andrea cardini 

The study of modularity and integration using Procrustes geometric morphometrics has become a prominent approach in evolutionary developmental biology. A most popular method is the ‘within a configuration’ approach, often used in combination with ‘high density’ morphometric data (i.e., large numbers of landmarks and semilandmarks). In 2019, I realized that this approach violates a basic assumption of shape analysis using superimposition methods and showed that this violation may increase the rate of false positives, beyond the nominal value, in statistical tests. A very recent study, however, argues that simulations in four different datasets indicate that the theoretical violation has a mostly negligible effect on tests, so that it “is not an obstacle to analyses of integration and modularity” (p. 167, Zelditch and Swiderski, 2023). Its authors also claim that I mischaracterized the methods, overstated the problem and published non-reproducible results. In this paper, I carefully compare their statements and mine, as well as our results, and demonstrate that: 1) the problem is always present; 2) the authors overlook the importance of statistical power and p/N ratios (p = number of variables; N = sample size); 3) results are case-specific but, in fact, perfectly congruent in the single dataset in common between both studies; 4) the impact is especially concerning, based on both mine and their recent findings, precisely in the ‘high-density’ morphometric analyses, claimed to be the state-of-the-art in the field; 5) unlike the recent study, that claims external validity and generalizes from a few cases, I explicitly stated multiple times that my findings were specific to the datasets I analysed, the parameters I used and the tests I explored. If confirmed by future research, the recent findings in fact fully corroborate my original suggestions that, despite the undeniable theoretical issue, its impact may vary, its assessment is complex and generalizations are unlikely to be easy. However, both my preliminary work and all their simulations, using semilandmarks slid according to the minimum bending energy criterion, strongly indicate that the most serious problems might affect precisely this highly advertised approach to the analysis of modularity and integration. Given its popularity, it is likely that dozens of studies in high impact journals have published results that may be little more than methodological artefacts.