Convergence, divergence, and macroevolutionary constraint as revealed by anatomical network analysis of the squamate skull, with an emphasis on snakes

Traditionally considered the earliest-diverging group of snakes, scolecophidians are central to major evolutionary paradigms regarding squamate feeding mechanisms and the ecological origins of snakes. However, quantitative analyses of these phenomena remain scarce. Herein, we therefore assess skull modularity in squamates via anatomical network analysis, focusing on the interplay between ‘microstomy’ (small-gaped feeding), fossoriality, and miniaturization in scolecophidians. Our analyses reveal distinctive patterns of jaw connectivity across purported ‘microstomatans’, thus supporting a more complex scenario of jaw evolution than traditionally portrayed. We also find that fossoriality and miniaturization each define a similar region of topospace (i.e., connectivity-based morphospace), with their combined influence imposing further evolutionary constraint on skull architecture. These results ultimately indicate convergence among scolecophidians, refuting widespread perspectives of these snakes as fundamentally plesiomorphic and morphologically homogeneous. This network-based examination of skull modularity—the first of its kind for snakes, and one of the first to analyze squamates—thus provides key insights into macroevolutionary trends among squamates, with particular implications for snake origins and evolution.


Sources of micro-CT scan data
All micro-CT scans of MCZ specimens were performed by CRCS and will be made  Finally, scans from the AMS and SAMA collections were provided courtesy of A. Palci, and scans of UAMZ specimens were provided courtesy of lab colleagues.

Supplementary Notes
Supplementary Results: Trends in topospace as revealed by pPC3 As discussed in the main text, pPC1 and pPC2 together reveal that fossoriality and miniaturization each characterize a distinct region of topospace, with their combined influence reflecting even further constraint on skull architecture relative to non-miniaturized-non-fossorial squamates (Fig. 9). Comparison of each of these axes of variation to pPC3 (Supplementary Figs S59-S60) also provides insight into the effect of habitat and body size on squamate skull architecture, extending these findings by revealing the influence of anatomical network parameters not captured by the first two components. As for the first two axes of variation, pPCA and PCA produced similar trends in relation to their respective third components; therefore, as in  Fig. S60e). However, whereas this pattern causes a reduction in overlap for pPC1 vs pPC2 (Fig. 9f), this is not the case for pPC2 vs pPC3 ( Supplementary Fig. S60f).
Instead, along the latter axes of variation, the miniaturized-fossorial versus non-miniaturizednon-fossorial regions are arranged such that they still overlap quite heavily, to the same extent as when considering miniaturization alone ( Supplementary Fig. S60e-f). These axes therefore do not provide as strong a signal for the influence of habitat and/or body size as that encapsulated by pPC1 vs pPC2 (Fig. 9).
In interpreting this difference, it is important to consider the various parameters driving each of pPC1, pPC2, and pPC3, with particular attention to their respective anatomical implications. Specifically, the distribution of taxa within the pPC1-pPC2 topospace ( Fig. 9 Notably, both of these sets of parameters bear clear anatomical implications (i.e., reflecting how thoroughly the skull is internally connected, and how large the overall network is, respectively), with intuitive relevance for both fossoriality and miniaturization (e.g., see Discussion in main text regarding structural reinforcement, paedomorphic skeletal reduction, and allometric scaling in relation to these parameters). In contrast, pPC3 is driven almost entirely by parcellation [P], a metric describing the overall 'level of modularity' within a given network (i.e., how many modules exist and how evenly nodes are distributed among those modules 3 ). Unlike the parameters driving pPCs 1 and 2, this latter metric does not bear such obvious anatomical relevance to the topics of habitat and body size; in other words, variation in parcellation does not confer an immediately evident adaptive advantage (unlike variations in D/C/L, which reflect structural reinforcement), nor is it as directly related to developmental phenomena like allometry or paedomorphosis (as discussed in the main text for D/C/L in the context of miniaturization, and N/K in the context of skeletal reduction, respectively). It is therefore perhaps unsurprising that a topospace based on pPC2 and pPC3-and thus excluding the information carried by pPC1-does not bear as strong a signal regarding the interplay between fossoriality and miniaturization. In light of these findings, it will therefore be important for future research to clarify the anatomical and adaptive implications of 'parcellation', so as to better understand how-and, in a broader evolutionary sense, why-this parameter varies across taxa.

List of specimens analyzed in this study
Taxonomic assignments are based on Burbrink et al. 5