Bony cranial ornaments are correlated with body mass

We tested whether species with cranial ornaments evolved larger sizes relative to species that lack such display features. Using maximum likelihood on a single consensus tree, the best fitting phylogenetic generalized least squares (PGLS) regression model includes the λ (phylogenetic signal) and κ (punctuation) parameters, with an Akaike Information Criterion (AIC) weight of 1. We followed this analysis with a Bayesian regression model (phylogenetically normalized t-test) where λ and κ were both estimated during the Markov-chain Monte Carlo (MCMC), and which sampled over 3,000 time-scaled trees to account for our uncertainty in time calibration. The posterior distribution of the slope parameter, a, ranged from 0.5 to 3 (median=1.83), indicating strong support for the hypothesis that large body size evolves coincidently with cranial ornamentation (phylogenetic t-test mean R2=0.32; Fig. 1). Testing the same model against the null hypothesis for regressions in which the slope is forced to 0 (that is, no correlation), a Bayes factor value of 21.5 indicates very strong support that large theropod dinosaurs evolved cranial ornamentation more often than smaller species. Phylogenetic signal was close to one in all analyses (Fig. 1). We also find low estimates for the κ (punctuation) parameter, with a posterior median of 0.31, suggesting that shorter branches contribute more to trait evolution than longer ones.

Figure 1: Phylogenetic t-test data distribution performed in BayesTraits. (a) Blue data points represent unornamented theropods, red represents ornamented species, open circles are non-maniraptoriform theropods, whereas closed circles are species found within Maniraptoriformes, total sample size in phylogenetic t-test is 111 theropod species. Horizontal black line shows the mean log e body mass (4.207) among all theropods in the sample. Boxes within the box plot shows the first and third quartiles of the data; whiskers expand through the 95th quartile. The estimated posterior distribution for (b) slope, (c) punctuation and (d) phylogenetic signal shown on right. Full size image

Augmenting the results from the PGLS, we took advantage of the discrete character analytical ability of the threshold model of evolution23,24. The threshold model of evolution is a method adapted by Felsenstein23 to calculate correlations between discrete and continuous variables. To accomplish this goal, we assume that a series of unknown, unobserved continuous variables underlies each observed discrete character. In our case, these quantitative biological variables such as metabolic rate, hormone levels, eyesight and so on, all possibly play a role in the appearance of crests through theropod lineages, but are unknown and unattainable. These invisible continuous traits are converted to liabilities by means of a multivariate normal Brownian motion model that randomly, continuously evolves a discrete trait until it passes over a threshold, thereby converting the original discrete character state to the next. Brownian evolution of the trait in question continues throughout the phylogenetic tree until the tips are reached, wherein the estimated liability for each tip is used in a correlation test with the known continuous variable23,24. Our analysis finds a high correlation between body mass and the presence of cranial ornaments in theropod dinosaurs (threshold model linear regression mean R2=0.759; Supplementary Table 1).

After establishing a correlation between large body mass and the presence of bony cranial ornaments, we set to estimate the body mass below which bony ornaments are not predicted to evolve. The PGLS analysis from above estimates a minimum of 55.2 kg for this body mass threshold, whereas the lowest estimate is predicted to be 36 kg simply by using the body mass of Syntarsus kyentakatae, the smallest ornamented theropod in our sample. A different method of determining the body mass minimum is to use the θ (theta) parameter estimated for unornamented theropods in generalized Hansen models25 (that is, modified Ornstein–Uhlenbeck model). We found that the best fitting model estimated a large difference between unornamented body mass optima (10.96 kg) and ornamented optima (1,396 kg). One reason for the discrepancy in body mass estimates between the PGLS and the generalized Hansen models is that the latter included data for only the non-maniraptoran portion of the phylogenetic tree (see ‘Methods’ section for explanation) and that estimating parameter values for single and mulitpeak OU models is prone to varying amounts of error based on provided data26 (see ‘Discussion’ section for further information on OU biases).

Larger body size evolution for adorned theropods

Many lineages, but certainly not all theropod lineages, underwent the morphological transition of gaining or losing osteological cranial ornamentation. We estimated the transition rates at which cranial ornamentation is gained and lost using reversible jump MCMC (RJMCMC), which is a Bayesian method that efficiently explores the possible model parameters without fully exploring the entire model space. One hundred per cent of the posterior distribution is a one-parameter model (where the rate of gaining cranial ornaments is equal to the rate of loss). To test the confidence in the equal rates model derived from the RJMCMC analysis, we also compared a non-reversible jump analysis using an exponential hyperprior (seeds the mean of the exponential prior from a uniform on the interval 0–10 and allowing rates to vary across the parameter estimates) to an equivalent analysis with the rates forced equal to one another. A Bayes factor of 2.5 indicates some support for the equal rates model. Results from the fitDiscrete function in the R package geiger27 concurred that an equal rates model best fit the data (although the symmetrical model fit equally well according to this analysis; Supplementary Table 2).

Next, we estimated the rate at which a theropod lineage crosses the 1,000 kg value of giantism among theropods, as defined by Erickson et al.28, with and without cranial ornamentation. An RJMCMC analysis suggests that discretized body mass (≥1,000 kg) evolved an order of magnitude faster ( × 20 faster) in lineages possessing cranial ornaments (average posterior transition rate to large body size in species lacking ornaments=0.01, in species with ornaments=0.2). These data indicate that body mass evolution across the 1,000 kg threshold in non-avian theropods was dependent on the prior acquisition of ornaments.

Generalized Hansen models provided similar results as RJMCMC. However, using the entire theropod tree produced parameter outcomes that were beyond biological reality, most likely because of conflicting patterns of crest development and large body size evolution among the maniraptorans29 compared with more basal species. For instance, α parameter values, those designating the attraction of lineages toward an optimum, were consistently estimated at exceedingly low values of 10−9 and σ2 values of evolutionary rate were estimated at low rates of 10−2. In addition, estimates of the two body mass optima, θ, for ornamented species were in many cases approaching 50% higher than the largest theropods in the database. Estimating the root θ produced even worse results with values well beyond reason (for example, exp[10−6] body mass for unornamented species and exp[107] body mass for ornamented species, with standard errors larger than the estimated θ values). Since we were most interested in the effect of bony cranial ornaments on the evolution of body size, we trimmed the theropod tree to exclude maniraptoriform species thereby removing noise from the dataset. As such only the results incorporating the non-maniraptoran portion of the theropod tree are presented here (57 total taxa, 21 unornamented and 36 ornamented).

The best fitting generalized Hansen model optimizations calculated over non-maniraptoran species overwhelmingly supported an OUMV model (Supplementary Tables 3,4; Supplementary Data 1,2), which is one where the body mass parameter estimate θ and rate parameter, σ2, varied across lineages, whereas the α parameter stayed constant (Supplementary Tables 3,4). Two optimal peaks of log e body mass between ornamented (7.241±0.334, root not estimated30) and unornamented (2.394±1.538, root not estimated30) theropods show that there is considerable difference between the ornamentation regimes. A single alpha rate parameter (α=0.131±0.049) describes how rapidly a lineage is hypothesized to evolve from the lower body mass optimum to the next or if a lineage begins away from the optimum this parameter estimates the pace that the lineage will move toward its optimal body mass. This best fit model also includes a rate parameter, σ2, that estimates the degree to which body masses vary over lineage evolution between the two optima. These results held with both the root estimated and non-estimated models. The standard error for θ in the unornamented regime is considerably higher than for the ornamented regime. This finding is not surprising given that both small and large species are unornamented. Since the vast majority of species that lack bony cranial ornaments are small bodied, the overall θ model averaged estimate for log e body mass (2.394) is much lower than the log e (7.241) model averaged estimated for ornamented lineages. The σ2 is much larger for unornamented lineages, meaning that jumps between body masses are larger and more sporadic than that in ornamented lineages. The latter regime appears to display a directed trend of body mass evolution, rapidly approaching the log e (7.241) body mass once a lineage obtains ornamentation. The highly variable σ2 parameter (evolutionary rate; σ2=1.358±0.642) among unornamented lineages compared with the quite small σ2 (0.313±0.117) for ornamented lineages indicates a directional trend toward phyletic giantism among ornamented theropod clades. An α parameter that is relatively small as in our data, combined with a high optima, produces the directional trend pattern within an Ornstein–Uhlenbeck context because once the α parameter approaches zero, OU models reduce to Brownian motion with a trend31. Although the α parameter is not extremely close to zero, when combined with the low σ2, together they can produce the same evolutionary result of directional evolution toward the optima25.

Albeit only a rough approximation25,31, using the alpha parameter to calculate the phylogenetic half-life31,32 predicts that once bony ornaments are acquired in a theropod lineage, body mass could have evolved halfway toward the gigantic optimum about every 5.291 Ma. Whereas this rate may not reflect true biological reality25, the predicted phylogenetic half-life is only 3% of the entire tree age, indicating rapid evolution among theropods into two optima instead of a single optimum with a trend. That is, this model suggests that once a lineage gained ornaments, body mass evolution became more directed with smaller lineages quickly attaining gigantic proportions toward the ornamented optima.

Cranial ornamentation evolved independently

We also evaluated the hypothesis that osteological cranial ornamentation evolved convergently in different theropod lineages by comparing analyses in which nodes are ‘fossilized’ to a given state. A Bayes factor test of 9.4 provides strong evidence that the ancestral theropod lacked cranial ornamentation, and therefore this trait evolved convergently in different groups of theropods. Our analyses further suggest that cranial ornamentation is ancestral for Allosauria33 (Allosaurus and kin; Bayes factor test=6.5), but the ancestral condition in Tyrannosauroidea (Tyrannosaurus and kin) is only weakly supported (Bayes factor test=2.5 favoring ornamentation), despite the two most primitive members of the clade possessing ornamentation. The analysis suggests that the ancestor of Dilong (which lacks ornaments) and Tyrannosaurus lacked cranial ornamentation (Bayes factor test=11.3). Among more derived tyrannosaurs, it is not until the ancestor of Appalachiosaurus and Tyrannosaurus that we find strong evidence for cranial ornamentation (Bayes factor test=15.3).

In an effort to posit hypotheses of causality, we assessed whether cranial ornamentation or large body size evolved first in different groups of theropods. We suggest that the common ancestor of Allosauria33 was large bodied (Bayes factor test=8.2 for binary analysis of body mass using RJMCMC, with a log e body mass of 7.3 using Brownian motion continuous models) and as noted above possessed cranial ornamentation. Our analysis suggests that the tyrannosauroid ancestor of Dilong and Tyrannosaurus was not large bodied (Bayes factor test=7.7 for binary analysis of body mass using RJMCMC, with a log e mass of 4.58 using Brownian motion continuous models). Paralleling results above, large body size, like cranial ornamentation, does not evolve in tyrannosauroids until the common ancestor of Appalachiosaurus and Tyrannosaurus, (Bayes factor test=7.3 for binary analysis of body mass using reversible jump MCMC, with a log e mass of 6.91 using Brownian motion continuous models); however, the basal tyrannosauroids Proceratosaurus and Guanlong do possess cranial ornaments.

Given the controversy of ontogenetic maturity in the only known specimen of Raptorex34 and the known skeletal immaturity of Dilong, our tyrannosauroid results may be slightly skewed because of coding these larger species with no cranial ornaments. Despite the fact that the adult body size is unknown for Dilong and Raptorex, if we suppose they follow the pattern of most every other tyrannosauroid by possessing cranial ornaments at maturity, their larger mature body size would only increase the fit of our model that bony cranial ornamentation is linked to large body size evolution in non-maniraptoran theropods. Contrary, if their body size remained close to the currently observed size, yet they grew cranial ornaments rapidly at a later ontogenetic stage than preserved, this would lower the slope of the regression line between the unornamented and ornamented body masses, moreover, it would lower the estimated threshold for the attainment of cranial ornaments (Dilong is smaller than the presently smallest ornamented species Syntarsus kyantakatae). However, the overall effect would likely be minimal provided that these are two taxa out of the whole sample. Nonetheless, ontogenetic uncertainty should be an area of consideration when interpreting the evolution of body size within Tyrannosaurioidea. An additional observation that may have a bearing on the supposed lack of ornamentation in Xiongguanlong and possibly Raptorex and Dilong is that ornamentation style shifted from thin elongated parasagittal crests in basal species Guanlong and Proceratosaurus to rugose knobs in Appalachiosaurus and kin.

Taxonomy does not affect model results

Maniraptoriform theropods have a noticeable lack of cranial ornamentation compared with more basal species, and comparing their inclusion in Generalized Hansen models to those withholding them from the same models suggests that a different evolutionary trajectory may be at play. PGLS was used to better define a predictive body mass threshold for species required before the acquisition of osteological cranial ornamentation, except in this instance we controlled for the effect of being a maniraptoriform on model predictions of body mass by including an interaction term. Using only non-maniraptoriform theropods produced a regression model of BM=1.98+2.09(Orna), (PGLS mean R2=0.32, ɛ=0.253) where Orna is the presence (1) or absence (0) of osetological cranial ornamentation. Next we tested nested models of the entire 111 species dataset. The simpler model produced a regression equation of BM=1.97+2.04(Orna), (PGLS mean R2=0.199, ɛ=0.395). The more complex model that included the dummy variable and interaction term produced a model of BM=1.97+2.15(Orna)−1.25(Phylo)−0.69(Phylo)(Orna), (PGLS mean R2=0.216, ɛ=0.394), where Phylo refers to either being included within (1) or excluded (0) from Maniraptoriformes. A Bayes factor test of 0.307 shows insignificant difference between the simpler versus more complex model. This means that simply being a maniraptoriform does not increase the model’s correlative power, and therefore synapomorphies of the entire clade (for example, presence of pennaceous feathers) do not seem to hold much role in body mass evolution for this clade. It should be noted that prediction via PGLS can be difficult and these body mass predictions should be used as a generalization of the true evolutionary model.

Comparison of the models incorporating the entire phylogeny versus only the more basal taxa shows a much better correlation for non-maniraptoriforms. In large part this is because maniraptoriform species vary more widely in body mass and almost exclusively do not possess osteological cranial ornamentation. Also, the two terms within the more complex model show that body mass within the maniraptoriform clade is generally much smaller than predicted for the basal taxa, and when ornamented maniraptoriform body masses are predicted, the estimate is considerably lower than any predicted for more basal ornamented taxa.