Measuring Fit of Sequence Data to Phylogenetic Model: Gain of Power using Marginal Tests

TL;DR

This paper evaluates how well phylogenetic models fit sequence data, demonstrating that marginalized tests reveal significant deviations from model assumptions, thus questioning the reliability of many current phylogenetic inferences.

Contribution

It introduces marginalized likelihood ratio tests that improve power to detect model misfit in phylogenetics, highlighting widespread deviations from model assumptions.

Findings

General tests do not reject data-model fit (p~0.5)

Marginalized tests strongly reject common phylogenetic models (p<0.001)

Sequences are not stationary in nucleotide composition

Abstract

Testing fit of data to model is fundamentally important to any science, but publications in the field of phylogenetics rarely do this. Such analyses discard fundamental aspects of science as prescribed by Karl Popper. Indeed, not without cause, Popper (1978) once argued that evolutionary biology was unscientific as its hypotheses were untestable. Here we trace developments in assessing fit from Penny et al. (1982) to the present. We compare the general log-likelihood ratio (the G or G2 statistic) statistic between the evolutionary tree model and the multinomial model with that of marginalized tests applied to an alignment (using placental mammal coding sequence data). It is seen that the most general test does not reject the fit of data to model (p~0.5), but the marginalized tests do. Tests on pair-wise frequency (F) matrices, strongly (p < 0.001) reject the most general phylogenetic (GTR) models commonly in use. It is also clear (p < 0.01) that the sequences are not stationary in their nucleotide composition. Deviations from stationarity and homogeneity seem to be unevenly distributed amongst taxa; not necessarily those expected from examining other regions of the genome. By marginalizing the 4t patterns of the i.i.d. model to observed and expected parsimony counts, that is, from constant sites, to singletons, to parsimony informative characters of a minimum possible length, then the likelihood ratio test regains power, and it too rejects the evolutionary model with p << 0.001. Given such behavior over relatively recent evolutionary time, readers in general should maintain a healthy skepticism of results, as the scale of the systematic errors in published analyses may really be far larger than the analytical methods (e.g., bootstrap) report.