Effects of Procrustes Superimposition and Semilandmark Sliding on Modularity and Integration: An Investigation Using Simulations of Biological Data

摘要

Abstract Modularity and integration are fundamental properties of organisms and central to theories of complex adaptation. Modularity and integration of shape can provide valuable information about the geometry and spatial structure of modules, but a recent study contends that Procrustes superimposition yields alarmingly high frequencies of statistically significant modularity and integration. We reexamine those claims, using data simulated with biologically realistic parameter values, extending the analyses to consider the impact of simulation procedure, model complexity, and landmark sampling scheme, as well as the impact of superimposition on the strength of modularity and integration and on model comparisons. We further extend analyses to evolutionary modularity and integration. We find that superimposition, followed by sliding semilandmarks to minimize bending energy almost invariably induces significant modularity and integration but sliding to minimize the Procrustes Distance, rarely does (no more than 11 of simulated populations are significantly modular) and even more rarely strengthens it. Integration is more often significant in simulated populations, and is more strongly affected by model complexity, density of semi-landmarks, simulation procedure and sample size. The frequency of significant modularity and integration can reach 17 of simulated lineages but neither evolutionary modularity nor integration are significantly strengthened by superimposition followed by sliding. The most alarming results are the extremely high frequency of significant integration in large samples (N = 500) and the non-normal distribution of effect sizes (Z-scores). Even so, the effect of superimposition is slight compared to the strength of variational or evolutionary modularity and integration found in empirical cases.