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.

Skeletal elements were scanned using a HDI-120 and a Macro R5X structured-light scanner (LMI technologies INC., Vancouver, Canada). 18 wild specimens of M. fascicularis were from the Museum of Comparative Zoology at Harvard University and 22 captive specimens were from the Department of Anthropology of University at Buffalo, SUNY. For the limb bones (scapula, humerus, radius, os coxa, femur, tibia), only 35 specimens (18 wild and 17 captive) out of total 40 specimens were available. The following 22 skeletal elements were quantified: cranium, mandible, 13 elements of the vertebral column (C1, C2, C3, C5, C7, T1, T4, T7, T10, T12, L1, L4, L7), sacrum, scapula, humerus, radius, os coxa, femur, and tibia (there were 3 specimens with T13 as the last thoracic vertebra, 4 specimens with L6 as the last lumbar vertebra, and 1 specimen with 4 sacral vertebrae). In the case of bilateral elements, the left side was landmarked. When the left side was damaged, the right side was landmarked instead. All landmarks were digitized using the software Landmark (Wiley et al. 2005) on the 3D scanned skeletal elements. Descriptions of the landmarking protocol for each skeletal element can be found in supplementary data (Supplementary Table 1-10). Traits were generated for each skeletal element by calculating all possible Euclidean distances between pairs of landmarks on each bone.