EMMLi: A maximum likelihood approach to the analysis of modularity

Area of Science:

• Evolutionary biology
• Quantitative genetics
• Morphometrics

Background:

• Phenotypic modularity, defined as semiautonomous sets of correlated traits, is crucial for understanding evolutionary processes.
• Existing methods like cluster analysis and RV coefficient analysis have limitations in comparing different modularity model structures.
• Confirmatory approaches, while statistically robust, often cannot compare models with varying parameterizations.

Purpose of the Study:

• To develop a novel maximum likelihood approach for comparing phenotypic modularity models with different parameterizations.
• To introduce the finite-sample corrected Akaike Information Criterion for comparing trait correlation matrices across diverse model structures.
• To test the new method's ability to accurately identify model structure and parameters using simulations and empirical data.

Main Methods:

• A maximum likelihood framework was employed to compare model log-likelihoods of trait correlation matrices.
• The finite-sample corrected Akaike Information Criterion was used to select among competing modularity hypotheses.
• Simulations were conducted to assess performance across varying model complexity and contrast levels; a dataset of macaque skull landmarks was analyzed.

Main Results:

• Simulations demonstrated the method's accuracy in identifying correct model structure and parameters under diverse conditions.
• Analysis of macaque skull data strongly supported a six-module model of phenotypic integration.
• This six-module pattern was consistent across all five age categories, indicating early development and conservation during postnatal ontogeny.

Conclusions:

• The developed maximum likelihood approach effectively compares models with different parameterizations, offering a significant advancement in modularity analysis.
• A complex six-module integration pattern is a conserved feature of the macaque skull throughout postnatal development.
• The method's robustness to small sample sizes makes it valuable for studying rare or extinct species.