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Examination of Sample Size Determination in Integration Studies Based on the Integration Coefficient of Variation (ICV)

Abstract

Although there are various indices available for calculating morphological integration, the integration coefficient of variation (ICV) is most suited for assessing magnitudes of integration within and between morphological variance/covariance (V/CV) matrices. However, it is currently not known what the effects of varying sample sizes are on the reliable estimation of distributions of ICV scores. In this regard, the effects of varying sample size on ICV was examined by simulating parameter V/CV matrices with varying underlying magnitudes of average trait correlation (r2). ICV distributions were generated using a trait resampling protocol for various sample sizes (11 through 150) within various parameter r2 values. Next, empirical r2 values were calculated based on data from 22 skeletal elements of 40 Macaca fascicularis specimens to examine whether the results from the simulation corresponded to real biological data. Mean ICV scores of various sample sizes were compared using Mann–Whitney U tests to examine which minimum sample sizes are required to reliably calculate mean ICV. Mann–Whitney U test results based on the simulated data showed that a sample size of 51 may be sufficient even for relatively low r2 values of 0.05. The empirical macaque data showed that 30‒40 individuals may be sufficient to reliably calculate mean ICV scores across skeletal elements. Our results correspond closely with previous assessments by Cheverud and colleagues that argued that a sample size of 40 is necessary to accurately estimate the structure of V/CV matrices.

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Data Availability

Data available from the Dryad Digital Repository https://doi.org/10.5061/dryad.p8cz8w9m6 (Jung, Conaway, & von Cramon-Taubadel, 2020).

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Acknowledgement

The authors are grateful to Mark Omura at the Museum of Comparative Zoology at Harvard University for granting assess to the primate collection for this study. We thank the SUNY Research Foundation for funding to support this research. This material is based upon work supported by the National Science Foundation under grant number BCS-1830745.

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HJ, MC, and NVC conceived the ideas and designed methodology. HJ and MC collected data. HJ ran computer simulation, analyzed data, and wrote the manuscript. All authors contributed critically to the drafts and gave final approval for publication.

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Correspondence to Hyunwoo Jung.

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Jung, H., Conaway, M.A. & von Cramon-Taubadel, N. Examination of Sample Size Determination in Integration Studies Based on the Integration Coefficient of Variation (ICV). Evol Biol 47, 293–307 (2020). https://doi.org/10.1007/s11692-020-09514-w

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Keywords

  • Morphological integration
  • Integration coefficient of variation
  • Computer simulation
  • Macaca fascicularis