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Comparing the strength of modular signal, and evaluating alternative modular hypotheses, using covariance ratio effect sizes with morphometric data
Author(s) -
Adams Dean C.,
Collyer Michael L.
Publication year - 2019
Publication title -
evolution
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.84
H-Index - 199
eISSN - 1558-5646
pISSN - 0014-3820
DOI - 10.1111/evo.13867
Subject(s) - modular design , modularity (biology) , covariance , pairwise comparison , biology , statistical hypothesis testing , signal (programming language) , statistics , analysis of covariance , measure (data warehouse) , computer science , data mining , mathematics , evolutionary biology , programming language , operating system
The study of modularity is paramount for understanding trends of phenotypic evolution, and for determining the extent to which covariation patterns are conserved across taxa and levels of biological organization. However, biologists currently lack quantitative methods for statistically comparing the strength of modular signal across datasets, and a robust approach for evaluating alternative modular hypotheses for the same dataset. As a solution to these challenges, we propose an effect size measure ( Z CR ) derived from the covariance ratio, and develop hypothesis‐testing procedures for their comparison. Computer simulations demonstrate that Z CR displays appropriate statistical properties and low levels of mis‐specification, implying that it correctly identifies modular signal, when present. By contrast, alternative methods based on likelihood ( EMMLi ) and goodness of fit ( MINT ) suffer from high false positive rates and high model mis‐specification rates. An empirical example in sigmodontine rodent mandibles is provided to illustrate the utility of Z CR for comparing modular hypotheses. Overall, we find that covariance ratio effect sizes are useful for comparing patterns of modular signal across datasets or for evaluating alternative modular hypotheses for the same dataset. Finally, the statistical philosophy for pairwise model comparisons using effect sizes should accommodate any future analytical developments for characterizing modular signal.