Investigating the performance of AIC in selecting phylogenetic models

Area of Science:

• Phylogenetic inference
• Information theory
• Statistical modeling

Background:

• Akaike's Information Criterion (AIC) is a widely used model selection tool based on information theory.
• AIC approximates Kullback-Leibler (KL) divergence but assumes a continuous likelihood function with finite second derivatives.

Purpose of the Study:

• To investigate the relationship between expected log-likelihood and expected KL divergence in phylogenetic estimation.
• To evaluate the accuracy of AIC for phylogenetic model selection when tree topology is unknown.

Main Methods:

• Theoretical analysis of AIC's properties in the context of phylogenetic tree estimation.
• Simulation studies to assess AIC's performance across different phylogenetic models.

Main Results:

• AIC is an unbiased estimator of expected KL divergence when tree topology is known.
• AIC underestimates expected KL divergence for phylogenetic models when tree topology is unknown.
• The degree of underestimation varies, potentially causing AIC to select incorrect models even with large sample sizes.

Conclusions:

• The violation of AIC's assumptions in phylogenetics leads to biased model selection.
• Improved accuracy of model selection criteria is crucial for reliable statistical phylogenetic inference.