Actinopterygians are the most diversified clade of extant vertebrates. Their impressive morphological disparity bears witness to tremendous ecological diversity. Modularity, the organization of biological systems into quasi-independent anatomical/morphological units, is thought to increase evolvability of organisms and facilitate morphological diversification. Our study aims to quantify patterns of variational modularity in a model actinopterygian, the zebrafish (Danio rerio), using 3D-geometric morphometrics on osteological structures isolated from micro-CT scans. 72 landmarks were digitised along cranial and postcranial ossified regions of 30 adult zebrafishes. Two methods were used to test modularity hypotheses, the covariance ratio and the distance matrix approach. We find strong support for two modules, one comprised of paired fins and the other comprised of median fins, that are best explained by functional properties of subcarangiform swimming. While the skull is tightly integrated with the rest of the body, its intrinsic integration is relatively weak supporting previous findings that the fish skull is a modular structure. Our results provide additional support for the recognition of similar hypotheses of modularity identified based on external morphology in various teleosts, and at least two variational modules are proposed. Thus, our results hint at the possibility that internal and external modularity patterns may be congruent.

Osteological data were obtained using X-ray micro-tomography (Skyscan 1173, Bruker-microCT, Belgium) on 30 alcohol-preserved wild-type specimens of adult Danio rerio. Scans were reconstructed using NRecon v1.6.6 and image segmentation was performed using Drishti Paint v.2.6.4. Fin and body shape variation among specimens was quantified using landmark-based geometric morphometrics. 72 homologous 3D-landmarks were digitised across 48 skeletal elements and 11 sutures or articulations between bones using Stratovan Checkpoint v.2018.08.07 (Stratovan Corporation). Landmarks' descriptions are available in Table S1 (see supplementary information of the article) and coordinates are available in TPS files. 

Seven a priori hypotheses of modularity were formulated. A full description of the hypotheses is available in Table S3 (see supplementary information of the article).

Landmark coordinates were scaled, translated, and rotated by performing a Procrustes superimposition. Two different methods were used to test these hypotheses: (1) the covariance ratio (CR) (Admas and Collyer, 2019); and (2) the distance matrix approach (Klingenberg and Monteiro, 2005; Magwene, 2001, 2009; Monteiro et al., 2005; Zelditch et al., 2009). To describe patterns of morphological integration, we quantified integration between modules for each hypothesis using partial least square (PLS) analyses (Adams and Collyer, 2016). We also estimated the global integration for the entire landmark configuration, as well as for the subsets comprising the skull and the postcranial regions. All statistical analyses were performed in R v.3.6.3 using the packages ‘morpho’, ‘geomorph’, and ‘ggm’.

R Programming software.