In genetics applications we believe the situation is different. Under standard population genetics assumptions such as a panmictic population, the natural null is that the eigenvalues of the true covariance matrix are equal, a formal test is appropriate, and deviations from the null are likely to be of real scientific and practical significance. To support this, in our experience on real data we take our null very seriously and attempt to explain all statistically significant axes of variation. Often the explanation is true population structure in the data, but we also often expose errors or difficulties in the data processing. Two examples follow.
