Data from: How many more? Sample size determination in studies of morphological integration and evolvability

The variational properties of living organisms are an important component
of current evolutionary theory. As a consequence, researchers working on
the field of multivariate evolution have increasingly used integration and
evolvability statistics as a way of capturing the potentially complex
patterns of trait association and their effects over evolutionary
trajectories. Little attention has been paid, however, to the cascading
effects that inaccurate estimates of trait covariance have on these widely
used evolutionary statistics. Here, we analyze the relationship between
sampling effort and inaccuracy in evolvability and integration statistics
calculated from 10-trait matrices with varying patterns of covariation and
magnitudes of integration. We then extrapolate our initial approach to
different numbers of traits and different magnitudes of integration and
estimate general equations relating the inaccuracy of the statistics of
interest to sampling effort. We validate our equations using a dataset of
cranial traits, and use them to make sample size recommendations. Our
results suggest that highly inaccurate estimates of evolvability and
integration statistics resulting from small sample sizes are likely common
in the literature, given the sampling effort necessary to properly
estimate them. We also show that patterns of covariation have no effect on
the sampling properties of these statistics, but overall magnitudes of
integration interact with sample size and lead to varying degrees of bias,
imprecision, and inaccuracy. Finally, we provide R functions that can be
used to calculate recommended sample sizes or to simply estimate the level
of inaccuracy that should be expected in these statistics, given a
sampling design.