minimal change in the fit statistics when\nthe data are in the range expected for the useful evolutionary distances and\nsimple Markov models of character change. In summary, both polynomial and\nexponential weighted least squares work well and justify further investment\ninto developing the fastest possible algorithms for evaluating evolutionary\ntrees.\n