Theoretical morphospace and optimality
Empirical morphospaces have been utilised extensively to explore the morphological and functional diversity of the jaw (2, 3, 20, 37-39). These patterns, while informative, are restricted to morphofunctional relationships seen in biological systems. Furthermore, the variety of shape within biological systems is controlled by many non-functional characters (40). The heterogeneous occupation of empirical morphospaces can be explained through three major constraints: phylogenetic constraints, due to which the limits of morphospace are a function of evolutionary time; morphogenetic constraints, in which certain regions of morphospace are inaccessible to a biological construction process; and function, where infeasible forms are selected against, leaving functionally suboptimal regions of morphospace empty. A theoretical morphospace approach allows us to identify which regions of morphospace are inaccessible to an evolving sample of empirical shapes, and for what reasons.
The occupation of jaw EFA morphospace during the origin of tetrapods is largely controlled by geometrically inaccessible morphospace in low PC1 regions (32). Phylogenetic bias is generally weak, but the rate of morphospace exploration is minimal for large portions of the early evolution of tetrapods. We measured the relationship between morphology and function across theoretical jaw shapes that either mirror fossil jaws or describe forms that are unrealised in the fossil record (28, 30, 32, 41). We utilised this to show that the relationships between jaw speed, strength and height are not only constrained by adaptation, but by a fundamental trade-off tied to properties of shape (Fig. 2). Understanding the functional limitations on biological form requires an understanding of the morphological limitations on function – such as antagonistic relationships between functions moderated by shape - which a theoretical morphology approach can achieve.
Functional constraints in aquatic and terrestrial taxa
Our results show that aquatic and semi-aquatic tetrapod jaws have tighter functional constraints than their terrestrial descendants. Terrestrialisation did not force a change in jaw morphology and function but allowed some taxa greater freedom to explore broader jaw morphospace. This freedom was largely granted by the evolution of herbivory, which promoted the evolution of stronger and slower jaw shapes. Phylogenetic signal in jaw morphology is weak, with many lineages crossing one another in the phylomorphospace, however the radiation into new morphospace is limited to mainly amniotic taxa (Fig. 1C). Our optimality landscapes show that the trade-off between strength, speed and hydrodynamics plays a noteworthy role in constraining the jaw morphology of almost all aquatic taxa, however it is less important in terrestrial taxa. Terrestriality must bring with it some change in functional demands beyond these metrics, possibly due to the evolution of static pressure feeding systems and herbivory. Specifically, these feeding modes (particularly herbivory) require large jaw musculature, giving selective advantage to jaws with greater area for muscle attachment (18). Terrestrial herbivores show a significant decrease in optimality for jaw rotational efficiency and jaw height, which may be brought about by taller jaws with larger muscle attachment area and more vertically inclined musculature (42, 43). The obsolescence of suction feeding during terrestrialisation does not appear to have applied constraint on morphospace occupation. Specifically, the similarity in performance occupation between terrestrial and aquatic taxa suggests that additional functional attributes became important to terrestrial taxa, or a replacement of functional criteria. Ultimately, this may suggest that imposing new selective pressures on an evolving system may allow more evolutionary freedom, rather than constraint. This hypothesis can be further tested by assessing the optimality during the many transitions from land to water in descendent tetrapod lineages, where the hypothesis expects aquatic taxa to be more constrained than their terrestrial ancestors.
The extremes of the extended terrestrial morphospace region are occupied by four taxa: the diadectomorph Diadectes; the pareiasaurs Deltavjatia and Pareiasaurus; and the therapsid Moschops (Fig. 1). These taxa all show convergent anatomical features. Specifically, they share cranial pachyostosis, and large, stocky, upright appendicular skeletons (44-55). This evidence, combined with tooth morphology and gut contents, has supported interpretations of these organisms as herbivorous (18, 45, 56-58). Our data corroborates this conclusion, as these taxa extend into regions of stronger and less rotationally efficient jaw morphospace while remaining optimised within this trade-off, which we may expect to be adaptively favourable to organisms processing tough plant material (18). This provides a new avenue through which the delayed morphological change in the terrestrialisation of the jaw can be understood. This hypothesis could be further tested with a fitness landscape approach (41, 59-66), combined with dietary proxies from fossil teeth (67-69). Alternatively, this dramatic shift in jaw shape may be due to tight integration between the skull and jaw within these taxa. This would result in jaw morphological convergence driven by the convergently developed cranial adaptations within each lineage (46, 49). Patterns of increased constraint between skeletal modules has been demonstrated in the skull throughout this period, but the covariation between the skull and jaw remains uninvestigated (26, 70).
Disparity and optimality
Our results confirm existing suggestions that the evolution of the jaw lagged behind other aspects of skeletal anatomy during the initial phase of tetrapod terrestrialisation (2, 3, 20, 26). Jaw morphological disparity fluctuates around an equilibrium until the Permian, where disparity spikes in terrestrial herbivorous tetrapod jaws (Fig. 4A-C). This is associated with maintaining intermediate functional optimality for jaw strength, speed and height in terrestrial and semi-aquatic taxa, while aquatic taxa remain heavily optimised for this trade-off. We interpret this trade-off as remaining functionally important in terrestrial taxa, albeit relaxed compared to aquatic species. This allows the jaws of terrestrial species to occupy the same morphospace as for aquatic taxa, while slowly exploring greater morphological variety.
Morphodynamic constraints
While the jaws of aquatic taxa (including semi-aquatic taxa) are constrained to optimal performance for our three functional metrics, they do not explore all Pareto optimal regions of morphospace. There may be some further constraint on their morphology not captured by our functional model. This could be a phylogenetic or morphogenetic constraint. While the phylogenetic signal in these morphological data is weak, wider areas of morphospace are occupied by amniotes and some diadectomorphs (Fig. 1). However, amniotes in this dataset are almost entirely terrestrial and so untangling the phylogenetic and functional biases on jaw form is difficult. The aquatic amniote Mesosaurus lies beyond the range of non-amniotic aquatic taxa, suggesting that the constraint on aquatic taxa may be partially phylogenetic (Fig. 1). However, Mesosaurus also does not lie in the extended region of terrestrial morphospace. Still, areas of Pareto optimal morphospace remain unoccupied by all taxa within this dataset. This could be due to thresholds acting on the individual performance metrics - for example, there may be a minimum strength the jaw must exceed in order to perform. Theoretical morphologies below this threshold can still be considered optimal if they have high rotational efficiency or a low jaw height (28).
Morphogenetic constraints may also play a role in the constraint of non-amniotic tetrapod jaws. Metamorphosis has been characterised in non-amniotic tetrapod fossils from this period, with the majority of taxa exhibiting aquatic larval forms (71). Aquatic larval stages can act to constrain and promote diversification in adults (72). However, studies on salamander morphology have shown that metamorphosis has promoted morphological diversification in bones associated with feeding (73). Instead, the limitation may arise from complex life cycle shifts during metamorphosis, between aquatic and terrestrial environments (74). Furthermore, the need to return to water for reproduction may strongly enforce these constraints, which provides an explanation for the similar constraint acting on both aquatic and semi-aquatic tetrapod jaws. The evolution of the amniotic egg would thus relieve this constraint, by allowing fully terrestrial juvenile forms, providing an explanation as to why some amniotes cross this morphospace boundary and explore greater PC1 regions.
Alternatively, this constraint may have been lifted by the evolution of a fully terrestrial feeding system, with a mobile neck and the remodelling of the ancestral hyobranchial system (11). Some aquatic taxa can feed on terrestrial food sources by either carrying them back to the water, or pumping water through the mouth to aid in intraoral transport of food (4, 8, 10, 12, 13, 15, 16). With the evolution of mobile necks and a prehensile tongue, the jaw may be alleviated from the evolutionary pressure to pump water efficiently. Future studies linking the morphology of the hyobranchial apparatus with jaw optimality can text this hypothesis.