Bootstrapping and shuffling

We have to check that the findings of the analysis are statistically robust. This requires that the populations are well-sampled, that is, we have enough images so that the in-sample variance of the mean wing is small, and as a result that measured direction between populations is stable and close to the ideal direction that would be achieved if we had an infinite number of wings. For this approach, we use the bootstrap method that requires that we randomly draw subsets of wings that have a size of 50% of the ensemble. We repeat this procedure for each ensemble individually, so we do not mix wings that correspond to different populations. For pairs of such samples, we compute mean wings and the directional vector between them. We found that the numerical value of the cos⁡θ is stable, and the difference between sampled in this way cos⁡θ and value that is computed for whole populations is extremely low (few percent of the corresponding values), suggesting that it is well estimated.

The second important check is to confirm that the trends we observe are biological in origin and not artifacts of our analysis. We perform a shuffle test. For this check, we construct new populations from images drawn randomly from the entire ensemble, which means that we mix wings from different populations (difference environmental and genetic conditions). We find that for these shuffled populations, a variation of the cosθ is relatively large, and the mean value is only a few percent of the unshuffled data. This suggests that the observed phenomenon depends on biological labels of the wings rather than artifacts introduced by the method and analysis itself.