Unexpectedly uneven distribution of functional trade-offs explains cranial morphological diversity in carnivores

Functional trade-offs can affect patterns of morphological and ecological evolution as well as the magnitude of morphological changes through evolutionary time. Using morpho-functional landscape modelling on the cranium of 132 carnivore species, we focused on the macroevolutionary effects of the trade-off between bite force and bite velocity. Here, we show that rates of evolution in form (morphology) are decoupled from rates of evolution in function. Further, we found theoretical morphologies optimising for velocity to be more diverse, while a much smaller phenotypic space was occupied by shapes optimising force. This pattern of differential representation of different functions in theoretical morphological space was highly correlated with patterns of actual morphological disparity. We hypothesise that many-to-one mapping of cranium shape on function may prevent the detection of direct relationships between form and function. As comparatively only few morphologies optimise bite force, species optimising this function may be less abundant because they are less likely to evolve. This, in turn, may explain why certain clades are less variable than others. Given the ubiquity of functional trade-offs in biological systems, these patterns may be general and may help to explain the unevenness of morphological and functional diversity across the tree of life.


Evolutionary modelling
We used EIC to calculate the relative support for each evolutionary model.The models' EIC display considerable overlap (Supplementary Figure 1) suggesting that BM, EB and OU models have similar fit.We assessed the mode of evolution of the weight w by fitting different models using the function fitContinuous accounting for standard error and the results are reported in Supplementary Table 4.
we performed a repeated measure test 3 considering males and females as repeated measures of the same species without finding significant differences (F = 0.22; P = 0.87).Then, we extracted the species shared between the two dataset and performed a repeated measure test, which failed to reject the null hypothesis of no difference in shape between corresponding shapes between the two datasets (F = 2.23; P = 0.15).This suggests that the species-level shape estimates are not consistently different between datasets.Furthermore, we tested whether potential differences between the two datasets could arise from size differences in the specimens used.To do so we computed the Procrustes distances between corresponding species in the two datasets and the absolute differences between the centroid sizes of the different configurations.Then we tested for the significance of the correlation of these Procrustes distances and differences in centroid size and found they were not significant (Pearson r = 0.31, P = 0.073; Spearman rho = 0.29, P = 0.084).
These two analysesand particularly the lack of significance in the repeated measures test on shape provided us with the necessary confidence to combine the two datasets as we do not find consistent differences (bias) in shape between datasets so combining them should not negatively affect downstream analyses.
We further evaluated digitization error in our dataset by generating three replicates of our dataset (49 species).The three replicates were digitized in three consecutive days by the same operator (GS).Then we compared, separately, each of three replicates and the average of the replicates with the original digitization using a repeated measure test 3 .In each case we did not find a significant difference between the original and replicate digitisations (F = 0.33; P = 0.57 and F = 0.096; P = 0.90 respectively).

Replication of macroevolutionary analyses using direct bite force estimates
We repeated the main analyses presented in this study using the bite forces estimated from our Finite element models, as detailed in the following steps: 1) The bite force values for the species in our study were compared to those obtained from previous studies [4][5][6][7] .Bite force estimates in previous studiesand their variation among species -are largely consistent, supporting the robustness of our simulations.
2) We computed the correlation between von Mises stress values and bite force values estimated from our models.Results indicated a strong correlation between the two metrics (Pearson r = 0.82, p-value < 0.001; Spearman rho = 0.88; p-value < 0.001).
3) We estimated the best fitting interpolation strategy following the framework described in the main text, and a second degree TPS showed the lowest RMSE for bite force values.The performance surface for bite force directly estimated form the models (Supplementary Figure 5) is, indeed, very similar to the one displayed in Figure 1c  5) We computed evolutionary rates for bite force values using the same approaches (Bayesian estimates from BayesTraits and Ridge Regression from RRphylo) described in the Methods section.
We computed correlations between shape evolutionary rates and trade-off weight w values (based on bite force values) evolutionary rates.Results showed that shape rates were again uncorrelated with the weight w rates based on bite force values (Pearson r = 0.026, p-value = 0.24; Spearman rho = 0.013, p-value = 0.81).The same holds when using phylogenetically corrected tip rates values (Pearson r = 0.022, p-value = 0.81; Spearman rho = 0.12, p-value = 0.16).The distribution of rates of the trade-off weight w based on bite force values (Supplementary Figure 6) is highly comparable with the distribution of rates of weight w based on von Mises stress as displayed in Fig. 2b-d.

Supplementary Figure 5. Distribution of trade-off weight w rates of evolution on the carnivore phylogeny (left panel). Density ridge plot of per clade trade-off weight w rates (right panel).
Source Data are available at https://doi.org/10.6084/m9.figshare.23553648 in the "Code and Source Data" folder, included in the Supp_Fig5.rdafile.
We then computed correlations between trade-off weight w tip rates based on von Mises stress and trade-off weight w tip rates based on bite force values.Results showed that tip rates of both tradeoff weights w were significantly correlated (Pearson r = 0.71, p-value < 0.001;Spearman rho = 0.83, p-value < 0.83).The same holds when using phylogenetically corrected tip rates values (Pearson r = 0.67, p-value < 0.001; Spearman rho = 0.72, p-value < 0.73).

6)
We repeated our analysis to understand the relationship between the force-velocity trade-off and morphological disparity.Again, we used the same approach described in the Methods section, but using the trade-off weight w based on estimated bite force values.The distributions of weight w volume and morphological disparity (measured as multivariate variance) showed an overlapping pattern, with three identifiable peaks (see Supplementary Figure 7).However, there are some differences in the shape of the peaks when compared to the distribution obtained using the weight w based on von Mises stress data.In particular, the peak around values of 0.41 which was higher.

Evolutionary rates
We evaluated the correlation between results generated from BayesTraitsV4.0 and RRphylo using Pearson correlation coefficients.Furthermore, we evaluated correlation between tip rates using the Xi coefficient 13 which is particularly suited for non-linear and non-monotonic relationships.To

Supplementary Figure 4 .
based on von Mises stress Performance surface estimated for direct estimates of bite force from Finite element models.Source Data are available at https://doi.org/10.6084/m9.figshare.23553648 in the "Code and Source Data" folder, included in the Supp_Fig4.rdafile.4) We computed the new trade-off weight w values based on bite force values and used them in downstream analyses.

Table 2 .
Position of landmarks used in this study.