Correcting for Complexity: Incorporating Trait-Numbers Enhances the Performance of EMMLi in Investigating Modularity.

Area of Science:

• Evolutionary biology
• Quantitative genetics
• Comparative anatomy

Background:

• Quantifying morphological modularity is crucial for understanding evolutionary processes.
• Previous methods like EMMLi showed statistical limitations, including inflated type I errors and model complexity bias.
• The Covariance Ratio (CR) approach offered an alternative but had its own sensitivities.

Purpose of the Study:

• To evaluate a trait-number corrected EMMLi approach (EMMLip) for statistical performance.
• To compare EMMLip with the CR approach in detecting and contrasting hypotheses of morphological modularity.
• To assess the combined utility of EMMLip and CR tests.

Main Methods:

• Performance analysis of a modified EMMLi approach (EMMLip) incorporating trait numbers.
• Comparison of EMMLip and CR test performance under varying conditions of covariation, effect size, and dataset size.
• Evaluation of model misspecification rates for both methods.

Main Results:

• EMMLip ameliorates false discovery rates and favors less complex models compared to the original EMMLi.
• EMMLip effectively differentiates modularity models with varying between- and within-module covariation, especially with larger effect or dataset sizes.
• CR tests remain superior for detecting overall modularity but can exhibit misspecification between hypotheses with different module numbers.

Conclusions:

• The trait-number corrected EMMLi (EMMLip) offers improved statistical rigor for modularity analysis.
• Combining EMMLip and CR tests provides a powerful, albeit imperfect, toolkit for investigating morphological modularity.
• Further refinements are needed to enhance the accuracy and scope of these statistical approaches.