Humerus shape variation

To capture morphological evolution of the humerus throughout synapsid evolution, we measured humeri from 70 fossil taxa and compared them to 141 extant quadrupedal tetrapods including amphibians, reptiles, and mammals (see S1 Table and S1 Fig). Shape variation was quantified using a novel, homology-free pseudo-landmarking approach to generate 3D coordinates along the surface of each bone (see Methods and S2 Fig). Procrustes aligned landmarks were ordinated using between-groups principal components analysis (bgPCA) to differentiate postural groups (sprawling versus parasagittal versus unknown for fossils) and produce a morphospace (Fig 1). Regarding our first hypothesis, humeri of major extant groups fall in distinct regions of morphospace (Procrustes ANOVA and pairwise comparisons, p < 0.05, see S2 Table), but the main axis of shape variation (bgPC1) does not separate them based on posture. Instead, bgPC1 differentiates the relatively gracile humeri of parasagittal therian mammals and sprawling “herptiles” (non-avian reptiles plus amphibians), from the robust humeri of sprawling monotremes and moles (Fig 1A and 1B). Therians separate from herptiles along the second axis of variation (bgPC2), which reflects differences in the offset between the proximal and distal ends of the humerus, curvature of the humeral shaft and relative width of the proximal versus distal ends of the humeral epiphyses (Fig 1A and 1B).

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Fig 1. Humerus morphological variation.

(A) Humerus between-groups principal components analysis (PCA) morphospace showing major axes of shape variation. (B) Warps illustrate representative humerus morphologies at each point in morphospace. (C) Subplots show positions of non-mammalian synapsid subgroups, relative to the convex hulls of the three extant groups. Axes are labeled with the percentage of between-groups variance explained. See S11 Fig for a comparison between PCA and bgPCA results. The data underlying this figure can be found in S1 Table and S1 Data.

https://doi.org/10.1371/journal.pbio.3003188.g001

Pelycosaurs, the earliest grade of NMS, occupy the region of morphospace between herptiles and monotremes—contra hypothesis 2—while overlapping neither, consistent with their “basal” phylogenetic position, and a unique sprawling posture [13,28] (significant pairwise differences between means, pelycosaurs versus herptile p < 0.05, pelycosaurs versus monotremes p < 0.05, see S2 Table). Other non-synapsid fossil taxa also plot in this part of morphospace (e.g., Eryops, Orobates, Seymouria [20,22]), indicating pelycosaur humeri do not deviate strongly from a general early crown-tetrapod condition. However, more derived grades of NMS—therapsids and cynodonts—diversify into much larger regions of morphospace and exhibit greater variation in humerus shape (Figs 1A, 1C, and S3).

In therapsids, this variation is partitioned across different subclades. Anomodonts and dinocephalians generally plot with pelycosaurs or closer to monotremes. The biarmosuchian Hipposaurus, our earliest-branching therapsid, plots within herptiles, gorgonopsians plot on the outer edges of the therian and herptile spaces, and therocephalians plot close-to or within the therian cluster (Fig 1C). Basal cynodonts generally occupy the central region of morphospace, as do the two more derived eucynodont subclades, cynognathians and probainognathians, but in both subclades some species independently move into the therian region of morphospace (see S3 Fig). Some mammaliaforms—Eozostrodon and Megazostrodon [29]—fall within therian morphospace, but others—Borealestes [30]—do not (Figs 1C and S3). The two stem therians included here fall well within the range of extant, crown-therian morphologies (Figs 1A and S3). While the overall mean humerus shape of each successive NMS radiation—pelycosaurs, therapsids, and cynodonts—gets closer to the mean therian shape (see pairwise distances in S2 Table), as outlined by hypothesis 3, there is considerable variation around these mean shape values.

Functional traits, performance surfaces, and trait optimization

Function was inferred by measuring seven osteological proxies—bone length, radius of gyration (an important inertial property), torsion, bending strength, and muscle force and speed leverage—for each humerus in our sample (see Methods and S4 Fig). Muscle leverage was separated into two components; ‘swing’ refers to motion of the limb through a horizontal or vertical arc during locomotion, and ‘spin’ refers to long-axis rotation of the limb [15]. We interpolated the measured functional traits across the morphospace [31], to produce seven distinct performance surfaces that illustrate the co-variation of humerus shape with each functional trait (Fig 2A). Performance surfaces were combined to produce adaptive landscapes for each species in the dataset using combinatorial optimization, weighting functional traits to maximize each species’ height on their resulting landscape [18,19,22]. Combinations of trait weights that produced optimal landscapes were then compared across taxa and along the synapsid phylogeny using ancestral state reconstructions (Fig 2B and 2C). Evolutionary shifts in functional trait weighting were identified using the SURFACE algorithm [32], and specific a priori hypotheses based on previous studies of synapsid locomotor evolution [5,12,13] (see S5 Fig) were tested against each other using mvMORPH [33] (see Methods).

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Fig 2. Functional trait variation.

(A) Performance surfaces of seven measured functional traits. (B) Trait weightings of adaptive landscapes calculated for individual species plotted onto the phylogeny. (C) Weightings of adaptive landscapes reconstructed at ancestral nodes plotted against a simplified phylogeny of non-mammalian synapsids. The data underlying this figure can be found in S1 Table and S1 Data.

https://doi.org/10.1371/journal.pbio.3003188.g002

Species-level analysis of trait weights shows considerable variation across groups (RRPP MANOVA, p < 0.05, r² = 0.39, see S3 Table), but also within major groups, especially within NMS (Figs 2B and S6). Centroid size also showed a statistically significant, but smaller, effect on trait weightings (RRPP MANOVA, p < 0.05, r² = 0.11, see S3 Table), and is likely important in structuring within-group variation. Examining adaptive landscapes based on ancestral-state reconstructions of humerus shape along the backbone of the synapsid phylogeny (Fig 2C) reveals the relative importance of individual traits through synapsid evolution, semi-independent of clade- or taxon-specific patterns. The reconstructed ancestral landscape for the Synapsida node heavily optimizes humeral torsion, as well as ‘spin’ muscle leverage, and this combination remains stable throughout early synapsid evolution. The landscape changes at the base of Theriodontia (gorgonopsians, therocephalians, and cynodonts), and throughout Cynodontia, with an increase in optimization for humeral length, ‘swing’ force leverage and a decrease in weighting for torsion (Fig 2C). Notable changes to the reconstructed landscapes occur prior to the origins of prozostrodontian cynodonts and Mammaliaformes: increased optimization for humeral length, radius of gyration, and ‘swing’ force leverage, with less of an emphasis on humeral torsion and ‘spin’ leverage (Fig 2C).

In addition to individual adaptive landscapes for each specimen, we calculated adaptive landscapes for major taxonomic groups within our dataset; here, the group mean is maximized on the resulting landscape. Extant species optimize different combinations of functional traits (Figs 2, 3, and S6), in support of hypothesis 1. Herptiles strongly emphasize humerus length and humeral torsion (Fig 3), traits associated with increasing stride length in sprawling tetrapods [34,35], as well as high-velocity advantage for humeral ‘swing’ (Fig 3), resulting in relatively fast limb movements and greater muscle working range [15]. Monotremes show high weighting for humeral torsion, ‘spin’ muscle leverage, and bending strength (Fig 3), reflective of both their sprawling posture and semi-fossorial lifestyle [15,36–38]. Therians optimize humerus length, radius of gyration, and ‘swing’ muscle force leverage for rotating the limb through an arc (Fig 3). Longer length and a shorter radius of gyration are associated with more efficient locomotion [39,40], whereas increasing muscle leverage for planar rotation would result in more powerful movements of the limb in the parasagittal plane [15,41].

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Fig 3. Adaptive landscapes and underlying trait weights.

(A) Trait weightings of adaptive landscapes calculated for major extant and fossil groups, which maximize the performance of the group mean humerus shape. (B) The reconstructed adaptive landscapes for each group, showing performance peaks and valleys across morphospace. Fossil taxa are indicated by the gray outline. The data underlying this figure can be found in S1 Table and S1 Data.

https://doi.org/10.1371/journal.pbio.3003188.g003

Individual NMS vary substantially in how different functional traits are optimized on their landscapes (Figs 2B, 3, S6, and S7). Pelycosaurs primarily emphasize humeral torsion, consistent with their reconstructed sprawling posture [42,43]. Other traits—‘spin’ leverage, ‘swing’ force, and humeral strength—also contribute to the pelycosaur landscape with varying importance across taxa (Figs 3 and S7). Pelycosaurs differ significantly in terms of trait weighting from herptiles, contra hypothesis 2, but not from monotremes (see S3 Table). Therapsids differ in functional trait optimization across subclades (Figs 2B, 3, S6, and S7). The biarmosuchian Hipposaurus emphasizes torsion and humeral length, similar to herptiles. Dinocephalians and anomodonts predominantly optimize strength and muscle force leverages. Gorgonopsians and therocephalians optimize humeral length, but whereas gorgonopsians emphasize ‘swing’ torque and strength, therocephalians put more importance on humeral torsion (Figs 3 and S7). Cynodonts show substantial variability in trait optimization, but generally emphasize either humerus length, or a combination of strength and muscle force leverages (Figs 2B, 3, S6, and S7). Most cynodonts do not optimize humeral torsion, but there are some exceptions including among derived prozostrodonts and mammaliaforms (S6 and S7 Figs). This contrasts with therian trait optimization, as well as that reconstructed along the synapsid backbone—the importance of torsion in these taxa may represent independent instances of trait diversification. As with humerus shape, the mean trait weightings of each successively derived NMS grade become more similar to the therian condition, in support of hypothesis 3. However, within each grade, there is substantial variation in trait optimization, which does not support the idea of a series of stepwise shifts toward therians.

Searching for shifts in how functional trait weightings may have evolved using SURFACE matched those from the ancestral state reconstruction for the backbone of the synapsid phylogeny (Figs 2 and S6). This analysis also recovered additional shifts within synapsid sub-groups, or along individual branches (S6 Fig). Fitting of different evolutionary regimes to the data using mvMORPH found historical hypotheses of morphofunctional shifts within synapsids [5,12,13] are significantly outperformed by more complex models featuring additional optima for subgroups within the major synapsid grades (see S4 Table for detailed model comparisons). These results are more consistent with the view of synapsid evolution as a sequence of radiations, with functional differentiation within and between each major grade.

Transitions from sprawling to parasagittal postures

To further investigate patterns of humeral transformation toward (or away from) the therian condition during the evolution of Synapsida, we created a transitional ‘sprawling-parasagittal’ landscape. We first created a composite “sprawling” landscape by combining the independently calculated landscapes for different sprawling groups (Fig 4A and see Methods). Then, for each point in morphospace, we subtracted the height on the “sprawling” landscape from the height on the therian (i.e., “parasagittal”) landscape (Fig 4B) to create the transitional landscape (Fig 4C). Transitional landscape scores indicate the relative performance of different humerus morphotypes for sprawling versus parasagittal limb functions, given the many-to-one mapping that exists between humeral traits and posture [20,36,44]. We plotted our taxa on this new ‘sprawling-parasagittal’ landscape (Fig 4C and 4D), determined their adaptive score (height), mapped these scores onto a phylogeny and reconstructed ancestral states using maximum likelihood (Fig 5). As with our functional traits, we used SURFACE and mvMORPH to test for evolutionary shifts both a posteriori and a priori in transitional landscape score within Synapsida and compared models of postural evolution in this group (see Methods).

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Fig 4. Transitional ‘sprawling-parasagittal’ landscape.

(A) Composite sprawling landscape (reptiles, salamanders, monotremes, and non-synapsid fossils), and (B) parasagittal (therian) landscape, (C) overlaid to create a transitional ‘sprawling-parasagittal’ landscape. (D) Density plots of scores on the transitional ‘sprawling-parasagittal’ landscape plotted for major extant and fossil groups. Points represent individual specimen scores. The data underlying this figure can be found in S1 Table and S1 Data.

https://doi.org/10.1371/journal.pbio.3003188.g004

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Fig 5. Evolution of sprawling and parasagittal posture.

Scores on the transitional ‘sprawling-parasagittal’ landscape are plotted on the phylogeny of all specimens, illustrated with select humeri. Stars indicate shifts in evolutionary regime for Synapsida identified by SURFACE (see Methods). Nodes labeled with letters; S, Synapsida, T, Therapsida; C, Cynodontia; M, Mammalia; Th, Theria. The data underlying this figure can be found in S1 Table and S1 Data.

https://doi.org/10.1371/journal.pbio.3003188.g005

We find statistically significant differences in postural scores between taxonomic groups with no statistical effect of centroid size (RRPP ANOVA, p < 0.05, see S5 Table). As expected, therians had the highest scores, and monotremes had the lowest, indicating trait combinations most and least associated with parasagittal postures respectively (Fig 4C and 4D). Herptiles were intermediate between monotremes and therians, due to sharing morphofunctional traits with both groups (humeral torsion with monotremes, and long humeri with therians), but still had negative scores indicating greater association with sprawling locomotion (Fig 4D). These results are consistent with hypothesis 1. Thus, the transitional landscape helps to conceptualize posture as a continuous variable; sprawling and parasagittal represent extremes, but we also show the great variation present within sprawlers and multiple paths between different postural groups [20,44,45]. Ancestral state reconstruction recovers the ancestor of crown-mammals as closer to therians than monotremes (Fig 5). Consequently, extant sprawling monotremes do not retain a plesiomorphic state for Synapsida but have rather converged on a suite of morphofunctional characters that resemble ancestral, sprawling synapsids. This convergence may have been facilitated by the incomplete acquisition of therian characters in early mammals and their close relatives (e.g., retention of humeral torsion in taxa such as Brasilodon, Morganucodon, and Gobiconodon).

Our analyses reconstruct ancestral humeri at the base of Synapsida with traits consistent with sprawling postures, which persist throughout the pelycosaur and early therapsid parts of the tree (Figs 4D and 5). Pelycosaurs, dinocephalians, and most anomodonts have humeri with very negative scores on the transitional landscape, providing strong evidence for sprawled postures (Figs 5 and S8). Although our analysis indicates a sprawled ancestor for Therapsida with monotreme-like traits, several early therapsids show less negative scores (e.g., Hipposaurus, Tiarajudens), more in-line with modern reptile values, possibly indicative of differences in locomotion (e.g., faster limb movements and different kinematics) (Figs 4D, 5, and S8). We also recovered a shift toward intermediate postural scores in theriodont therapsids: the gorgonopsians and therocephalians (Figs 5 and S9). Although these groups have humeri with distinctly higher transitional landscape scores than earlier synapsids, their scores are generally still negative, like modern reptiles. Another shift on the transitional landscape occurs at the origin of Cynodontia, with most taxa possessing intermediate postural scores (Figs 4D, 5, S8, and S9). However, there is considerable heterogeneity within cynodonts and later mammaliaforms, with taxa evolving humeri with both more negative (e.g., Chiniquodon, Exaeretodon) and more positive scores (e.g., Massetognathus, Probainognathus) (Figs 5 and S8). By contrast, within crown mammals, the two stem therians (Adalatherium and Gobiconodon) both scored positively on the transitional landscape (Fig 5).

In line with the complex series of shifts recovered by SURFACE (Figs 5 and S9), we found the best fitting a priori models were those with additional subgroup optima within the major synapsid grades. By contrast, models with only three regimes—here corresponding to proposed sprawling, intermediate and parasagittal postural groups [5,12,13]—are poor fits to the data (see S6 Table for detailed model comparisons). Once again, we interpret these results as evidence for synapsid evolution as a sequence of radiations, with both functional and postural variation within and between groups.

Performance trade-offs and optimal evolutionary pathways

To determine whether synapsids followed “optimal” paths through morphospace over the course of their evolution as they transitioned from one adaptive optimum to another, we calculated Pareto optimality landscapes [25,46]. Trade-offs necessarily occur between high fitness on different landscapes due to differences in the underlying functional traits being optimized. Pareto optimality finds points in morphospace whose height on one landscape is maximized, given their height on another landscape [25,47]. By combining adaptive landscapes reconstructed for major nodes in the synapsid phylogeny, we determined if taxa evolve optimally through morphospace from an ancestral peak to that of the next more derived taxonomic group (see Methods). Deviation from high Pareto optimality implies exploration of novel morphologies and functions, and either the presence of new functional drivers distinct from those along the synapsid backbone or the weakening of functional constraints and lowering of restrictions on limb evolution over time [25].

Contrary to expectations that synapsids would follow a consistently optimal path toward a more therian morphology, our results based on reconstructed landscapes for major nodes show statistically significant fluctuations in optimality across the major synapsid groups (with marginally non-significant effects of centroid size; RPPP ANOVA, p < 0.05, see S7 Table). This pattern is driven by individual subclades branching off to explore both more and less optimal regions of morphospace (Figs 6 and S10). Pelycosaurs undergo a small radiation but are mostly restricted to regions of high optimality that connect their adaptive peak with that for the reconstructed therapsid ancestor (Fig 6). Therapsids have lower optimality than pelycosaurs, as several clades—biarmosuchians, gorgonopsians, and therocephalians—explore parts of morphospace with lower optimality on the landscape connecting Therapsida with Cynodontia (Figs 6 and S10). Dinocephalians and anomodonts both exhibit greater Pareto optimality on this landscape, clustering around the inferred Therapsida optimum (Figs 6 and S10). Basal cynodonts and eucynodonts generally occupy regions of lower Pareto optimality, but certain taxa evolve toward distinct peaks on the cynodont-prozostrodont landscape, with some species evolving toward the reconstructed ancestral cynodont optimum, associated with more robust humeri, and others evolving toward the prozostrodont optimum, associated with more gracile humeri (Fig 6). Finally, prozostrodont cynodonts and mammaliaforms also occupy sub-optimal regions, although there does seem to be a shift in morphospace occupation toward the optimum reconstructed for ancestral therians (Figs 6 and S10).

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Fig 6. Pareto optimality across synapsid evolution.

(A) Functional adaptive landscapes reconstructed for major ancestral nodes within synapsid evolution and (B) the Pareto landscapes created by combining these landscapes together. Pareto optimality for a group of taxa is defined based on their ancestral peak, and the peak of the next major node. (C) Pareto optimality plotted on the non-mammalian synapsid phylogeny. The data underlying this figure can be found in S1 Table and S1 Data.

https://doi.org/10.1371/journal.pbio.3003188.g006

Sample and phylogeny

Humeri from a range of fossil synapsids (9 pelycosaur, 32 therapsid, 22 cynodont, and 2 stem therian specimens, representing at least 58 distinct taxa), were compared to a diverse array of extant taxa (5 salamanders, 56 reptiles, 3 monotremes, and 77 therian mammals, S1 Table). With respect to understanding the evolution NMS, monotremes possess several functional and morphological similarities to fossil taxa [14,36,78], and extant sprawling reptiles have long been used as analogues for NMS and other fossil amniotes [12,13,20]. Our extant sample covers a great diversity in body size and ecology, but all engage in quadrupedal terrestrial locomotion; volant and fully aquatic taxa were excluded because these derived specializations are not relevant to the ‘sprawling-parasagittal’ transition. We also included a small sample of generalized early fossil amniotes and temnospondyls (n = 5) to assist with establishing character polarity for the earliest NMS taxa. All information regarding data provenance, acquisition method, and processing to derive a 3D surface mesh is listed in S1 Table.

Relationships and branch lengths among extant species are based on consensus phylogenies downloaded from timetree.org [79], constructed based on comparison of all published phylogenies of the taxa of interest. Relationships of fossils (including fossil crown-mammals) are based on a combination of two existing large-scale phylogenies of living and extinct synapsids [80,81], which provide a backbone phylogeny of all non-mammalian synapsid fossils. Specimens missing from these two phylogenies were assigned the position of their closest relative present in the trees. The fossil supertree was time-calibrated with occurrence data downloaded from the Paleobiology Database (palaeobiodb.org), using the function timePaleoPhy from the paleotree package in R. The final phylogeny was then constructed by grafting the phylogenies of extant taxa onto the appropriate places in the fossil tree (e.g., salamanders as sister to Eryops, reptiles as sister to Captorhinus, etc.), and pruning the tree to only include sampled fossil taxa.

Geometric morphometrics and morphospace

Humerus shape was quantified using a novel semi-automated approach for slice-based landmarking (S2 Fig). Three-dimensional surface meshes of each humerus were manually aligned to a global coordinate system using a standard protocol in Materialise 3-Matic (v14, Materialise, Leuven, Belgium). The long-axis of the humerus was aligned to the global Z-axis, and the bone was then rotated about its long-axis until the distal medial-lateral epicondyles were horizontal, parallel with the global X axis, and the extensor surface of the humerus (i.e., the face of the humerus to which the elbow extensor muscles attach), faced upwards (S4 Fig). The final sample consisted of only left humeri; any right humeri were mirrored. Once all humeri were consistently oriented, the 3D meshes were converted to ‘.ply’ format and imported into R for landmarking.

Meshes were landmarked with a slice-based approach, using custom code based on the Morphomap R package [82] (S2 Fig). This slice-based landmarking produces a regular array of landmarks on the bone, describing the entire shape in detail, analogous to other morphometric methods, e.g., eigensurface analysis [83]. It works best on topologically simple structures with a well-defined long axis, such as limb bones. Each humerus was ‘sliced’ at 21 points evenly spaced along its length, by drawing a plane normal to the long axis that intersected with the bone mesh. In each of the 21 slices, the intersection between the plane and the mesh defined the bone’s outer contour, and equidistant landmarks (n = 24) were placed around the contour’s length. This produced a final set of 504 regularly spaced landmarks for each humerus, and these final landmark sets were subjected to general Procrustes alignment in the R package geomorph [84]. Differences in shape between groups, as well as potential allometric effects, were tested using a Procrustes ANOVA in the geomorph package [85] (S2 Table).

Data were ordinated using standard principal components analysis (PCA), which produced generally good separation between taxonomic and postural groups (S11 Fig). However, as we were specifically testing hypotheses of shape change as it relates to postural and functional change, we chose to incorporate a priori information on posture and ordinated the data using a bgPCA, in the R package Morpho [86]. This produced a morphospace that emphasized differences between postural groups (sprawling versus parasagittal versus ‘unknown’ for fossil taxa), and the bgPC axes are highly correlated with measured functional traits (Fig 2). Comparison with the traditional PCA shows a similar overall distribution of groups in morphospace, and that our bgPCA did not create ‘false groups’ [87]. Therefore, we proceeded with the more structured bgPCA morphospace in subsequent analyses.

Measuring functional traits

Functional traits and performance surfaces

Performance surfaces were created using the R package Morphoscape [22]. For each of the seven functional traits measured, values were standardized by scaling them to range between 0 and 1, with 0 representing the lowest measured performance, and 1 representing the highest measured performance. Functional traits measured on humerus models from all specimens were mapped onto the morphospace using ordinary Kriging to interpolate trait values across the space. This resulted in seven unique performance surfaces, which clearly show high-level performance gradients and form-function relationships (Fig 2) but are more ‘rugose’ than those from other studies [18,19,22]. Kriging as an interpolation method tends to produce more rugose surfaces than others (e.g., polynomial surface fitting), but it also makes no a priori assumptions about the number of performance peaks or the shape of the performance surface. It should also be noted that while the landmarking protocol is free from biological homology, the functional measurements (e.g., torsion and muscle leverage) are not, which may cause some occasional disconnects between form and function visible as local hills and valleys in the performance surface (see S14 Fig).

Adaptive landscapes

Adaptive landscapes were created using the R package Morphoscape. For each major taxonomic group of interest and for individual species, landscapes were calculated by iteratively summing the seven performance surfaces, where each one had its contribution to overall performance weighted. All possible combinations of weights were tested, ranging from 0 to 1 in increments of 0.05, which for seven functional traits resulted in a total of 230,230 possible adaptive landscapes. Combinations of weights were favored that maximized the height of the point of interest—a group mean, an individual taxon or a reconstructed ancestral nod—on the resulting landscape. For some taxa (e.g., reptiles and therians), despite clear functional differences between them, the very top landscapes tended to have similar combinations of weights; therefore, all final landscapes presented here are based on the mean of the top 10% of weight combinations. Differences in trait weighting combinations that produced optimal landscapes between taxonomic groups, and possible correlations of trait weighting with size, were statistically tested using an RRPP MANOVA in R (S3 Table).

Postural and transitional landscapes

To trace the evolution of the humerus as synapsids transitioned from sprawling to parasagittal limb postures, we first calculated an extant ‘sprawling’ versus ‘parasagittal’ landscape. As therians were the only group in our analysis with parasagittal posture, the parasagittal landscape is equivalent to the therian adaptive landscape. However, the sprawling groups differed significantly from each other and were more broadly distributed across morphospace. Therefore, we created a composite sprawling landscape by overlaying the adaptive landscapes of individual sprawling groups (‘herptiles’, monotremes and non-synapsid fossils) and choosing the highest value in each grid cell as the value for the new landscape. High values on this new, composite landscape therefore indicated high functional performance for some form of sprawling, whether that be sprawling like a monotreme, reptile, salamander, or other tetrapod [13,20,36,45]. To calculate a transitional landscape and determine relative performance for sprawling or parasagittal postures in synapsids and other tetrapods, the difference between these ‘sprawling’ and ‘parasagittal’ landscapes was calculated by subtracting the values in each grid cell on the ‘sprawling’ landscape from the ‘parasagittal’ landscape. The resulting transitional landscape varies around 0, with negative values indicating increased performance on a sprawling landscape, and positive values indicating increased performance on the parasagittal therian landscape. Statistical differences in transitional landscape scores between groups and across body sizes were tested using an RRPP ANOVA in R (S5 Table).

Phylogenetic modeling

To formally evaluate possible evolutionary shifts in posture and limb function across the ‘sprawling-parasagittal’ transition, we used the SURFACE package in R [32] to fit OU models for different evolutionary regimes for posture (scores on the transitional landscape) and limb function (trait weightings for a species adaptive landscape). As SURFACE can be prone to favoring overly complex models [110], we applied an AIC threshold of 4 during the model fitting process, so that more complex models with additional regimes had to provide a substantial improvement in model fit to be accepted over simpler models [111]. While SURFACE searches for shifts with no a priori assumptions, we also tested several explicit Brownian motion (BM) and Ornstein–Uhlenbeck (OU) models of postural evolution using mvMORPH [33]. We compared single-rate BM, BM with a trend, and single-peak OU models, as well as multi-rate BM and multi-peak OU models. For the multi-rate and multi-peak models, groupings were defined based on proposed timings of shifts in synapsid posture from Jenkins (shifts at Cynodontia and Theria) [13], Romer (shifts at Therapsida and Mammalia) [12] and Kemp (shifts at Therapsida and Mammaliaformes) [5]. We tested these against additional models where each synapsid grade was assigned a separate regime, or where further regimes were added for specific subclades (S5 Fig). For a full list of models tested, see S4 and S6 Tables.

Phylogenetic comparative methods can be sensitive to phylogenetic uncertainty and estimated branch lengths. Although there may be some uncertainty in the phylogenetic position of individual taxa or certain sub-clades [81], the higher-level relationships of Synapsida are well recognized and established in the literature [6,57,112,113], and our analyses mainly focus on these high-level relationships, i.e., differences between grades. We assessed the effects of uncertainty in branch length by generating a distribution of 50 trees with variations in time scaling (timepaleophy function in paleotree with dateTreatment = “minMax”) and re-running the mvMORPH analyses to obtain a distribution of model support values. Analyzing posture (scores on the transitional landscape) revealed overwhelming support across all sampled trees for the original preferred model: an OU model with peaks for individual synapsid subclades (S4 Table) (S15 Fig). When analyzing limb function (trait weightings for a species adaptive landscape), we found a similar result to the main analysis (S6 Table): high support for models with regimes for individual synapsid subclades (both multi-rate BM and multi-peak OU) (S15 Fig). This sensitivity testing suggests that the major results of our comparative analyses are not strongly affected by uncertainties in branch length.

Pareto landscapes

To determine whether synapsids evolved along optimal evolutionary trajectories through morphospace, maintaining maximum overall performance even if the performance traits themselves might change, we constructed a series of Pareto landscapes [25,46,114]. The grid cells in morphospace, which represent humerus morphologies, can be considered as solutions to an optimization problem, and they experience trade-offs between different performance metrics and fitness on different adaptive landscapes. A subset of these solutions will be Pareto optimal, i.e., no other solution has better or equal performance in all metrics [47]. This optimal subset of solutions is assigned rank 1, and then removed from the list of solutions before a second optimal subset (assigned rank 2) is determined. This process continues until all solutions have been ranked, thereby generating a Pareto ranking system.

Each Pareto landscape was calculated based on combining two adaptive landscapes reconstructed for major nodes in the Synapsid phylogeny—Synapsida, Therapsida, Cynodontia, Prozostrodontia and Theria. We ranked all locations in morphospace, based on their performance on the adaptive landscape reconstructed for a major synapsid node, and that for the next more derived major node (e.g., Synapsida and Therapsida, Therapsida and Cynodontia, etc.) toward which they might presumably be evolving. Optimality was ranked using a modified Goldberg ranking system [25,115], first calculating the optimal ranking (R_O) and then ranking again with the optimality of each metric reversed (suboptimal ranking, R_S), using the R package Rpref [116]. We then used the following equation to calculate Pareto optimality:

This equation produces a linear rank from 0 to 1, where 1 denotes Pareto optimal regions and 0 denotes the most suboptimal regions. We plotted the Pareto landscapes for four regions of the Synapsid phylogeny, based on differences in the adaptive landscapes reconstructed along the synapsid backbone (Fig 2C). We also mapped Pareto optimality calculated for each specific subset of non-mammalian synapsid taxa onto the phylogeny—tip values were taken from the Pareto landscape, and ancestral states were calculated via maximum likelihood. Relationships of Pareto optimality with taxonomic group and centroid size were statistically tested in R using an RRPP ANOVA (S7 Table).