Disconnecting bones within the jaw‐otic network modules underlies mammalian middle ear evolution

Data collection

We gathered information on the anatomy of the lower jaw and middle ear for 43 synapsid taxa, including species of basal synapsids, non‐mammalian therapsids, non‐mammalian cynodonts, Mesozoic mammals and extant mammals (see Table S1 for details). We included in our analysis those bones of the head that articulate to, or share a muscular attachment with, bones of the lower jaw or middle ear (see Table S2 for the complete list of bones). This allowed us to consider cranial bones related by muscular attachments to the lower jaw as an intrinsic part of the anatomical system under study; thus, following the idea that the increase of the jaw adductor musculature is one of the main reasons for the synapsid's lower jaw evolution (Watson, 1953; Hopson, 1966; Kemp, 1969, 1979, 2007; Romer, 1970; Reisz, 1972; Kermack et al., 1973; Fourie, 1974; Crompton & Parker, 1978; Carroll, 1988, pp. 393–395; Luo & Crompton, 1994; Rybczynski, 2000; Wang et al., 2001; Martinelli & Rougier, 2007; Luo, 2011; Huttenlocker & Abdala, 2015; Lautenschlager et al., 2017, 2018). The embryonic Meckel's cartilage was probably persistent in the adult lower jaw of some synapsid taxa (Kermack et al., 1973; Sues, 1986; Rougier et al., 1996; Wang et al., 2001; Rich et al., 2005; Kemp, 2007; Luo, 2011; Luo et al., 2016; Ramírez‐Chaves et al., 2016; Han et al., 2017), as could be inferred by the Meckelian groove or sulcus in the lingual side of some lower jaws (Kermack et al., 1973; Sues, 1986; Bonaparte et al., 2003, 2005; Rich et al., 2005; Kemp, 2007; Meng et al., 2011; Ramírez‐Chaves et al., 2016; Anthwal et al., 2017; Luo et al., 2017; Urban et al., 2017). However, connectivity only can be reliably inferred in fossils when the element is present as hard fossilized tissue; thus, to register the connectivity of Meckel's cartilage, we have only coded it when newly ossified in early mammals.

Phylogenetic context

To map the evolution of modularity patterns on the phylogeny, we assembled a tree for the 43 taxa studied, following consensus phylogenies for the Synapsida crown group (Rubidge & Sidor, 2001; Sidor, 2003), basal synapsids (Spindler, 2015; Brocklehurst et al., 2016), non‐mammalian therapsids (Fröbisch & Reisz, 2008; Huttenlocker et al., 2011; Kammerer, 2011, 2016, 2017; Huttenlocker & Smith, 2017), non‐mammalian cynodonts (Martinelli & Soares, 2016; Martinelli et al., 2017) and mammals (Luo, 2011; O'Leary et al., 2013; Bi et al., 2014; Benton et al., 2015; Han et al., 2017). We built the phylogenetic tree using R packages ape (Paradis et al., 2004), phytools (Revell, 2012), paleotree (Bapst, 2012) and strap (Bell & Lloyd, 2015), using the time data reported in the Paleobiology Database (Peters & McClennen, 2016), Fossil Calibration Database (Ksepka et al., 2015) and the International Chronostratigraphic Chart (v2017/02) of the International Commission on Stratigraphy (Cohen et al., 2014) for calibration (see Supporting information for more details about the building of the phylogenetic tree).

Network modeling

We built network models of the lower jaw and middle ear complex, in which each node codes for one bone and each link connecting two nodes codes for a physical contact between two bones (following Rasskin‐Gutman & Esteve‐Altava, 2014). Networks were modeled as binary adjacency matrices (A) of dimension N × N, where N is the number of bones. Aij = 1 if there is a physical contact between bones i and j; Aij = 0 if there is none. All analyses were performed in R (R Core Team, 2017) using functions of the package igraph (Csárdi & Nepusz, 2006).

Modularity analysis

We delimited anatomical modules by optimization of the network modularity parameter Q, as implemented in the function cluster_optimal. This algorithm maximizes the modularity measure defined by Newman & Girvan (2004), as $Q={\sum }_{s=1}^m\left[\frac{k_s}{K}-{\frac{d_s}{2K}}^2\right]$, where m is the number of modules of the partition, k _s is the number of links within module s, and d _s is the total number of links of nodes in s (both inside and outside s). We calculated the expected error of Q using a jackknife algorithm where each connection is an independent observation (Newman & Girvan, 2004; see details of this analysis in Table S3).

Topological characterization of the jaw and otic modules

We characterized the topology within the jaw and otic modules by measuring their number of nodes (N _m), number of connections (K _m), density of connections (D _m), mean path length (L _m), mean cluster coefficient (C _m) and heterogeneity of connections (H _m; Rasskin‐Gutman & Esteve‐Altava, 2014). N _m measures the total number of nodes in the module: the total number of anatomical elements that are part of the module. K _m measures the number of physical contacts among the bones of the module, thus capturing the intra‐module integration. D _m measures the density of connections into the module, that is, the number of connections in the module with respect to the maximum possible, as $D_m=\frac{2K_m}{N_m(N_m-1)}$; it captures the structural organization and serves as a proxy for morphological complexity. L _m measures the characteristic path length, the proximity of each node to other nodes within the module in terms of number of connections, as $L_m=\frac{1}{N_m-1}\sum d_{n_i,n_j}$, where d is the shortest distance in number of connections between the nodes n _i and n _j; this parameter measures the functional efficiency as the interdependence between parts (i.e. proxy of integration). C _m measures the cluster coefficient, the number of interconnections between the neighbors of a node into the module, that is, the triangular loops between 3‐nodes, as $C_m=\frac{1}{N_m}\sum \frac{\sum {\mathrm{\tau }}_i}{K_i(K_i-1)}$, where τ_i is the number of links among the neighbors of node i; this parameter captures the co‐dependency between parts and serves as another proxy of integration. Higher values of D _m and C _m are indicative of high complexity, while L _m is inversely proportional to it (Esteve‐Altava et al., 2013; Rasskin‐Gutman & Esteve‐Altava, 2014). Finally, H _m quantifies the heterogeneity or variance of connections of the nodes in the module, as $H_m=\frac{{\mathrm{\sigma }}_{\mathit{Km}}}{{\mathrm{\mu }}_{\mathit{Km}}}$, where σ _Km and μ _Km are the standard deviation and mean of K _m, respectively; thus, capturing the structural disparity in the number of links per node. This last parameter is a proxy for anisomerism, a property related to structural specialization by the heterogeneity of body parts: the less similar they are, the more specialized (Gregory, 1934, 1935a,b; Esteve‐Altava et al., 2013; Rasskin‐Gutman & Esteve‐Altava, 2014).

Role of lower jaw and middle ear bones

We characterized the topological role of the dentary and middle ear bones within their modules by measuring their degree (K _i) and betweenness centrality parameter (BC_i). K _i is the total number of connections for a given element in the network, $K_i=\sum A_{\mathit{ij}}$, and serves as a proxy of the total amount of functional and developmental dependences of this element within the anatomical system (Rasskin‐Gutman & Esteve‐Altava, 2014; Arnold et al., 2017). BC_i measures the number of geodesics (shortest paths) in the network passing through a given node, where each shortest path is the minimum distance in number of links that connects two nodes in the network. ${\text{BC}}_i={\sum }_{j\ne i\ne p\in N}\frac{L_{\mathit{jp}}(i)}{L_{\mathit{jp}}}$, where L _jp is the total number of shortest paths from node j to node p, and L _jp (i) is the number of those paths that pass through the node i. Nodes with higher BC_i may have considerable influence within a network because they are more involved in the information passing through the nodes (Brandes, 2001; Dos Santos et al., 2017). We have measured these parameters for the dentary, malleus, incus and stapes bones, excluding the gonial and ectotympanic bones because they disappeared by fusing to other structures in some groups, becoming untraceable as independent elements.

Data and code availability

The data and code that support the findings of this study are available from Figshare at https://figshare.com/articles/Network_Modularity_Middle_Ear_Evolution/7173125.

Modularity of the jaw‐otic complex

The jaw‐otic complex of synapsids can take one of three alternative network modular configurations: (i) mandibular; (ii) transitional otic‐mandibular; and (iii) otic. The mandibular module includes only bones of the lower jaw: dentary, splenial, coronoids, angular, surangular, pre‐articular, articular and the ossified Meckel's cartilage (green modules in Figs. 2, 3, 4). The transitional otic‐mandibular module includes both mandibular and middle ear bones: the above‐referred jawbones plus the quadrate/incus and stapes bones (orange modules in Fig. 5). The otic module includes the middle ear bones ectotympanic, malleus, incus and stapes, and excludes the only bone that forms the lower jaw in mammals, the dentary (golden modules in Fig. 6).

Evolutionary stages

The three alternative modular configurations of jaw‐otic complexes map into five evolutionary stages on the phylogeny of synapsids (Fig. 7). This definition of evolutionary stages is based on: (i) the type of anatomical module (mandibular, transitional otic‐mandibular and otic); (ii) the type of jaw joint (quadrate‐articular, surangular‐squamosal, dentary‐squamosal or a shared mixture of these); and (iii) the presence of a de novo ossification of the Meckel's cartilage.

The first evolutionary stage (S1) is found in basal synapsids and all major groups of therapsids except eucynodonts (plus the eucynodont family Tritylodontidae, represented by Kayentatherium). Their anatomical networks included two mandibular modules that connect to the cranial modules by the reptilian jaw joint between the quadrate and articular bones (Fig. 2B,D).

The second evolutionary stage (S2) is found in advanced non‐mammalian cynodonts, or eucynodonts. A single mandibular module characterizes their anatomical networks due to the fusion of dentary and splenial bones in the symphysis. The connections between the mandibular module and the cranial modules match the double jaw joint present in eucynodonts (Fig. 3B): the primitive jaw joint quadrate‐articular, and a new complementary jaw joint surangular‐squamosal (Fig. 3D), or dentary‐squamosal (Fig. 3E).

The third evolutionary stage (S3) is found in mammaliaforms and some early mammals such as the haramiyidian Vilevolodon (Fig. 7), which present a mandibular module with the auditory bones joined to the dentary. S3 includes a new bone within the mandibular modules in these mammals, the ossified Meckel's cartilage (orange spherical node OMC, ossified Meckel's cartilage, in Fig. 4D,E). In this stage, the mandibular network has split into two contralateral modules due to an unfused symphysis, while keeping a double jaw joint shared between the reptilian quadrate‐articular and the new mammalian dentary‐squamosal (Fig. 4B,C).

The fourth evolutionary stage (S4) is found in Mesozoic mammals that have the middle ear bones partially detached from the lower jaw. The post‐dentary bones connect to the dentary indirectly, through the ossified Meckel's cartilage (Fig. 5B). As a result, S4 differs from S3 in presenting two transitional otic‐mandibular modules. This new pair of modules includes the middle ear bones, quadrate/incus and stapes, in addition to the jawbones (orange modules in Fig. 5D,E). The primitive jaw joint quadrate‐articular is now part of these transitional modules.

Finally, the fifth evolutionary stage (S5) is found in derived mammals that have a definitive middle ear with its ear bones totally disconnected from the mandible, with the dentary as the only jawbone (Fig. 6A–C). The ossified Meckel's cartilage is absent in S5 and ear bones organize in a new type of module, the otic module (golden colored modules in Fig. 6D,E); the two otic modules include the middle ear bones only. At this later stage, the modularity‐searching algorithm separates modules preserving the known homology between the angular, pre‐articular, articular and quadrate bones of basal synapsids with the ectotympanic, gonial, malleus and incus bones of mammals, respectively.

Evolutionary trends in complexity and specialization

Network parameters (Table S4) show that through the mammalian middle ear evolution the otic module in S5 has lost half of the bones (N _m) present in the ancestral mandibular module in S1, with a tendency toward decreasing the module connectivity (K _s). In S5 the characteristic path length (L _m) increases their values in the otic module, while both density of connections (D _m) and clustering coefficient (C _m) increase. This suggests a reduction in the structural complexity, or a simplification, of anatomical modules through evolution. The heterogeneity (H _m) values also increase through stages, suggesting a greater specialization of the jaw‐otic complex.

Topological changes in bone role

The analysis of connectivity (K) and betweenness centrality (BC) in the dentary and the middle ear bones showed differences throughout the five evolutionary stages (Table S5). Figure 8 compares the values of K and BC for each bone and evolutionary stage.

Regarding bones’ connectivity, the middle ear bones – articular/malleus, quadrate/incus and stapes – present their highest number of connections in S1 (Fig. 8A; Table S5). From this first evolutionary stage, there is a trend toward reducing the number of connections or disconnecting the middle ear bones in S2 and S3. In S4, the quadrate/incus and stapes bones keep the same values of K as in S3, while the articular/malleus remains disconnected. The K for the dentary and middle ear bones is the lowest in the last evolutionary stage S5, where the trend of bone disconnection produces the modern configuration in mammals: a group of middle ear bones separated from a single lower jaw bone.

Regarding bones centrality, the BC values for the dentary and the middle ear bones are similar to K (Fig. 8B; Table S5). The articular and quadrate bones have the highest values of BC in S1 (Figs 8B and 9A). However, the high BC values of these bones decrease in S2 (Fig. 8B), where the emergence of the double jaw joint increases the BC in the dentary, surangular and squamosal bones that form the new complementary jaw joint (Fig. 9B). S3 also follows this pattern, the dentary and squamosal bones are now the ones with the highest values of BC, after acquiring a new role as main elements of the double jaw joint in mammaliaforms (Fig. 9C). S4 shows a slight decrease of BC for the dentary (Fig. 8B), but it is still the node with the highest BC value within the new transitional otic‐mandibular module, in which the middle ear bones keep their low centrality (Figs 8B and 9D). However, the ear bones slightly increase their BC values within the otic module in S5; here, the auditory bony chain is completely disconnected from the dentary, which in turn decreases its BC value (Figs 8B and 9E).

Evolution of the modular organization of the jaw‐otic complex

Our analysis of the jaw‐otic complex using anatomical networks delimits three alternative modular configurations for the bones involved in the mammalian middle ear evolution: (i) mandibular; (ii) transitional otic‐mandibular; and (iii) otic modules. The mandibular module is analogous to the mandibular middle ear complex described in non‐mammalian synapsids and mammaliaforms; the transitional otic‐mandibular module occurs in the intermediate stage of the mammalian middle ear evolution and is analogous to the transitional mammalian middle ear described in some Mesozoic mammals, in which the ear bones connect only partially to the lower jaw; and the otic module is analogous to the definitive mammalian middle ear described for extant mammals (Wang et al., 2001; Luo et al., 2007, 2016; Ji et al., 2009; Luo, 2011; Meng et al., 2011; Anthwal et al., 2017; Han et al., 2017; Urban et al., 2017). The different organizational steps of these network modules allowed us to divide the evolution of the mammalian ear into five evolutionary stages (Fig. 7).

The first evolutionary stage (S1) shows two mandibular modules (in green, Fig. 2B,D), which connect to the cranial modules by the plesiomorphic quadrate‐articular jaw joint (Kermack et al., 1973, 1981; Crompton & Parker, 1978; Carroll, 1988, p. 395; Han et al., 2017). S1 is conserved during the evolution of synapsids, with a few variations in basal synapsids, non‐cynodont therapsids and epicynodonts (Fig. 7). All mandibular modules group jawbones, but taxa differ in their anatomical organization; for example, a different number of bones involved in the mandibular symphysis, or some bony fusions in the articular complex (see Supporting information figures). In addition, the more derived non‐mammalian eucynodont Kayentatherium, from the family Tritylodontidae, has its two mandibular rami grouped in a single mandibular module, perhaps due to a low number of mandibular elements forming its lower jaw (Figure S27). This configuration is typical of S2 for eucynodonts (see below), so it is not surprising that the tritylodontid Kayentatherium has it too. In fact, the only mandibular feature to classify Kayentatherium in S1 is its reversion to the reptilian quadrate‐articular jaw joint (Sues, 1986), trait of focus of many discussions about the origin of mammals (Carroll, 1988, pp. 388–392; Luo, 1994; Bonaparte et al., 2003; Liu & Olsen, 2010; Martinelli et al., 2017; Bonaparte & Crompton, 2018).

A single mandibular module characterizes the second evolutionary stage (S2) of eucynodonts (green module in Fig. 3D,E). This module connects to the cranium by a double jaw joint (Fig. 3B), a feature related to an improved masticatory system in non‐mammalian eucynodonts (Jasinoski & Abdala, 2017; Lautenschlager et al., 2017, 2018), similar to that developed in mammals (Fourie, 1974). The mandibular symphysis is often fused in these taxa (Fig. 3D), which confers a greater pressure bite (Ivakhnenko, 2008). The primitive reptilian jaw joint was reinforced with a new surangular articulation on the squamosal bone (Fig. 3B,D) that would have provided resistance to the dislocation of the lower jaw during biting because of the reduction in size of the quadrate and articular bones (Luo & Crompton, 1994; Han et al., 2017). The double jaw joint improved when the enlarged dentary began articulating to the squamosal (Fig. 3E), thus excluding the surangular from the joint (Fig. 3D). This novel dentary‐squamosal articulation formed the definitive mammalian jaw joint (Luo, 2011; Han et al., 2017), which places tritheledontids and brasilodontids eucynodonts close to the origin of the mammalian crown group (Bonaparte et al., 2003, 2005; Martinelli & Rougier, 2007; Liu & Olsen, 2010; Soares et al., 2011; Bonaparte & Crompton, 2018).

As a novelty, the third evolutionary stage (S3) presents the emergence of a newly ossified Meckel's cartilage within the two mandibular network modules (orange spherical nodes, OMC, into the green modules in Fig. 4D,E), here connected themselves by an unfused dentary symphysis. The potential existence of the Meckel's cartilage in the previous evolutionary stages can be inferred by the presence of Meckelian grooves in the lower jaw of some non‐mammalian eucynodonts (Kermack et al., 1973; Sues, 1986; Bonaparte et al., 2005; Kemp, 2007); nonetheless, this new endochondral ossification constitutes a developmental novelty and a crucial step in the mammalian middle ear evolution (Sidor, 2001; Anthwal et al., 2017). The earliest record of an ossified Meckel's cartilage is found in small mammaliaforms such as Morganucodon (Fig. 4A,B), which retained the feeble, but still functional, quadrate‐articular jaw joint by reinforcing it with a stronger dentary‐squamosal articulation (Fig. 4B,C; Luo & Crompton, 1994), thus allowing mammals to have a more effective control of the adductor musculature and jaw articulation (Kermack et al., 1973). Once the mammalian dentary‐squamosal articulation was in place, the ancestral quadrate‐articular jaw joint was free to evolve as a sound transmission structure (Hopson, 1966; Luo, 2011; Anthwal et al., 2013).

The fourth evolutionary stage (S4) corresponds to a transitional state of the mammalian middle ear evolution. S4 is characteristic of those Mesozoic mammals having a Meckelian groove on the dentary surface, as a trace of attachment for a persistent ossified Meckel's cartilage (Fig. 5C; Wang et al., 2001; Luo, 2011; Meng et al., 2011; Ramírez‐Chaves et al., 2016; Urban et al., 2017). Their lower jaws comprise only the dentary bone, with some vestiges of splenial and coronoid bones (Luo et al., 2007, 2017; Han et al., 2017), and there is no trace of connections to post‐dentary bones inferred by the absence of post‐dentary trough (Meng et al., 2011; Han et al., 2017; Luo et al., 2017). However, ear bones were not completely isolated, remaining indirectly connected to the mandible via the ossified Meckel's cartilage (Fig. 5B), which now serves as a stabilizing bridge for the migration of ear bones from the jaw to the base of the skull (Luo et al., 2007; Meng et al., 2011). In S4, the exclusively mandibular modules of S1 to S3 include now also the auditory ossicles quadrate/incus and stapes (orange modules in Fig. 5D,E), thus showing these new transitional otic‐mandibular modules a mix of mandibular and ear bones. The structure of the anatomical network changed in S4 and so did its modularity. The mammalian dentary‐squamosal articulation is already fully functional in S4, freeing the quadrate‐articular joint to, together with the pre‐articular and angular, evolve for transmitting airborne sounds (Wang et al., 2001; Kemp, 2007; Han et al., 2017). This transitional mammalian middle ear fills the morphological gap between the ancestral mandibular middle ear found in S1 to S3 and the derived definitive mammalian middle ear found in S5 (Meng et al., 2011).

Finally, a middle ear fully disconnected from the lower jaw (now only the dentary) characterizes the fifth evolutionary stage (S5; Fig. 6A–C). All extant mammals belong to S5, as well as those mammals of the fossil record whose dentaries lack the Meckelian and post‐dentary grooves on their surface. The ossified Meckel's cartilage disappears in S5, while the angular, pre‐articular‐articular and quadrate bones form the definitive middle ear bones ectotympanic, malleus and incus, respectively (Fig. 6A–C; Meng et al., 2011). The otic modules defining S5 (golden modules in Fig. 6D,E) show a full disconnection of the middle ear bones from their mandibular origin. Such evolutionary transition needed the resorption of Meckel's cartilage before its ossification during development (Luo, 2011; Anthwal et al., 2013, 2017; Maier & Ruf, 2016; Urban et al., 2017). Ontogenetically, the proximal part of Meckel's cartilage is medially displaced from the mandible and ossifies forming the incus and malleus bones (Fig. 5B), which display a negative allometry compared with the size of the dentary and the skull (Luo, 2011). The dentary grows until it meets the squamosal in a functional jaw joint (Luo, 2011; Anthwal et al., 2013, 2017). At this point in development, processes of apoptosis and chondroclast activity degrade the Meckelian cartilaginous matrix before the onset of osteogenesis (Anthwal et al., 2013, 2017; Urban et al., 2017). This distal resorption of the Meckel's cartilage breaks the connection between the middle ear and the lower jaw, allowing the formation of the mammalian middle ear (Anthwal et al., 2013, 2017; Urban et al., 2017). In fact, the absence of chondroclast activity generates the full endochondral ossification of Meckel's cartilage in mice and opossum mutants, resulting in a physical joint of the middle ear bones with the lower jaw that mirrors the ancestral phenotype of S4 (Luo, 2011; Luo et al., 2016; Anthwal et al., 2017; Urban et al., 2017). Thus, the complete disconnection of the middle ear bones from the lower jaw was the key evo‐devo event that triggered the second modularity change, from the transitional otic‐mandibular network modules found in S4 to the otic network modules found in S5, generating the definitive mammalian middle ear.

Various lineages independently acquired the mammalian middle ear by homoplasy (Luo, 2011) , just like our modularity analysis has shown for S5 (Fig. 7). Placental and marsupial mammals have different cellular and apoptosis mechanism involved in degradation of the Meckel's cartilage (Urban et al., 2017), and there is evidence for the independent acquisition of a middle ear separation in monotremes and some Mesozoic mammalian clades (Rich et al., 2005; Luo, 2011; Han et al., 2017). The modularity changes concomitant to the evolution of the mammalian middle ear that we reported also evolved convergently.

Disconnection of the middle ear bones as a developmental evolutionary trigger

Our comparison of the number of connections and betweenness centrality for key bones (Table S5; Fig. 8) suggests that there was an evolutionary trend toward bone disconnection in the jaw‐otic complex underlying the above‐described changes of modularity.

S1 presents the highest values of K and BC for the bones of the middle ear (Fig. 8). While the larger size of the articular and quadrate bones of basal synapsids explains their high values of K, high BC values of these bones appear because they are the only bones that connect the cranium to the mandibular complex (Fig. 9A). For the stapes, its high K value is also due to its massive size at this stage (the larger the bone, the more contacts it can make), playing a structural role supporting the braincase by linking a fenestra ovalis bounded by up to four bones in non‐mammalian synapsids: the prootic, opisthotic, basioccipital and parabasisphenoid (Fig. 2A; Mendrez, 1974; Crompton & Parker, 1978; Carroll, 1988, pp. 363, 394; Reisz et al., 1992; Clack, 1998, 2002; Sigurdsen et al., 2012). The mammalian middle ear bones could have functioned transmitting low‐frequency sounds from the ground to the inner ear in S1 (Reisz et al., 1992; Ivakhnenko, 2008; Huttenlocker & Sidor, 2016); in fact, our results suggest that the amplitude of vibrational movements could have been constrained not only by their size, but also by their many connections (K _articular = 4, K _quadrate = 6, K _stapes = 5; Fig. 8A; Table 1).

From the ancestral S1 configuration, the middle ear bones began a trend of disconnection from the mandibular complex in S2 and S3 (Fig. 8A). The new connection of the squamosal with the surangular bone in S2 (Fig. 9B), and with the dentary in S3 (Fig. 9C), increased their BC values at these two stages above the highest BC values that the quadrate‐articular joint had at S1. This replacement of the BC value could indicate that the new mammalian dentary‐squamosal connection joint is now assuming the compressive load transmission carried out by the ancestral quadrate‐articular jaw joint; the miniaturization of the mandible at these stages could have facilitated this new functional role (Lautenschlager et al., 2018). In turn, the quadrate and articular bones had mostly a masticatory role in S2 and S3, making eucynodonts and mammaliaforms less sensitive to high‐frequency sounds (Kermack et al., 1981; Kemp, 2007; Manley & Sienknecht, 2013), presumably because their ear bones still had too many connections to the cranium (K _articular = 5, K _quadrate = 5, K _stapes = 3, for S2; and K _articular = 4, K _quadrate = 3, K _stapes = 2, for S3; Fig. 8A, Table 1). However, unlike S1, the post‐dentary bones lose sutural contacts on the dentary surface at these stages, becoming sometimes isolated as a single rod suspended over the dentary trough by connective tissue, thus allowing vibrational movements under the influence of intense low‐frequency sounds (Kermack et al., 1981; Carroll, 1988, pp. 387, 393–394; Laurin, 1998; Kemp, 2007). At the same time, the quadrate developed a syndesmotic joint within the squamosal recess, instead of being attached to it by a suture (Fig. 3C), thus freeing it from some constraints and allowing it to achieve a more vibrational mobility (Kemp, 1979, 2007; Luo & Crompton, 1994; Luo, 1994). Finally, the stapes was also freed from its supporting role and performed a better sound transmission to the inner ear (Kemp, 1979; Carroll, 1988, p. 394; Clack, 2002). The key event that boosted these bony disconnections was the development of a new jaw joint. In stages S2 and S3, the quadrate‐articular joint became simpler (Luo & Crompton, 1994), but still played a dual function maintaining the jaw joint and transmitting low‐frequency sounds (Kermack et al., 1981; Kemp, 2007; Meng et al., 2011; Han et al., 2017; Lautenschlager et al., 2018).

A partial decoupling of feeding and hearing functions occurred at stage S4, in which the new mammalian dentary‐squamosal jaw joint presents higher BC values than the primitive quadrate‐articular jaw joint (Fig. 9D). The dentary and middle ear bones are more disconnected (Fig. 8A), resulting in a transitional otic‐mandibular module whose ear bones could function more efficiently transmitting airborne sounds, although still constrained by the chewing function because of their mandibular connections with the ossified Meckel's cartilage (Fig. 5B,C; Meng et al., 2011; Han et al., 2017). In stage S5, when the Meckel's cartilage is ontogenetically degraded and the middle ear bones are completely disconnected from the dentary, feeding and hearing functions were finally fully dissociated. Due to these events of bone disconnections in S4 and S5, the dentary decreased both its K and its BC values (Fig. 8). Similarly, the middle ear bones also displayed the progressive reduction of K values in S4 (K _articular = 2, K _quadrate = 3, K _stapes = 2) and reached their lowest values in S5 (K _articular = 2, K _quadrate = 2, K _stapes = 2; Fig. 8A, Table 1). Because the incus and stapes are the central components of the auditory chain in S5, it is not surprising that their BC values are slightly higher than in S4 (Figs 8B and 9E). The otic network configuration of S5, that of a definitive mammalian middle ear, allows ear bones to reach a greater vibrational mobility making them more sensitive to high‐frequency airborne sounds (Hopson, 1966; Kermack et al., 1981; Luo, 2011; Manley & Sienknecht, 2013).

Changes in complexity, specialization and bone contribution to the jaw‐otic complex

Morphologically, the single dentary of mammals is a more specialized bone than the compound lower jaw of their synapsid ancestors (Anthwal et al., 2013). Throughout its evolution, the dentary has developed a multitude of bony processes for the insertion of different muscles to perform all the chewing functions once shared by multiple bones in the lower jaws of non‐mammalian synapsids (Fig. 1; Anthwal et al., 2013; Lautenschlager et al., 2018). As suggested by Williston's Law, evolution tends to reduce the number of cranial elements whilst increasing the specialization of the remaining ones, a process called anisomerism (Williston, 1914; Gregory, 1934, 1935a; Esteve‐Altava et al., 2013; Rasskin‐Gutman & Esteve‐Altava, 2014). Heterogeneity (H _m), a network proxy for anisomerism, captures this phenomenon showing that otic modules in S5 have fewer bony elements (N _m) and are more specialized anatomical units than the mandibular modules from which they evolved (Table S4).

However, our results for the within‐module complexity show that the mammalian middle ear evolution led to an otic module that is simpler than the ancestral mandibular module from which it evolved (D _S5 < D _S1; C _S5 < C _S1; L _S5 > L _S1; Table S4). The loss and the massive disconnection of the bones involved in the jaw‐otic modules (K _m values in Table S4) caused the evolutionary simplification of the whole anatomical region, resulting in a bony chain that improves the transmission of sound. This result opposes to the general trend observed for the overall mammalian skull, whose anatomical transformations led to an increase in anatomical complexity accompanying the reduction in bone number (Esteve‐Altava et al., 2013, 2014; see also Sidor, 2001, and McShea & Hordijk, 2013 for a different interpretation). This would suggest that the mammalian middle ear and the overall skull evolved semi‐independently, following decoupled evolutionary trends of morphological complexity.