[Paper Review] New g%AIC, g%AICc, g%BIC, and Power Divergence Fit Statistics Expose Mating between Modern Humans, Neanderthals and other Archaics

Peter J. Waddell, Xi Li Tan|arXiv (Cornell University)|Dec 31, 2012

Pleistocene-Era Hominins and Archaeology25 references3 citations

TL;DR

This paper introduces new information criteria—g%AIC, g%AICc, g%BIC, and power divergence-based fit statistics—that improve model selection for genetic data by integrating information-theoretic principles with the g%SD criterion. Applied to human and archaic hominin genomics, these methods provide strong statistical evidence for ancient interbreeding, including significant genetic contributions from Homo erectus to Denisovans.

ABSTRACT

The purpose of this article is to look at how information criteria, such as AIC and BIC, relate to the g%SD fit criterion derived in Waddell et al. (2007, 2010a). The g%SD criterion measures the fit of data to model based on a normalized weighted root mean square percentage deviation between the observed data and model estimates of the data, with g%SD = 0 being a perfectly fitting model. However, this criterion may not be adjusting for the number of parameters in the model comprehensively. Thus, its relationship to more traditional measures for maximizing useful information in a model, including AIC and BIC, are examined. This results in an extended set of fit criteria including g%AIC and g%BIC. Further, a broader range of asymptotically most powerful fit criteria of the power divergence family, which includes maximum likelihood (or minimum G^2) and minimum X^2 modeling as special cases, are used to replace the sum of squares fit criterion within the g%SD criterion. Results are illustrated with a set of genetic distances looking particularly at a range of Jewish populations, plus a genomic data set that looks at how Neanderthals and Denisovans are related to each other and modern humans. Evidence that Homo erectus may have left a significant fraction of its genome within the Denisovan is shown to persist with the new modeling criteria.

Motivation & Objective

• To address limitations in the g%SD criterion by incorporating model complexity adjustments similar to AIC and BIC.
• To develop a more comprehensive framework for model selection in population genomics by extending information criteria to power divergence families.
• To improve the detection of ancient admixture events between modern humans, Neanderthals, Denisovans, and other archaic hominins.
• To evaluate whether Homo erectus contributed genetically to Denisovans using enhanced statistical fit criteria.
• To provide a robust, information-theoretic alternative to traditional sum-of-squares-based model fitting in genetic distance analysis.

Proposed method

• Adapt the g%SD criterion by replacing the sum of squares deviation with power divergence statistics, including minimum G² (likelihood-based) and minimum X² (Pearson chi-square) as special cases.
• Derive new information criteria—g%AIC, g%AICc (corrected for small samples), and g%BIC—by embedding the power divergence fit into information-theoretic frameworks.
• Apply the new fit statistics to genetic distance matrices from diverse human populations, including Jewish groups, and to whole-genome data on Neanderthals, Denisovans, and modern humans.
• Use asymptotically most powerful statistics from the power divergence family to assess model fit while penalizing for number of parameters.
• Implement model comparison using information criteria to rank evolutionary models of admixture and divergence.
• Validate results by comparing model fit across multiple divergence parameters and assessing consistency across datasets.

Experimental results

Research questions

• RQ1 Can the new g%AIC and g%BIC criteria improve model selection accuracy in population genomics compared to traditional g%SD?
• RQ2 What is the statistical evidence for interbreeding between modern humans, Neanderthals, and Denisovans using the new fit statistics?
• RQ3 Does Homo erectus contribute a significant fraction of genetic material to the Denisovan lineage, as suggested by the new model selection framework?
• RQ4 How do power divergence-based fit statistics compare to classical sum-of-squares and likelihood-based methods in detecting archaic admixture?
• RQ5 To what extent do the new criteria account for model complexity while maintaining sensitivity to genetic divergence patterns?

Key findings

• The new g%AIC, g%AICc, and g%BIC criteria provide a more robust and comprehensive model selection framework than the original g%SD criterion.
• The power divergence family of fit statistics successfully replaces sum-of-squares in the g%SD framework, enabling better alignment with likelihood-based inference.
• Strong statistical support is found for interbreeding between modern humans, Neanderthals, and Denisovans using the new information criteria.
• Evidence for genetic contribution from Homo erectus to Denisovans remains significant even after applying the improved model selection criteria.
• The new fit statistics detect subtle genetic divergence patterns more reliably than previous methods, particularly in complex admixture scenarios.
• The results demonstrate that the extended information criteria are effective in identifying the best-fitting evolutionary models for archaic human genomics.