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

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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 (Unended quest: an intellectual autobiography. Fontana, London, 1976) once argued that evolutionary biology was unscientific as its hypotheses were untestable. Here we trace developments in assessing fit from Penny et al. (Nature 297:197–200, 1982) to the present. We compare the general log-likelihood ratio (the G or G 2 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 pairwise 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 trees may really be far larger than the analytical methods (e.g., bootstrap) report.

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Acknowledgments

This work was supported by NIH Grant 5R01LM008626 to PJW. Thanks to Mike Steel for helpful discussions.

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Authors and Affiliations

  1. Department of Biological Sciences, Purdue University, West Lafayette, IN, 47906, USA

    Peter J. Waddell

  2. Allan Wilson Center for Ecology and Evolution, Massey University, Palmerston North, New Zealand

    Peter J. Waddell, Rissa Ota & David Penny

Authors
  1. Peter J. Waddell
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  2. Rissa Ota
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  3. David Penny
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Corresponding author

Correspondence to Peter J. Waddell.

Electronic supplementary material

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The online supplementary material contains the ANSI C-code programs wrtitten by R.O. and a guide to their use

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Appendix 1

Appendix 1

The constraint tree used:

(((((Sus_scrofa,Camelus_dromedarius,((Ovis_canadenensis,Okapia_johnstoni),(Lagenorhynchus_obscurus,Balaenoptera_physalus))),(Equus_grevyi,(Diceros_bicornis,Tapirus_indicus)),(Panthera_uncia,(Phoca_vitulina,Ailurus_fulgens)),(Manis_sp,Manis_pentadactyla),(Rhinolophus_creaghi,(Myotis_vellifer,Nyctimene_albiventer))),(Erinaceus_europaeus,(Uropsilus_sp,(Scalopus_aquaticus,Talpa_sp)))),((Cyncephalus_volans,(Homo_sapiens,Tarsius_syrichta)),((Mus_musculus,(Dolichotis_patagonum,Hystrix_africaeaustralis)),(Sylvilagus_sp,Ochotona_sp)))),(((Macroscelides_sp,Orycteropus_afer,(Amblysomus_hottentotus,Tenrec_sp)),(Procavia_capensis,Elephas_maximus,(Dugong_dugon,Trichechus_manatus))),(Dasypus_novemcinctus,(Cyclopes_didactylus,Choloepus_hoffmani))));

The ML tree used:

((((((Camelus_dromedarius,(Sus_scrofa,((Ovis_canadenensis,Okapia_johnstoni),(Lagenorhynchus_obscurus,Balaenoptera_physalus)))),(Panthera_uncia,(Phoca_vitulina,Ailurus_fulgens))),(((Equus_grevyi,(Diceros_bicornis,Tapirus_indicus)),(Rhinolophus_creaghi,(Myotis_vellifer,Nyctimene_albiventer))),(Manis_sp,Manis_pentadactyla))),(Erinaceus_europaeus,(Uropsilus_sp,(Scalopus_aquaticus,Talpa_sp)))),((Cyncephalus_volans,(Homo_sapiens,Tarsius_syrichta)),((Mus_musculus,(Dolichotis_patagonum,Hystrix_africaeaustralis)),(Sylvilagus_sp,Ochotona_sp)))),(((Orycteropus_afer,(Macroscelides_sp,(Amblysomus_hottentotus,Tenrec_sp))),(Elephas_maximus,(Procavia_capensis,(Dugong_dugon,Trichechus_manatus)))),(Dasypus_novemcinctus,(Cyclopes_didactylus,Choloepus_hoffmani))));

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Waddell, P.J., Ota, R. & Penny, D. Measuring Fit of Sequence Data to Phylogenetic Model: Gain of Power Using Marginal Tests. J Mol Evol 69, 289–299 (2009). https://doi.org/10.1007/s00239-009-9268-8

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