Starless bias and parameter-estimation bias in the likelihood-based phylogenetic method

Abstract

I analyzed various site pattern combinations in a 4-OTU case to identify sources of starless bias and parameter-estimation bias in likelihood-based phylogenetic methods, and reported three significant contributions. First, the likelihood method is odd in that it may not generate a star tree with sequences that are equidistant from each other. This behaviour, dubbed starless bias, happens in a 4-OTU tree when there is an excess (i.e., more than expected from a star tree and a substitution model) of conflicting phylogenetic signals supporting the three resolved topologies equally. Special site pattern combinations leading to rejection of a star tree, when sequences are equidistant from each other, were identified. Second, fitting gamma distribution to model rate heterogeneity over sites is strongly confounded with tree topology, especially in conjunction with the starless bias. I present examples to show dramatic differences in the estimated shape parameter α between a star tree and a resolved tree. There may be no rate heterogeneity over sites (with the estimated α > 10000) when a star tree is imposed, but α < 1 (suggesting strong rate heterogeneity over sites) when an (incorrect) resolved tree is imposed.Thus, the dependence of "rate heterogeneity" on tree topology implies that "rate heterogeneity"is not a sequence-specific feature, cautioning against interpreting a small α to mean that some sites are under strong purifying selection and others not. Thirdly, because there is no existing (and working) likelihood method for evaluating a star tree with continuous gamma-distributed rate, I have implemented the method for JC69 in a self-contained R script for a four-OTU tree (star or resolved), in addition to another R script assuming a constant rate over sites. These R scripts should be useful for teaching and exploring likelihood methods in phylogenetics.

Major Revisions in Arthropod Phylogeny Through Improved Supermatrix, With Support for Two Possible Waves of Land Invasion by Chelicerates

“…Arthropod phylogeny has been controversial. The deep divergence can lead to equally supported trees leading to phylogenetic distortion 1,2 and rapid radiation in some lineages such as Arachnida results in short branch lengths that are difficult to resolve. 3,4 However, much of the controversy is due to diverse types of data that have been used, including molecular data ranging from rRNA to protein-coding genes from nuclear or mitochondrial source, and morphological characters based on fossils or on various developmental stages of extant organisms.…”