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.
Similar content being viewed by others
Data Availability
Data available from the Dryad Digital Repository https://doi.org/10.5061/dryad.p8cz8w9m6 (Jung, Conaway, & von Cramon-Taubadel, 2020).
References
Ackermann, R. R. (2009). Morphological integration and the interpretation of fossil hominin diversity. Evolutionary Biology, 36(1), 149–156.
Ackermann, R. R., & Cheverud, J. M. (2000). Phenotypic covariance structure in tamarins (genus Saguinus): A comparison of variation patterns using matrix correlation and common principal component analysis. American Journal of Physical Anthropology, 111(4), 489–501.
Ackermann, R. R., & Cheverud, J. M. (2002). Discerning evolutionary processes in patterns of tamarin (genus Saguinus) craniofacial variation. American Journal of Physical Anthropology, 117(3), 260–271.
Adams, D. C. (2016). Evaluating modularity in morphometric data: Challenges with the RV coefficient and a new test measure. Methods in Ecology and Evolution, 7(5), 565–572.
Armbruster, W. S., Pélabon, C., Bolstad, G. H., & Hansen, T. F. (2014). Integrated phenotypes: Understanding trait covariation in plants and animals. Philosophical Transactions of the Royal Society B, 369(1649), 20130245.
Arnold, P., Forterre, F., Lang, J., & Fischer, M. S. (2016). Morphological disparity, conservatism, and integration in the canine lower cervical spine: Insights into mammalian neck function and regionalization. Mammalian Biology-Zeitschrift für Säugetierkunde, 81(2), 153–162.
Botton-Divet, L., Houssaye, A., Herrel, A., Fabre, A. C., & Cornette, R. (2018). Swimmers, diggers, climbers and more, a study of integration across the mustelids’ locomotor apparatus (Carnivora: Mustelidae). Evolutionary Biology, 45(2), 182–195.
Cheverud, J. M. (1984). Quantitative genetics and developmental constraints on evolution by selection. Journal of Theoretical Biology, 110, 155–171.
Cheverud, J. M. (1996). Developmental integration and the evolution of pleiotropy. American Zoologist, 36(1), 44–50.
Cheverud, J. M., & Marroig, G. (2007). Comparing covariance matrices: Random skewers method compared to the common principal components model. Genetics and Molecular Biology, 30(2), 461–469.
Conaway, M. A., Jung, H., & von Cramon-Taubadel, N. (2019). The effects of morphometric protocol on morphological integration statistics: A case study in scapulae. American Journal of Physical Anthropology, 168, 47–47.
Conaway, M. A., Schroeder, L., & von Cramon-Taubadel, N. (2018). Morphological integration of anatomical, developmental, and functional postcranial modules in the crab-eating macaque (Macaca fascicularis). American Journal of Physical Anthropology, 166(3), 661–670.
de Oliveira, F. B., Porto, A., & Marroig, G. (2009). Covariance structure in the skull of Catarrhini: A case of pattern stasis and magnitude evolution. Journal of Human Evolution, 56(4), 417–430.
Escoufier, Y. (1973). Le traitement des variables vectorielles. Biometrics, 29, 751–760.
Goswami, A., Smaers, J. B., Soligo, C., & Polly, P. D. (2014). The macroevolutionary consequences of phenotypic integration: From development to deep time. Philosophical Transactions of the Royal Society B, 369(1649), 20130254.
Gould, S. J., & Lewontin, R. C. (1979). The spandrels of San Marco and the Panglossian paradigm: A critique of the adaptationist programme. Proceedings of the Royal Society, London B, 205(1161), 581–598.
Grabowski, M., & Porto, A. (2017). How many more? Sample size determination in studies of morphological integration and evolvability. Methods in Ecology and Evolution, 8(5), 592–603.
Hallgrímsson, B., Jamniczky, H., Young, N. M., Rolian, C., Parsons, T. E., Boughner, J. C., et al. (2009). Deciphering the palimpsest: Studying the relationship between morphological integration and phenotypic covariation. Evolutionary Biology, 36(4), 355–376.
Joe, H. (2006). Generating random correlation matrices based on partial correlations. Journal of Multivariate Analysis, 97(10), 2177–2189.
Jones, K. E., Benitez, L., Angielczyk, K. D., & Pierce, S. E. (2018). Adaptation and constraint in the evolution of the mammalian backbone. BMC Evolutionary Biology, 18(1), 172.
Kazi-Aoual, F., Hitier, S., Sabatier, R., & Lebreton, J. D. (1995). Refined approximations to permutation tests for multivariate inference. Computational Statistics & Data Analysis, 20(6), 643–656.
Kelly, E. M., Marcot, J. D., Selwood, L., & Sears, K. E. (2019). The development of integration in marsupial and placental limbs. Integrative Organismal Biology, 1(1), oby13.
Klingenberg, C. P. (2009). Morphometric integration and modularity in configurations of landmarks: Tools for evaluating a priori hypotheses. Evolution & Development, 11(4), 405–421.
Klingenberg, C. P. (2014). Studying morphological integration and modularity at multiple levels: Concepts and analysis. Philosophical Transactions of the Royal Society B, 369(1649), 20130249.
Lande, R. (1979). Quantitative genetic analysis of multivariate evolution, applied to brain: Body size allometry. Evolution, 33, 402–416.
Marroig, G., & Cheverud, J. M. (2004). Cranial evolution in sakis (Pithecia, Platyrrhini) I: Interspecific differentiation and allometric patterns. American Journal of Physical Anthropology, 125(3), 266–278.
Marroig, G., Shirai, L. T., Porto, A., de Oliveira, F. B., & De Conto, V. (2009). The evolution of modularity in the mammalian skull II: Evolutionary consequences. Evolutionary Biology, 36(1), 136–148.
Melo, D., Garcia, G., Hubbe, A., Assis, A. P., & Marroig, G. (2015). EvolQG-An R package for evolutionary quantitative genetics. F1000Research, 4, 925.
Olson, E. C., & Miller, R. L. (1958). Morphological integration. Chicago: University of Chicago Press.
Penna, A., Melo, D., Bernardi, S., Oyarzabal, M. I., & Marroig, G. (2017). The evolution of phenotypic integration: How directional selection reshapes covariation in mice. Evolution, 71(10), 2370–2380.
Porto, A., de Oliveira, F. B., Shirai, L. T., De Conto, V., & Marroig, G. (2009). The evolution of modularity in the mammalian skull I: Morphological integration patterns and magnitudes. Evolutionary Biology, 36(1), 118–135.
Porto, A., Shirai, L. T., de Oliveira, F. B., & Marroig, G. (2013). Size variation, growth strategies, and the evolution of modularity in the mammalian skull. Evolution, 67(11), 3305–3322.
Qiu, W., Joe, H., & Qiu, M. W. (2006). The clusterGeneration package.
Randau, M., & Goswami, A. (2017). Morphological modularity in the vertebral column of Felidae (Mammalia, Carnivora). BMC Evolutionary Biology, 17(1), 133.
Roff, D. A. (1995). The estimation of genetic correlations from phenotypic correlations: A test of Cheverud's conjecture. Heredity, 74(5), 481.
Rohlf, F. J., & Corti, M. (2000). Use of two-block partial least-squares to study covariation in shape. Systematic Biology, 49(4), 740–753.
Rolian, C. (2014). Genes, development, and evolvability in primate evolution. Evolutionary Anthropology, 23(3), 93–104.
Shirai, L. T., & Marroig, G. (2010). Skull modularity in neotropical marsupials and monkeys: Size variation and evolutionary constraint and flexibility. Journal of Experimental Zoology Part B: Molecular and Developmental Evolution, 314(8), 663–683.
Wiley, D. F., Amenta, N., Alcantara, D. A., Ghosh, D., Kil, Y. J., Delson, E., et al. (2005). Evolutionary morphing.
Young, N. M., Wagner, G. P., & Hallgrímsson, B. (2010). Development and the evolvability of human limbs. Proceedings of the National Academy of Sciences, 107(8), 3400–3405.
Zelditch, M. L., & Carmichael, C. (1989). Ontogenetic variation in patterns of developmental and functional integration in skulls of Sigmodon fulviventer. Evolution, 43(4), 814–824.
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.
Author information
Authors and Affiliations
Contributions
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.
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Electronic supplementary material
Below is the link to the electronic supplementary material.
Rights and permissions
About this article
Cite this article
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
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11692-020-09514-w