Thirty years of geometric morphometrics: Achievements, challenges, and the ongoing quest for biological meaningfulness

Abstract

The foundations of geometric morphometrics were worked out about 30 years ago and have continually been refined and extended. What has remained as a central thrust and source of debate in the morphometrics community is the shared goal of meaningful biological inference through a tight connection between biological theory, measurement, multivariate biostatistics, and geometry. Here we review the building blocks of modern geometric morphometrics: the representation of organismal geometry by landmarks and semilandmarks, the computation of shape or form variables via superimposition, the visualization of statistical results as actual shapes or forms, the decomposition of shape variation into symmetric and asymmetric components and into different spatial scales, the interpretation of various geometries in shape or form space, and models of the association between shape or form and other variables, such as environmental, genetic, or behavioral data. We focus on recent developments and current methodological challenges, especially those arising from the increasing number of landmarks and semilandmarks, and emphasize the importance of thorough exploratory multivariate analyses rather than single scalar summary statistics. We outline promising directions for further research and for the evaluation of new developments, such as “landmark‐free” approaches. To illustrate these methods, we analyze three‐dimensional human face shape based on data from the Avon Longitudinal Study of Parents and Children (ALSPAC).

First evidence of the link between internal and external structure of the human inner ear otolith system using 3D morphometric modeling

“…While bony and membranous tissue of the utricle show significant integration with and without semilandmarks, integration within the saccule is driven by a strong association between the saccular macula and spherical recess (see Supplementary Table 8 ). Caution should be exercised, however, when interpreting single summary statistics (e.g., p values) of geometric data based on biological structure due to the inherent multivariate nature of landmarking analyses on living forms 41 . Such statistics are gross oversimplifications but provide a starting point to explore features of biological size and shape.…”

Skull variation in Afro-Eurasian monkeys results from both adaptive and non-adaptive evolutionary processes

“…The 39 cranial traits were carefully chosen to be directly comparable to previous analyses of platyrrhines 8 . Additionally, although we are aware of the power of geometric morphometric data (raw and Procrustes transformed landmarks) for visualization and analyses of shape (e.g., 66 – 68 ), here we chose to use interlandmark distances to mirror the approaches of previous studies that have utilized the particular quantitative genetic framework we used in our study 20 . Analyses were conducted on both raw and log-shape ratio data.…”

A replication that requires replication: Commentary on Caton et al. (2022)

“…The GM is rigorously mathematically founded and repeatedly validated procedure that analyses shape variation (Adams et al, 2004;Bookstein, 2018;Cardini & Loy, 2013;Mitteroecker & Schaefer, 2022;Slice, 2005;Zelditch et al, 2012a). Morphometricians, such as those cited above, have developed a set of recommendations whose purpose is to help scholars conduct valid and reliable research.…”