An effect size for comparing the strength of morphological integration across studies

Area of Science:

• Evolutionary Biology
• Quantitative Genetics
• Morphological Integration

Background:

• Understanding phenotypic trait covariation is crucial in evolutionary biology.
• Comparing morphological integration across taxa has been challenging due to a lack of standardized measures.
• Existing methods struggle with sample size and variable number variability.

Purpose of the Study:

• To propose a standardized effect size for quantifying and comparing morphological integration.
• To develop a reliable statistical procedure for assessing trait covariation.
• To provide a tool for evolutionary biologists to compare integration levels across different species.

Main Methods:

• Evaluation of eigenvalue dispersion indices, identifying relative eigenvalue variance ($$) as the most stable.
• Demonstration of $$ accuracy in characterizing covariation patterns after excluding redundant dimensions.
• Transformation of $$ into a standardized effect size (Z-score) for robust comparisons.

Main Results:

• The relative eigenvalue variance ($$) was found to be stable across varying sample sizes and numbers of variables.
• $$ accurately reflects covariation patterns when redundant dimensions are removed.
• A Z-score transformation and a two-sample test were developed to enable valid comparisons of integration strength between taxa.

Conclusions:

• The proposed standardized effect size (Z-score) and two-sample test offer a reliable method for quantifying and comparing morphological integration.
• This approach addresses previous limitations in comparing trait covariation across diverse taxa.
• The developed software and empirical example facilitate the application of this new procedure in evolutionary biology research.