Measuring the magnitude of morphological integration: The effect of differences in morphometric representations and the inclusion of size

Abstract

The magnitude of morphological integration is a major aspect of multivariate evolution, providing a simple measure of the intensity of association between morphological traits. Studies concerned with morphological integration usually translate phenotypes into morphometric representations to quantify how different morphological elements covary. Geometric and classic morphometric representations translate biological form in different ways, raising the question if magnitudes of morphological integration estimates obtained from different morphometric representations are compatible. Here we sought to answer this question using the relative eigenvalue variance of the covariance matrix obtained for both geometric and classical representations of empirical and simulated datasets. We quantified the magnitude of morphological integration for both shape and form and compared results between representations. Furthermore, we compared integration values between shape and form to evaluate the effect of the inclusion or not of size on the quantification of the magnitude of morphological integration. Results show that the choice of morphological representation has significant impact on the integration magnitude estimate, either for shape or form. Despite this, ordination of the integration values within representations is relatively the same, allowing for similar conclusions to be reached using different methods. However, the inclusion of size in the dataset significantly changes the estimates of magnitude of morphological integration, hindering the comparison of this statistic obtained from different spaces. Morphometricians should be aware of these differences and must consider how biological hypothesis translate into predictions about integration in each particular choice of representation.

The preeminent role of directional selection in generating extreme morphological change in Glyptodonts (Cingulata; Xenarthra)

“…These results agree with previous evidence that stabilizing selection is the dominant evolutionary process shaping mammalian morphological diversification (5,7,9). Our results further indicate that stabilizing selection is more expressive for shape than for size, consistent with the idea that shape is more constrained by functional demands than size (31)(32)(33).…”

“…When lineages escape such region, thus invading a new adaptive zone, this is usually associated with more intense changes in morphology and ecology, a feature usually observed in major evolutionary transitions and inovations (42,43). If, as some have suggested, shape features are more strongly associated with functional demands (44)(45)(46)(47)(48), than changes in functional requirements would probably lead to shape evolution, and possibly to the invasion of a new adaptive zone (31,47). Size changes, on the other hand are less likely to impact ecomorphological relationships, being associated with within-zones evolution (31,47).…”

Statistics of eigenvalue dispersion indices: quantifying the magnitude of phenotypic integration

“…Such phenomena are probably to be seen as properties of shape variables, rather than necessarily nuisance artefacts (Klingenberg, 2021). Whether these can be of concern or not would depend on the scope of individual analyses (see also Machado et al, 2019).…”

“…It is obvious that V ( Σ ) takes a single minimum of 0 at . On the other hand, for a fixed , it takes a single maximum of at (e.g., Van Valen, 1974; Machado et al, 2019). Hence, not only is V ( Σ ) scale-variant, but also its range depends on p − 1.…”

“…The presence of estimation or sampling bias in eigenvalue dispersion indices has been well known in the literature (Wagner, 1984; Cheverud et al, 1989; Grabowski & Porto, 2017; see also Marroig et al, 2012). Simulation-based approaches have been taken to sketch sampling distributions of eigenvalue dispersion indices and related statistics (Haber, 2011; Grabowski & Porto, 2017; Machado et al, 2019; Jung et al 2020). However, these approaches hardly give any systematic insight beyond the specific conditions considered.…”