The concept of homology underpins the cladistic analysis of morphological data. Testing of homology is usually considered a two-step process (Patterson, 1982a; Pinna, 1991). First, provisional statements of homology are made (primary homology), which are hypotheses based on comparative anatomy. Primary homologues are then subjected to cladistic analysis, and those that correspond to synapomorphies are then considered ‘secondary homologues’; this term corresponds to the vernacular use of the term homology (similarity due to common ancestry). The starting point for a cladistic analysis, the character-by-taxon matrix, is a set of primary homology statements. Primary homology statements are based upon ‘homology criteria’ (Patterson, 1988; Rutishauser and Moline, 2005). The first and most important criterion for primary homology is similarity: structures should correspond in position and structural details (developmental similarity is part of this criterion). Second is the test of conjunction: if two structures are found together on a single animal, they cannot be homologous (Patterson, 1988).

Placoderms are stem gnathostomes, and the evolution and morphology of their jaws is thus of particular interest. The upper jaw bones of placoderms present a major unresolved example of a homology problem. Arthrodiran placoderms possess two upper gnathal plates in their jaws, termed the anterior and posterior supragnathals (Figure 1A). These have traditionally been considered primary homologues of the vomers and dermopalatines of osteichthyans (Stensiö, 1963a; Stensiö, 1969), which are palatal bones sitting on the roof of the mouth, inside the maxilla and premaxilla (Figure 1C). This proposed homology of placoderm supragnathals and osteichthyan palatal bones is based on positional criteria.

Figure 1

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The discovery of maxillate placoderms reignited debates about the homology of placoderm and osteichthyan skull bones (Zhu et al., 2013; Zhu et al., 2016), and a new hypothesis regarding the homology of arthrodiran gnathal plates was proposed (Zhu et al., 2016; Zhu et al., 2019). Maxillate placoderms have premaxillae and maxillae with both palatal and facial laminae (Figure 1D). The palatal laminae articulate with the ventral surface of the braincase, and therefore correspond in position to arthrodiran supragnathals. The facial laminae are continuous with the external dermal bones of the skull, and are equivalent in position to osteichthyan premaxillae/maxillae. Zhu et al., 2016 therefore proposed the homology of arthrodiran supragnathals with the premaxilla and maxilla of osteichthyans. This negates a putative homology with the osteichthyan vomer-dermopalatine series, which would otherwise fail the test of conjunction (placoderm supragnathals cannot be homologous to both the premaxilla-maxilla and vomer-dermoplatine series). Nevertheless, the traditional hypothesis for the homology of arthrodiran supragnathals continues to be discussed in the literature (Hu et al., 2017). There are therefore two opposing possibilities for the primary homology of arthrodiran gnathal bones.

A number of approaches have been proposed to distinguish between conflicting hypotheses of primary homology. Jardine, 1969 provided a method that selected between alternative homologies of rhipidistian skull roof bones without reference to phylogeny, based on the criterion of preservation of spatial relationship. Lee, 1998 used parsimony to distinguish between conflicting conjectures of homology on a fixed tree topology. The latter was essentially the approach taken by Zhu et al., 2016 to support their hypothesis regarding placoderm supragnathal bones. However, choices regarding primary homology statements necessarily restrict the search for secondary homologues: phylogenetic analyses can only find the optimal tree given the input character matrix. Indeed, it has been suggested that the two-step approach to homology entails a degree of circularity (Rieppel, 1996), although this is likely to only be an issue when a phylogeny is weakly supported. A solution to this issue is the simultaneous inference of primary and secondary homology, termed dynamic homology.

Dynamic homology of molecular sequence data in a parsimony framework has been implemented in the software POY (Wheeler et al., 2006; Varón et al., 2010). Models for dynamic homology of molecular data have also been developed (Lunter et al., 2005; Redelings and Suchard, 2005; Wheeler, 2006) and implemented within the phylogenetic software Bali-Phy (Suchard and Redelings, 2006) and POY 5.0 (Wheeler et al., 2015). Agolin and D’Haese, 2009, used the parsimony implementation in POY to analyze morphological data (specifically the setae of collembolans). However, morphological characters, with their hierarchical dependence relationships and arbitrary sequence within a data matrix, are often not amenable to models used to align molecular data. Ramírez, 2007 presented a parsimony approach to dynamic homology, using the empirical example of sclerites on the male copulatory organs of anyphaenid spiders. In this method, multiple matrices with alternative alignments of morphological characters were analysed, and the phylogenetic tree and homology combination with the shortest tree length was selected.

Dynamic homology methods for morphological data have thus far been rarely explored, and are restricted to parsimony-based approaches. However, a Bayesian approach would confer a number of advantages. Alternative homology statements could be considered as ‘nuisance parameters’, such that phylogenetic trees could be estimated while accounting for uncertainty in primary homology statements. Conversely, if discovering homology is the aim, the tree topology could be considered the ‘nuisance parameter’. Bayesian tip-dated analysis of morphological data allows comparative analysis (such as biogeography or ancestral state reconstruction) to occur simultaneously with tree search (e.g. Lee et al., 2018). Comparative analyses could therefore be performed while accounting for uncertainty in both tree topology and primary homology statements.

Here, we present an approach to dynamic homology within a Bayesian tip-dating framework, which we use to test the alternative conjectures of placoderm jaw bone homologies. The homology relations of placoderm jaw bones have implications for our understanding of character evolution in early vertebrates. In particular, homology of placoderm supragnathal bones with the marginal jaw bones of osteichthyans suggests a deep (early) origin for these bones. Zhu et al., 2016 proposed their hypothesis within the framework of placoderm paraphyly (Brazeau, 2009; Davis et al., 2012; Zhu et al., 2013), but an alternative hypothesis of placoderm monophyly (excluding maxillate placoderms) is supported by an essentially equivalent amount of morphological data, and is strongly supported under Bayesian tip-dated methods (King et al., 2017). The implications of the hypothesis of Zhu et al., 2016 within the framework of placoderm monophyly have not been discussed. We therefore simultaneously estimated a credible set of phenotypes for the (apomorphy-defined) gnathostome common ancestor to explore character evolution in early gnathostomes while accounting for phylogenetic uncertainty, divergence date uncertainty, and alternative placoderm jaw bone homologies.

Dynamic homology

We implemented a method for dynamic homology of morphological characters within the open source BEAST2 software package homology (https://github.com/king-ben/homology; King, 2021; copy archived at swh:1:rev:6e6dbd77443b0d963640b3cb603c4310b5a4b47e). The method takes as inputs alternative character coding alignments, here called homology alignments, which are alternative character codings corresponding to alternative homology hypotheses for morphological features (for example placoderm jaw bones). Homology alignments can be included alongside fixed alignments (Figure 2), such that only a subset of characters has dynamic homology. During a BEAST2 MCMC run, the homology alignment used to calculate the posterior is determined by a homology state parameter, which is changed by an operator (Figure 2). The MCMC will spend more time in the homology state corresponding to the homology alignment that returns the highest tree likelihood.

Figure 2

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The homology package contains two java classes corresponding to CalculationNodes (which calculate a part of the posterior based on inputs). These are HomologyTreeLikelihood and HomologyMultiplexer (Figure 3). The HomologyTreeLikelihood class is an extension of the core BEAST2 TreeLikelihood class, and differs in associating a particular homology alignment with a homology state. The HomologyMultiplexer takes as input two or more HomologyTreeLikelihoods and a homology parameter, the latter is an integer parameter with states (0, 1,…,N) corresponding to N homology states (one for each HomologyTreeLikelihood). During an MCMC run, the homology-multiplexer returns the value of the homology tree likelihood corresponding to the current state of the homology parameter. Due to the possibility of correlated tree- and homology-space, the package also contains two updated tree operators which simultaneously change the tree topology and homology state: HomologySAWilsonBalding and HomologySAExchange.

Figure 3

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Homoplasy-partitioned Bayesian tip-dated analysis (with dynamic homology of placoderm upper jaw bones) of the gnathostome fossil dataset results in the majority-rule consensus tree shown in Figure 4. Core placoderms (placoderms excluding maxillate forms) are monophyletic (posterior probability, pp = 1.0). The maxillate placoderms Entelognathus and Qilinyu are resolved as the sister group to core placoderms, but with weak support (pp = 0.70). Janusiscus is resolved as a stem osteichthyan, sister to Dialipina, but support for this grouping is again weak (pp = 0.57).

Figure 4

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We find strong support for homology state 1 (pp = 0.984), corresponding to the hypothesis that placoderm supragnathal bones are homologous to premaxillae and maxillae (Zhu et al., 2016). The mean log likelihood for homology alignment 0 is −85.099, and for homology alignment 1 –79.883. The MCMC chain therefore rarely accepts proposals for homology state 0 (Figure 5).

Figure 5

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Principal coordinates (PCO) analysis of gnathostome fossils reveals chondrichthyans (including acanthodians), osteichthyans and core placoderms form three discrete and well-separated groups (Figure 6A), concordant with the results of Davis et al., 2012. Janusiscus is an outlier, lying equidistant from the three groups, whereas maxillate placoderms plot close to core placoderms.

Figure 6

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We used ancestral sequence logging in BEAST2 to reconstruct the phenotype of the gnathostome ancestor in each sample from the posterior. A sample of 90 of these reconstructed ancestors included in the PCO mostly plot close to placoderms, with a small number plotting in outlier positions closer to Janusiscus. A second PCO using only placoderms (maxillate and core) and the reconstructed ancestors is shown in Figure 6B, with the point cloud of reconstructed ancestors converted to a 2D density plot. Entelognathus plots close to the center of the ancestral area, while Qilinyu, arthrodires, petalichthyids and acanthothoracids are equidistant. Antiarchs and ptyctodontids plot the furthest from the reconstructed ancestors. However, it should be noted that the two principal axes account for less than 10% of the total variance.

Plotting the raw distance measures shows that maxillate placoderms are the most similar taxa to the reconstructed ancestors (Figure 6C). The individual taxon with the lowest distance to the reconstructed ancestor (in each sample from the posterior, n = 1801) was a maxillate placoderm for 95% of the reconstructed ancestors (Figure 6D). This suggests that of the known gnathostome fossils, the maxillate placoderms (in particular Entelognathus) are the least divergent known descendants of the gnathostome common ancestor.

The reconstructed ancestors also allow us to calculate the posterior probability of particular character states at the gnathostome node (i.e. the proportion of reconstructed ancestors with a particular character state). Table 1 displays a number of characters of interest, including characters of the upper jaw bones and characters possessed by some core placoderms, argued to be retained plesiomorphies under the hypothesis of placoderm paraphyly (Brazeau, 2009; Dupret et al., 2014). Results for all characters are available in the supplementary information (Table 1; Source data 1). Our results suggest that the gnathostome ancestor had a premaxilla and maxilla with both palatal and facial laminae, no vomer-dermopalatine series, anterior/ventral nasal capsules and lateral orbits not surrounded by neurocranium. Putative core placoderm synapomorphies (claspers, optic fissure) are reconstructed as absent at the gnathostome node with moderate support (Table 1). This uncertainty is likely due to the high proportion of missing data for these characters. Critically, it is unknown whether or not maxillate placoderms possessed these putative core placoderm synapomorphies.

We find strong support for the hypothesis of Zhu et al., 2016, that placoderm supragnathal bones are homologous to the maxilla and premaxilla of osteichthyans and maxillate placoderms (Figure 5). However, we present a distinct scenario regarding the trajectory of upper jaw bone evolution (Figure 7). Zhu et al., 2016 proposed that the plesiomorphic states of the maxillae and premaxillae were as palatal bones, exemplified by the arthrodiran condition. Facial laminae were then gained in the common ancestor of maxillate placoderms and crown gnathostomes, and palatal laminae were lost in osteichthyans. We instead propose that the common ancestor of (apomorphy-defined) gnathostomes possessed maxillae and premaxillae with both facial and palatal laminae. Facial laminae were subsequently lost in core placoderms and palatal laminae were lost in osteichthyans. The stem osteichthyans Lophosteus and Andreolepis show a possibly intermediate condition, in which the marginal jaw bones have internal (oral or palatal) laminae that are more strongly developed compared to other osteichthyans (Botella et al., 2007; Cunningham et al., 2012; Chen et al., 2016; Chen et al., 2020).

Figure 7

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In concordance with Zhu et al., 2016, we find strong support for a lack of the vomer-dermopalatine series in the gnathostome ancestor. Our scenario suggests that arthrodires, for which morphological data of the jaws is best known (Hu et al., 2017), exhibit a specialized condition. Independent evidence for this hypothesis comes from recently described acanthothoracids (Vaškaninová et al., 2020), which exhibit marginal dentitions and jaw bones quite unlike those of arthrodires. In addition, the inner dental arcade of the stem osteichthyan Lophosteus consists of many ‘tooth cushions’ bearing no resemblance to arthrodire gnathal plates (Chen et al., 2017).

The divergent trajectories of the premaxilla and maxilla in osteichthyans and core placoderms may be associated with alternative ecological roles among their earliest members. Osteichthyans from the Silurian Kuanti formation include the large Megamastax (Choo et al., 2015). The maxillate placoderms from the same formation however are clearly not apex predators, lacking large teeth on their jaw bones and in the case of Entelognathus, possess immovable eyes (Zhu et al., 2013). The loss of facial laminae in core placoderms may be associated with increased focus on crushing invertebrate prey, and may be analogous to the loss of the maxilla and specialization of the vomers in lungfishes. Conversely, the predatory osteichthyans emphasized the external tooth row and thus facial laminae.

Homology of the arthrodiran supragnathals with the premaxillae and maxillae of maxillate placoderms is consistent with observations from comparative anatomy (Zhu et al., 2016; Zhu et al., 2019). The snouts of maxillate placoderms differ from those of arthrodires mainly in the degree of dermal bone cover and are very similar in terms of their gross morphology. An early arthrodiran snout, such as that of Kujdanowiaspis (Dupret, 2010) differs from the maxillate placoderm condition by absence of facial laminae and a relatively small internasal plate compared to the large anterior premedian plate of Entelognathus (Zhu et al., 2013). Zhu et al., 2019 suggested that the arthrodiran condition results from the inward shift of the upper jaw bones. However, the downturned, ventrally directed, snouts of maxillate placoderms means that reduction of the facial laminae and premedian plate are the only transformations required to leave the upper jaw bones separated from the dermal skull roof and in a palatal position, as in arthrodires.

The results of our phenetic analysis of reconstructed ancestors suggest maxillate-placoderm-like conditions in the last common ancestor of (apomorphy-defined) gnathostomes. Due to the nested position of acanthothoracids and antiarchs within a monophyletic core placoderms, we find strong support for anterior-ventral nasal capsules and lateral eyes in the gnathostome ancestor (Table 1). Under this hypothesis, the dorsal nasal capsules of antiarch, acanthothoracid and rhenanid placoderms are convergent with those of the jawless osteostracans and galeaspids, rather than representing shared plesiomophies (King et al., 2017). Conversely, the shared cranial architecture of arthrodires, maxillate placoderms and osteichthyans (Dupret et al., 2014), represent shared plesiomorphies (Table 1; King et al., 2017). Within agnathan fishes, the braincase proportions of the jawless heterostracans, which probably possess paired anterior nasal capsules (Halstead, 1973; Janvier, 1996), may represent the plesiomorphic gnathostome condition more closely than osteostracans or galeaspids.

Although our phenetic analysis suggests that maxillate placoderms are the gnathostomes morphologically closest to the ancestral condition, we are not suggesting that they are directly ancestral. The distance from each reconstructed ancestor is usually in the range 0.2–0.3, suggesting that even maxillate placoderms are highly derived from the gnathostome common ancestor. This result is not surprising given that our analysis suggests gnathostomes diverged during the Ordovician (Figure 4). Tentative support for this divergence might be found in the enigmatic fossils of Skiichthys (Smith and Sansom, 1997) and Mongolepidae (suggested to be early chondrichthyans, Andreev et al., 2016). Maxillate placoderms are never recovered as sampled ancestors in the analysis, and the fact that they are of the same age as the osteichthyan Guiyu (Zhu et al., 2009) precludes this. Entelognathus and Qilinyu are themselves quite disparate and possess their own specializations, most notably the eyes of Entelognathus (Zhu et al., 2013; Zhu et al., 2016).

The results of our analysis are contingent on a phylogenetic hypothesis, in particular the monophyly of core placoderms, which is only strongly supported under a Bayesian tip-dating approach. The differences between parsimony and Bayesian tip-dated trees are discussed at length in King et al., 2017. The hypothesis of placoderm paraphyly (Brazeau, 2009; Davis et al., 2012; Zhu et al., 2013), implies a radically different scenario for character evolution (Dupret et al., 2014), in which the maxillate placoderms are not representative of ancestral conditions.

Our study proposes the application of dynamic homology concepts to morphological characters in a Bayesian framework. In this manuscript we have applied the method to placoderm jaw bones, but it could also potentially be used to examine skull roof homologies in the future. It should be noted that the simultaneous analysis of primary and secondary homology has been criticized (Simmons, 2004), because adding new morphological characters to a data matrix should be a test of phylogenetic relationships, rather than simply adding further support to a given phylogenetic hypothesis. Thus, it can be argued that multiple conflicting primary homology statements should only be analysed with dynamic homology when they are equally plausible. In such cases, supporting the primary homology statement that best fits a phylogenetic hypothesis is preferable to an arbitrary choice. There may also exist cases where alternative primary homology statements support different tree topologies, and in this case arbitrary choices of primary homology statements could lead to suboptimal phylogenetic trees.

We compiled a morphological data matrix of gnathostome fossils (Supplementary file 1). The matrix is based on King et al., 2017 with a revised taxon and character matrix. The taxon list was updated with the addition of Gladbachus adentatus, Milesacanthus antarctica, Nerepisacanthus denisoni, Rhinodipterus kimberleyensis, Chirodipterus australis, Dipterus valenciennesi, Tungsenia paradoxa, Diplocercides kayseri, Qingmenodus yui, Raynerius splendens, Lehmanosteus hyperboreus, Shearsbyaspis oepiki, and Qilinyu rostrata. Ramirosuarezia boliviana, Wuttagoonaspis fletcheri, Gavinaspis convergens and Osorioichthys marginis were removed.

Characters concerning the premaxillae, maxillae, dermopalatines and vomers were coded into two alternative homology alignments. These characters included presence and absence of these bones, as well as dependent characters. One alignment (homology state 0) was coded according the traditional interpretation of placoderm jaw bones (Figure 1A), in which the placoderm supragnathal bones are considered primary homologues of the vomer-dermopalatine series of osteichthyans. A second alignment (homology state 1) was coded according to the alternative interpretation (Zhu et al., 2016), in which placoderm supragnathal bones are considered primary homologues of the premaxilla-maxilla series of osteichthyans and maxillate placoderms. In total, the matrix had 489 characters with fixed homology, and 18 with variable homology.

We analysed the matrix in BEAST2.6.2 (Bouckaert et al., 2019), using the beagle calculation library (Ayres et al., 2019). We used homoplasy-based partitioning (Rosa et al., 2019) to account for rate variation among characters. Homoplasy was calculated using an implied weights parsimony analysis in TNT (Goloboff and Catalano, 2016), with concavity constant k = 10. Characters with different homoplasy values depending on homology state were assigned the lower value. Characters were partitioned according to the number of states as well as homoplasy. Each partition was assigned a separate mutation rate parameter and was analysed using the Mk substitution model (Lewis, 2001). The weighted mean value of the mutation rates was fixed at one, and each individual mutation rate parameter was assigned a normal distribution prior, with mean one and standard deviation 2.

We implemented a sampled ancestor birth-death model (Gavryushkina et al., 2014). The birth rate was assigned a lognormal prior with mean (in real space) 0.14 and standard deviation 0.9. Extinction and sampling rates were assigned exponential priors with mean 0.1. Tip dates were assigned to fossil sites with uniform priors on fossil site ages (King and Rücklin, 2020). Gnathostomes, gnathostomes+osteostracans and polybranchiaspids were constrained to be monophyletic. The clock model was an uncorrelated lognormal relaxed clock (Drummond et al., 2006) with a lognormal prior (mean −5.5, standard deviation 2) on clock rate and an exponential prior (mean 1) on clock standard deviation. We used ancestral sequence logging to reconstruct ancestral states for all characters at the (apomorphy-defined) gnathostome node at every sampled generation of the MCMC. This leads to 1801 ‘reconstructed ancestors’, which comprise a credible set of phenotypes at the gnathostome crown node.

We ran the analysis for 800 million generations, and for four independent runs. The MCMC chain was sampled every 400000 generations, and 10% of the run was discarded as burn-in, resulting in a posterior sample of 1801 trees. Convergence of 4 independent runs was confirmed in Tracer 1.7 (Rambaut et al., 2018) and RWTY (Warren et al., 2017). Following the recommendations of O'Reilly and Donoghue, 2018, we calculated the 50% majority-rule tree in the R package ape (Paradis and Schliep, 2019), then time-scaled and annotated this tree using TreeAnnotator 1.10.2 (Suchard et al., 2018). The Beast2 xml file is available in the supplementary information (Supplementary file 2).

We used distance-based methods to determine the similarity of known fossil taxa to the reconstructed sequences at the gnathostome node. Principal coordinates analysis was performed in the package Claddis (Lloyd, 2016) in R 4.0.0 ‘Arbor Day’ (R Development Core Team, 2018). We used the Maximum-Observable Rescaled Distance, equivalent to the Gower, 1971 coefficient for our dataset. First, we performed ordination using the gnathostome fossils in our dataset, and a sample of the reconstructed ancestors from BEAST2 (Figure 6A). This sample consisted of 5% of the posterior sample, from which we excluded those sampled generations where the homology state was 0 (n = 1), for a total of 90 reconstructed ancestors. Homology alignment 1 was used for distance calculations. A second ordination was performed using only placoderms (both core placoderms and maxillate placoderms)(Figure 6B). The point cloud of reconstructed ancestors was converted to a density plot using ggplot (Wickham, 2016). We also plotted the raw distance measures of each gnathostome taxon to each of the 90 reconstructed ancestors (Figure 6C). Finally, we calculated the taxon with the shortest distance to the reconstructed ancestor for the entire posterior distribution (1801 reconstructed ancestors). These calculations used the homology alignment corresponding to the sampled homology state.

The data matrix in nexus format and the BEAST2 xml file are available in the supplementary information. The beast2 source code and R analysis scripts are available at https://github.com/king-ben/homology (copy archived at https://archive.softwareheritage.org/swh:1:rev:6e6dbd77443b0d963640b3cb603c4310b5a4b47e).

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