Sample Size and Geometric Morphometrics Methodology Impact the Evaluation of Morphological Variation

Abstract

Geometric morphometrics has had a profound impact on our understanding of morphological evolution. However, factors such as sample size and the views and elements selected for two-dimensional geometric morphometric (2DGM) analyses, which are often dictated by specimen availability and time rather than study design, may affect the outcomes of those analyses. Leveraging large intraspecific sample sizes (n > 70) for two bat species, Lasiurus borealis and Nycticeius humeralis, we evaluate the impact of sample size on calculations of mean shape, shape variance, and centroid size. Additionally, we assessed the concordance of multiple skull 2D views with one another and characterized morphological variation in skull shape in L. borealis and N. humeralis, as well as a closely related species, Lasiurus seminolus. Given that L. seminolus is a morphologically cryptic species with L. borealis, we assessed whether differences in skull shape and in 2DGM approach would allow species discrimination. We found that reducing sample size impacted mean shape and increased shape variance, that shape differences were not consistent across views or skull elements, and that trends shown by the views and elements were not all strongly associated with one another. Further, we found that L. borealis and L. seminolus were statistically different in shape using 2DGM in all views and elements. These results underscore the importance of selecting appropriate sample sizes, 2D views, and elements based on the hypothesis being tested. While there is likely not a generalizable sample size or 2D view that can be employed given the wide variety of research questions and systems evaluated using 2DGM, a generalizable solution to issues with 2DGM presented here is to run preliminary analyses using multiple views, elements, and sample sizes, thus ensuring robust conclusions.

Fig. 1

Centroid size calculated for subsampled bins containing 75, 50, 25, and 10% of the data, permuted 1000 times, as well as the true mean centroid size as calculated from 100% of the data for each of the three data subsets (lateral cranium, ventral cranium, lateral mandible) for L. borealis and N. humeralis. The full dataset for L. borealis includes 72 specimens and the N. humeralis includes 81 specimens.

Fig. 2

Procrustes distances from the true mean (100% of the sample) across subsampled bins containing 75, 50, 25, and 10% of the data, permuted 1000 times, for each of the three data subsets (lateral cranium, ventral cranium, lateral mandible) for L. borealis and N. humeralis. The full dataset for L. borealis includes 72 specimens and the N. humeralis includes 81 specimens.

Fig. 3

Mean shapes in principal component morphospace relative to the true mean shape, visualized using convex hulls. Each hull represents a subsample containing mean shapes generated using 75, 50, 25, and 10% of the data, with 1000 permutations each, to visualize how variance in mean shape changes with decreasing sample size.

Fig. 4

Partial least squares analyses testing for association of views and skull elements for L. borealis (left) and N. humeralis (right). (A, B) Lateral cranium view compared to ventral cranium view. (C, D) Lateral cranium view compared to mandible view. (E, F) Ventral cranium view compared to mandible view. Reported in each plot are rPLS correlation coefficient between blocks and p-values based on 1000 permutations.

Fig. 5

Principal component analyses and violin plots showing differences in shape and size (represented using log10-transformed centroid size) for Lasiurus borealis (orange) and L. seminolus (purple) in (A) lateral cranial view, (B) ventral cranial view, and (C) lateral mandible view. Circles are females, triangles are males.