Resampling-Based Approaches to Study Variation in Morphological Modularity

Carmelo Fruciano,Axel Meyer,Paolo Franchini,Axel Janke

doi:10.1371/journal.pone.0069376

Abstract

Modularity has been suggested to be connected to evolvability because a higher degree of independence among parts allows them to evolve as separate units. Recently, the Escoufier RV coefficient has been proposed as a measure of the degree of integration between modules in multivariate morphometric datasets. However, it has been shown, using randomly simulated datasets, that the value of the RV coefficient depends on sample size. Also, so far there is no statistical test for the difference in the RV coefficient between a priori defined groups of observations. Here, we (1), using a rarefaction analysis, show that the value of the RV coefficient depends on sample size also in real geometric morphometric datasets; (2) propose a permutation procedure to test for the difference in the RV coefficient between a priori defined groups of observations; (3) show, through simulations, that such a permutation procedure has an appropriate Type I error; (4) suggest that a rarefaction procedure could be used to obtain sample-size-corrected values of the RV coefficient; and (5) propose a nearest-neighbor procedure that could be used when studying the variation of modularity in geographic space. The approaches outlined here, readily extendable to non-morphometric datasets, allow study of the variation in the degree of integration between a priori defined modules. A Java application – that will allow performance of the proposed test using a software with graphical user interface – has also been developed and is available at the Morphometrics at Stony Brook Web page (http://life.bio.sunysb.edu/morph/).

Highlights

Organisms, to function as a whole, need their parts to be connected and establish relationships, i.e. they need a degree of ‘‘integration’’ [1]
Modular structure can be recognized at multiple levels of biological organization and, in the case of variational modularity in morphology, it is assumed to reflect evolutionary or developmental processes that result in modularity itself [6]
In the present paper we have dealt with the problem of studying variation in morphological modularity

Summary

Introduction

To function as a whole, need their parts to be connected and establish relationships, i.e. they need a degree of ‘‘integration’’ [1]. While comparisons of the levels of overall integration across groups of observations can be performed using measures of the dispersion of the eigenvalues of the principal components [14], no specific method to analyze variation in the RV coefficient between a priori defined groups of observations exists This represents an interesting area of research as, if modularity promotes evolvability, inferring variation in levels of modularity might highlight variation in the levels of evolvability. Jojicand colleagues [22], when comparing traditional and geometric morphometric approaches to the study of modularity, while cautioning against potential discrepancies between methods, suggested that direct comparisons among studies on the mouse mandible are reliable It has been shown [23], using random data, that the RV coefficient decreases when sample size increases. Another shortcoming of reporting the RV coefficient is that, even in the case of equal sample sizes, it does not represent a formal test of the null hypothesis of no variation in levels of modularity but, at best, an exploratory approach

Methods

Results

Conclusion