Electronic Supplementary Material for: Temporal and phylogenetic trends of body mass evolution in herbivorous coelurosaurian dinosaurs. Lindsay E. Zanno1,2,3* and Peter J. Makovicky3

1Department of Paleontology & Geology, Nature Research Center, North Carolina Museum of Natural Sciences, Raleigh, NC 27601, USA

2Department of Biology, North Carolina State University, Raleigh, NC 27607, USA

3Department of Geology, Field Museum of Natural History, Chicago, IL 60640, USA *Corresponding author. Email: lzanno@fieldmuseum.org CONTENTS:

S1. Taxon sampling and body mass estimation S2. Protocol for tree construction S3. Branch scaling and taxon ages S4. Phylogenetic signal and sampling S5. Stratigraphic fit to phylogeny S6. AD comparisons: modified protocol and simulations S7. Model fitting S8. Temporal patterns S9. Ecological/Taphonomic Effects on Body Mass Sampling

S10. References FIGURES: Figure S1. Sensitivity plots for femoral length estimates

Figure S2. Ornithomimosaurian tree topologies Figure S3. Oviraptorosaurian tree topologies Figure S4. Therizinosaurian tree topologies Figure S5. Ancestor descendant comparison data plots Figure S6. Method simulations Figure S7. Mass/time regressions

TABLES:

Table S1. Theropod body mass estimates Table S2. Akaike weigh distributions for various femoral length estimates Table S3. AD comparison results Table S4. Sympatric species locality and mass data

S1. Taxon sampling and body mass estimation We estimated body masses for theropods (table S1) using the theropod specific equation relating body mass to femoral length developed by Christiansen & Fariña (2004). We recognize that different body mass equations produce greatly varying results (Carrano 2006), which is why raw femoral lengths have been used in lieu of body mass estimates in some studies (Carrano 2006; Butler & Goswami 2008; Hone et al. 2008). However, the relationship between femoral length and raw body mass is not linear, and proportionately small differences in femoral length may reflect orders of magnitude in body mass difference. Reduction in the scope of body mass across clades negatively affects trend detection so we opt to use body mass estimates. Although mass estimates are subject to biases, our use of a single taxonomically specific formula for estimating body mass is an attempt at minimizing inconsistencies in this regard.

Earlier studies of body mass evolution have culled species lacking data on femoral length (e.g., Carrano 2006; Butler & Goswami 2008; Hone et al. 2008), resulting in dramatically reduced sample sizes. In our study sample such a procedure would underestimate the range of body masses in herbivorous coelurosaurian clades because many of their largest members do not preserve the proximal hind limb (e.g. Deinocheirus, Therizinosaurus, Hagryphus). For specimens that lack a complete femur, we estimated femoral length by deriving skeletal ratios from a similarly sized taxon of the same theropod subclade. When possible we also took into account phylogenetic proximity; however, in instances of conflict, size-class was given priority because allometry has been shown to have a greater impact on bone proportions than phylogenetic proximity (Kilbourne & Makovicky 2010). We prioritized ratios derived from the hind limb in accordance with this approach, yet out of necessity, used the lengths of other skeletal elements, such as those of the skull and forelimb. When using skeletal ratios, we avoided uniquely modified areas of the skeleton in proportion to the femur and prioritized conservative skeletal ratios that were derived from our primary data. For example, the ratio of skull-to-femur length is relatively conservative in oviraptorosaurians (< 15% variation from the mean) and was used for several taxa. Specific information regarding body mass estimates is provided below.

Femoral lengths for the majority of specimens were derived from the literature, first hand measurements, or photographs of specimens. Femoral lengths for Nanshiungosaurus bohlini, Nanshiungosaurus brevispinus, Erlikosaurus, Nothronychus mckinleyi, and Therizinosaurus were calculated using skeletal ratios derived from the relatively complete skeleton of Nothronychus graffami: Erlikosaurus was based on relative humerus length; Therizinosaurus was based on relative length of the second metacarpal; and Nanshiungosaurus brevispinus and Enigmosaurus were based on the relative craniocaudal width of the acetabulum. Garudimimus, Gallimimus, Shenzhousaurus, and Beishanlong were used to estimate femur lengths for Deinocheirus, Pelecanimimus, Qiupalong, and Harpymimus: Deinocheirus was based on relative humeral length; Pelecanimimus was based on relative skull length; Qiupalong was based on relative tibial length; and Harpymimus was based on relative length of the second metatarsal. Femoral lengths for Hagryphus and Machairasaurus were derived from the relative length of metacarpal two of CM 78003 (large-bodied Hell Creek Fm. caenagnathid) and Khaan respectively; Incisivosaurus, Nemegtomaia/Rinchenia, and Banji/Conchoraptor) were derived from the relative skull lengths of Protarchaeopteryx, Citipati, and Caudipteryx, respectively.

We recognize that deriving select body mass data from estimated femoral lengths and ontogenetic variation among our sampled specimens has the potential to negatively affect the precision of our data. To explore this problem, we derived linear regressions between the various

elements used for femoral length estimation and femur length in therizinosaurians, the clade with the fewest complete specimens, and estimated femoral lengths and their corresponding body mass estimates derived from the Christiansen and Fariña (2004) equation. We examined regressions for six elements: tibia, humerus, Metacarpal II, posterior cervical, Metatarsal III. Relatively complete skeletal measurement data are available for three taxa (an unnamed Yixian Formation taxon similar to Falcarius; Neimongosaurus; Nothronychus graffami) to derive regressions, though only two points were available for tibial and MCII measurements. Of these four biplots based on three data points, three regressions showed tight correlations (R2<0.977) and two of these had slopes departing significantly from zero, while the third (posterior cervical length) was nearly significant (p=0.065). Only metatarsal length exhibits a poor correlation coefficient (R2=0.56) and a slope that is not statistically different from zero, but this is clearly related to the fact that the autapomorphic foreshortened foot observed in derived therizinosauroids is not present in the basal Yixian taxon, which has hind limb proportions more typical for basal coelurosaurians. Given the low number of data points, confidence intervals are wide especially surrounding large bodied taxa for which femoral lengths are being extrapolated such as "Nanshiungosaurus" bohlini and Therizinosaurus. For these taxa, upper confidence intervals can range to extreme masses in excess of 20 tons while lower limits are negative. We compared the regression derived body masses to our chosen approach based on using the closest sized relative as a base for estimations. For taxa that fall within the range of measurements used to derive regressions allowing for interpolation, body mass estimates from the two methods were close with differences of less than 15% (Figure S1). These values are less than the differences that can arise from using equations for different elements (e.g. femur versus tibia) developed by Christiansen and Fariña (2004). However, for the two largest therizinosaurian species, body mass extrapolations from regressions are 30% higher than values attained by scaling from the closest sized relative (Figure S1). Notably, for both of these taxa extrapolation gives femoral lengths in excess of 1500 mm and thus significantly larger than any bipedal theropod femur found to date including tyrannosaurids and carcharodontosaurids. These questionably high values suggest that regressions based on few data points from a limited body size range relative to the range being estimated fail to account properly for allometry, and that scaling from the closest sized relative is more conservative. However, this method assumes that similar allometries apply to similar sized animals form each clade, which may reduce the magnitude of inferred body size changes and bias analyses toward the discovery of a random walk in body size evolution over directional models.

Table S1. Estimated body mass (kg) for species in the omnivorous/herbivorous bird-like dinosaur clades Ornithomimosauria, Therizinosauria, and Oviraptorosauria. Body mass estimates follow Christiansen and Fariña (2004) using estimated and measured femur length (FL) (estimated FL denoted with asterisk). taxon mass (kg) taxon mass (kg) Ornithomimosauria Suzhousaurus megatheriodes 1361.5 Deinocheirus mirificus* 6013.9 "Nanshiungosaurus" bohlini* 1037.3 Beishanlong grandis 626.0 Nothronychus graffami 843.5 Anserimimus planinychus 161.0 Enigmosaurus mongoliensis* 566.9 Harpymimus okladnikovi* 130.8 Oviraptorosauria Pelecanimimus polyodon* 11.5 Chirostenotes pergracilis 54.8 Archaeornithomimus asiaticus 57.2 Microvenator celer 2.9 Gallimimus bullatus 666.6 Citipati osmolskae 121.7 Ornithomimus edmontonicus 163.4 Khaan mckennai 12.1 Garudimimus brevipes 97.8 Ingenia yanshini 24.0 Struthiomimus altus 276.2 Conchoraptor gracilis* 10.0 Shenzhousaurus orientalis 11.5 Oviraptor philoceratops 51.0 Sinornithomimus dongi 62.6 Rinchenia mongoliensis* 73.2 Qiupalong henanensis* 96.2 Caudipteryx zoui 5.2 Therizinosauria Incisivosaurus gauthieri* 8.5 Falcarius utahensis 127.7 Protarchaeopteryx robusta 2.7 Beipiaosaurus inexpectus 27.4 Avimimus portentosus 10.9 Alxasaurus elesitaiensis 358.2 Heyuannia huangi* 19.5 Nothronychus mckinley*i 673.0 Gigantoraptor erlianensis 3246.1 Erliansaurus bellamanus 137.2 CM 78003 247.8 Nanshiungosaurus brevispinus* 6279.6 Hagryphus giganteus* 179.6 Neimongosaurus yangi 93.7 Nomingia Gobiensis 41.8 Segnosaurus galbiensis 1468.8 Machairasaurus leptonykus* 30.4 Erlikosaurus andrewsi* 278.0 Nemegtomaia barsboldi* 88.8 Therizinosaurus cheloniformis* 6646.5 Banji long* 2.8

Figure S1. Comparison between body mass estimates (in kg) generated for several therizinosauroid taxa with different methods for femoral length estimation. Blue dots represent results derived from inter-element ratios from the nearest sized relative, while red dots represent results from length extrapolated from linear regression biplots. In order to ascertain whether these differences in estimation would influence our analyses of body mass evolution, we ran model fitting analyses for both sets of estimates. Akaike weights distribution for both favored random walk models by a factor of more than four as much as the next most favored model, with only minor differences in the distribution of Akaike weights across models (table S2). Estimation method

Random walk

Trend Stasis Kappa Early burst

RBE 57.78

14.71

6.39

11.89

9.24

NSR 55.95

10.19

14.67

10.25

8.95

Table S2. Comparison of Akaike weight distributions (in %) across the five evolutionary models when using regression based mass estimates (RBE) versus the nearest sized relative method (NSR).

S2. Protocol for tree construction To account for the effect of phylogenetic uncertainty on our results we tested three topologies each for Ornithomimosauria (figure S2) and Oviraptorosauria (figure S3) and six topologies of Therizinosauria (figure S4). Trees were constructed based on them most recent and comprehensive phylogenetic analyses, and designed to capture areas of the greatest uncertainty with specific attention to the position of large bodied taxa, which have the major influence on the trend results presented here.

Ornithomimosaurian relationships were derived from the most recent ingroup analysis (Xu et al. 2011). Ji et al. (2003) was used to resolve topology at the base of the tree. The large-bodied, yet fragmentary taxon Deinocheirus was posited basal to Pelecanimimus following Kobayashi & Barsbold (2006) and Senter (2007). We tested an additional topology positing Deinocheirus as a member of the derived, large-bodied, latest Cretaceous clade containing Gallimimus as well as a final topology excluding Deinocheirus from Ornithomimosauria following (Kobayashi & Barsbold 2006). The large-bodied taxon Beishanlong was grafted following Makovicky et al. (2009).

Evolutionary relationships among derived therizinosaurids are poorly understood due to inaccessibility of materials and a lack of overlapping elements between taxa. The most recent phylogenetic analysis (Zanno 2010) recovers nine most parsimonious trees (MPTs), which differ in hypothesized relationships among therizinosauroids more derived than Enigmosaurus. We tested six of the nine MPTs capturing the best and worst fits to the stratigraphic record (as measured by Manhattan Stratigraphic Measure*). Alternate positions of Therizinosaurus and Erlikosaurus capture the majority of variation among tested topologies. The taxon “Nanshiungosaurus” bohlini was excluded from this study..

We investigated three recent topologies depicting unique relationships among oviraptorosaurians, yet similar in taxonomic scope (Lu et al. 2002, Longrich et al. 2010; Xu et al. 2010). Taxon sampling between these datasets varied (ranging from 12 to 14 species) and numerous well-known species were unaccounted for in each. Species absent on one or more trees and whose position was not contradicted among all three trees (e.g., Incisivosaurus, Microvenator, Banji, Nomingia) were grafted accordingly. Protarchaeopteryx, Elmisaurus, and Hagryphus were missing from all three analyses and were grafted based on the analysis of Senter 2007. Caenagnathus and Chirostenotes were combined into the single OTU “Chirostenotes”. Two taxa were not posited consistently due to topological differences between all three trees (Heyuannia and Machairasaurus). Machairasaurus was grafted as the sister-taxon to the most exclusive clade containing Heyuannia (with or without Ingenia) and Heyuannia was grafted as the sister-taxon to Ingenia following Longrich et al. (2010). We also posited the undescribed taxon CM 78003 in Caenagnathidae, as sister-taxon to the large-bodied Hagryphus. Elmisaurus was not included in this study because its body size overlaps with those of other oviraptorosaurians and a reasonable test of its phylogenetic placement is not available.

Figure S1. Three alternate topologies of Ornithomimosauria used our analyses, showing lability in the massive Deinocheirus.

Figure S2. Three alternate topologies of Oviraptorosauria used in our analyses, showing lability in the massive taxon Gigantoraptor, as well as variable relationships within Caenagnathidae and Oviraptoridae.

Figure S3. Six alternate topologies of Therizinosauria used in our analyses, showing variable relationships among therizinosauroids more derived than Enigmosaurus.

S3. Branch length scaling and taxon ages Branch lengths were calibrated chronostratigraphically. For taxa from radiometrically-dated formations we employed these dates as upper, lower, or range boundaries. For taxa from strata of uncertain age we used mid-stage or mid-range estimates based on published age ranges derived from the 2009 geologic time scale (Walker et al. 2009). Maximum likelihood methods require that all branches have a length greater than zero, to allow for finite rate estimations. Because fossil-calibrated cladograms include zero-length branches subtending the oldest fossil taxon at each node, we employed two methods for scaling branch lengths. In the first, we set a fixed branch length adjustment (FLA) by adding one million years to each zero length branch leading to a tip, and adjusted neighboring branches accordingly following (Laurin 2004; Butler & Goswami 2008, Kilbourne & Makovicky 2010). In the second method we employed the smoothing distribution (SD) approach developed by Brusatte et al. (2008), in which an arbitrarily chosen stratigraphic range extension is added to the root of a calibrated phylogeny, and then smoothed between zero length branches across the tree. We performed this adjustment with both the one million year default range extension in the script developed by G. T. Lloyd (http://www.graemetlloyd.com/methdpf.html) as well as with a five million year range extension. The former forces a more punctuated model of evolution on to the employed topologies, whereas the latter represents a more gradual scenario. These two values were also selected because they bracket the shifts in 'root age' imposed by the first method (2 million years for oviraptorosaurs and therizinosaurs; 1 or 5 million years for ornithomimosaurs depending on inclusion and phylogenetic position of Deinocheirus). S4. Phylogenetic signal and sampling We tested BM for phylogenetic signal using the K statistic and its associated permutation probability test developed by Blomberg et al. (2003). This test permits an assessment of whether sample sizes are sufficiently large, as one of the reasons for non-significance of a calculated K value may be insufficient sampling (Blomberg et al. 2003). Analyses were run on all three differently scaled versions of each topology. S5. Stratigraphic fit to phylogeny We measured stratigraphic fit of alternate species-level tree topologies using a script for the Manhattan Stratigraphic Measure* (Pol & Norell 2001, 2006) executed in TNT (Goloboff 2008) and ASCC software suite (Boyd et al. 2010) with 1000 iteration per topology. Stratigraphic data was derived following the methodology employed for branch length estimation. S6. AD comparisons: modified protocol and simulations Recent studies use values derived from ancestor-descendant (AD) comparisons to test for evolutionary trends in dinosaurian body mass (Carrano 2006; Butler & Goswami 2008). In order to make comparisons with these studies and because nonparametric methods are less sensitive to deviations from normal data distribution (Zar 1999) we also tested for BM trends using an AD approach (figure S5). However, we find problems with the method as conventionally used (especially for smaller sample sizes) and present modifications designed to increase its power.

Ancestor-descendant comparisons (Alroy 1998) require reconstructing ancestral states at hypothesized nodes. Weighted squared change parsimony (WSCP) (Maddison 1991) is most commonly employed for reconstructing intranode values from continuous characters (e.g., Carrano 2006; Finarelli & Flynn 2006; Butler & Goswami 2008; Hone et al. 2008). Significance

is tested by comparing the sum of positive and negative mass changes against a null hypothesis predicting equal number of increases and decreases using the nonparametric chi-squared goodness of fit test (Carrano 2006; Butler & Goswami 2008).

Weighted squared change parsimony performs poorly when trends are present in the data (Oakley & Cunningham 2000; Pagel 1999a, 1999b; Carrano 2006; Webster & Purvis 2002). When a positive or negative directional trend exists, WSCP can produce intranodal values that are either inflated or underestimated, respectively (Oakley & Cunningham 2000).

To investigate the effect of WSCP and LP optimization techniques on trend analysis, we conducted four simple simulations on an idealized data set (figure S6). We created two randomly simulated body mass data sets for 13 taxa (the minimum number of species in our clades) and depicted the phylogenetic relationships of these taxa to represent universal increases in body mass (i.e., a consistent and idealized phylogenetic trend of increase mass). We then used WSCP and LP methods to reconstruct ancestral node values and tested these using both the chi-squared goodness of fit test (as performed in previous studies, e.g., Carrano 2006; Butler & Goswami 2008) and the nonparametric Wilcoxon signed rank test. The signed rank test has the power to detect trends when the summed number of increases and decreases are not different from random, but the ranked magnitude of those differences is significant. We also tested the effect of concentrating branch length on terminal branches or along the spine of the tree. Select results from these simulations are shown in figure S6. Our simulations demonstrate that when coupled with goodness of fit tests WSCP is susceptible to type II errors on small data sets, with failure to accept even uncontroversial trends in body mass change regardless of branch length methodology. The use of signed rank tests is superior to chi-squared tests and improves the power of WSCP by detecting trends under select parameters; however, these combined methods still fail to detect trends in the majority of our tests. In contrast, simulations using linear parsimony (LP) produce significant trends when tested by both chi-squared and signed rank tests.

Here we follow Turner et al. (2007) in using LP to derive body mass values at internal nodes. Although linear parsimony can also produce poor estimates of ancestral reconstructions (Oakley & Cunningham 2000) and cannot account for variation in branch length, our method simulations demonstrate that it is preferable for our trees, which have low sample size and pectinate topology—two factors that can exacerbate the error of WSCP. The LP approach also bypasses the intranode over-/underestimation problem by allowing rates of change to vary across the tree independent of branch length, which is preferable if the tempo of change is dynamic (Webster & Purvis 2002) and LP performs well if branches are generally short or change is rare (Pagel 1999b; Oakley & Cunningham 2000; Finarelli & Flynn 2006; Turner et al. 2007; Webster & Purvis 2010). Body mass estimates were labeled as continuous characters and mapped in Mesquite version 2.74 (Maddison & Maddison 2010). When linear parsimony produced a range of values at ancestral nodes, we employed midpoints following Webster and Purvis (2010).

Rather than comparing the absolute number of mass increases versus decreases as in previous studies (e.g., Carrano 2006; Butler & Goswami 2008) we employed the nonparametric Wilcoxon signed rank test also used by Hone et al. (2005), which compares the ranked magnitudes of increases and decreases and proved to have greater power to detect trends in our simulations.

When ancestor-descendant comparisons are applied, positive mass changes outweigh negative changes in all subclades; however these differences are not significant when tested by chi-squared goodness of fit tests (table S3). Differences between the sums of ranked magnitudes are more pronounced, with the magnitude of positive changes exceeding that of negative changes

by at least 2:1 in almost all topologies. Nonetheless, these values are only significant for two of the 12 trees considered, representing one topology each for Ornithomimosauria and Oviraptorosauria (table S3; figure S2-S3). A tree depicting sister-taxon relationships between the four largest therizinosaurians as ((Suzhousaurus, Therizinosaurus) (Segnosaurus, Nanshiungosaurus)), is the only topology of the 12 examined that achieves significance with PGLS (table 3). The low proportion of analyses (<13%) yielding significant (p ≤ 0.05) trends are most conservatively interpreted as artifacts of small sample sizes coupled with hypotheses involving large mass ranges and iterative evolution of large mass rather than real biological signals, because our results are highly sensitive to phylogenetic topology (specifically the relative position of the largest taxa and total number of mass increases) and body size parameterization (e.g., BM vs. FL, base for log-transformation; see ESM A.1). Table S3. Results of ancestor-descendant pair (AD) analysis of body mass evolution in the omnivorous/herbivorous theropod dinosaur clades Ornithomimosauria, Therizinosauria, and Oviraptorosauria. Results reflect three to six different topologies per clade. Stratigraphic fit to phylogeny as determined by Manhattan Stratigraphic Measure star (MSM*) values and ranks (1owest rank best fit) reported. Significance evalutated using both Wilcoxon signed-rank and goodness-of-fit tests. Asterisk marks clades and trees significant at p < 0.05. MSM* Wilcoxon signed-rank goodness-

of-fit value rank rank

sum (+)

rank sum (-)

n (rank)

p-value obs. changes (+)

obs. changes (-)

χ2

Ornithomimosauria Tree 1: n=13 93 60 17 9 8 0.06 Tree 2: n=12 70 21 13 8 5 0.69 Tree 3*: n=13 84 21 14 0.05 9 5 1.14

Therizinosauria Tree 1: n=13 0.2683 2 78 27 14 9 5 1.14 Tree 2: n=13 0.3034 3 80 25 14 10 4 2.57 Tree 3: n=13 0.2418 1 63 27 13 8 5 0.69 Tree 4: n=13 0.2683 2 82 23 14 10 4 2.57 Tree 5: n=13 0.2418 1 80 25 14 9 5 1.14 Tree 6: n=13 0.2418 1 71 20 13 9 4 1.92

Oviraptorosauria* Tree 1: n=20 0.5217 1 169 62 21 13 8 1.19 Tree 2*: n=20 0.5455 3 173 58 21 0.05 14 7 2.33 Tree 3: n=20 0.5294 2 130.5 100.5 21 10 11 0.05

Figure S5. Ancestor descendant comparison results. Change in natural log-transformed mass plotted against ancestral natural log-transformed mass for the herbivorous theropod clades Ornithomimosauria, Therizinosauria, and Oviraptorosauria. Plots indicate large jumps in mass occur a both large and small ancestral reconstructed body sizes.

Figure S6. Trees depicting the effect of parsimony optimization, significance testing, and branch length on the power of AD pairs to detect a trend of increasing mass in idealized trend simulations. We used a 13-taxon dataset (the minimum number of taxa in our sampled clades). Taxa were arranged phylogenetically to depict a uniform trend of increasing mass. Weighted squared change parsimony (WSCP) was used as the ancestral state optimization method in trees A, C, & D. Linear parsimony (LP) was used in tree B. Branch lengths were not stipulated in trees A & B. Trees C & D were modeled to test the effect of concentrating branch length on terminal branches (tree C) and intranode branches (tree D). Significance was tested using both goodness-of-fit tests (χ2) and Wilcoxon signed rank test (WSR) on all trees. Red circles indicate reconstructed mass decreases, blue circles indicate reconstructed mass increases. Decreases and increases are tallied in legend. Numbers in grey boxes represent mass values (kg) for terminal taxa and reconstructed ancestral nodes. Wilcoxon signed rank tests are significant for all parameterizations except when branch length was confined to terminal branches under WSCP, whereas goodness-of-fit tests detect a significant trend only when LP is used for ancestral state reconstructions. Concentrating branch length on terminal branches increases the power of (χ2) to detect trends but inversely affects WPC results when squared change parsimony is used. S7. Model fitting We used a model fitting approach (Hunt & Carrano 2010; Sookias et al. 2012) to test which of five evolutionary models best fits BM evolutionary patterns in herbivorous coelurosaur clades. The five candidate models were chosen because they each represent a theoretically relevant and reasonable hypothesis of how BM may have evolved in these lineages (and in amniotes more generally). Brownian Motion (= random walk for our purposes [Hunt & Carrano 2010]) is generally used as the null model in these types of studies, and has been shown to be a prevalent passive process behind the evolution of large body sizes in many fossil lineages (Carrano 2006; Sookias et al. 2012). A directional trend model was used to describe active selection for larger BM in a lineage (i.e. 'Cope's rule'). Sookias et al. (2012) recently found stasis (i.e., white noise model in R) to be the best fitting model in several herbivorous archosaur lineages such as aetosaurs and sauropods, so we chose to employ this model as well. Because our study concerns itself particularly with the evolution of herbivory, it is reasonable to consider an evolutionary model in which the selection for increasing body size occurs early in the history of a clade as the dietary shift is occurring, whereas selective pressure either drops off after an optimum size is reached, or other selective pressure such as predation come to exert a greater influence. The 'early burst' (EB) model (Harmon et al. 2010) describes this type of scenario. The opposite scenario, in which evolution of the trait occurs later in clade history and is concentrated toward the tips of the tree, is described by the kappa model (based on Pagel's [1999a] kappa parameter). We included this model mainly as a contrast for the EB model (i.e., to see whether EB performed much better than its opposite or not.) Model fits were evaluated using using AICc scores and Akaike weights (Hunt & Carrano 2010). The R analyses also offered the potential of assessing the effects of uncertainty in BM estimation on our results. In order to gauge this uncertainty, we supplement permuted data sets in which BM was chosen from within a distribution of values bounded by the standard deviations estimated for the Christiansen & Fariña (2004) body mass equation. Specifically, we estimated the standard deviation as half the distance between the mean and the respective upper and lower 95% CI values for each taxon. For each combination of topologies and branch scaling methods, we conducted 100 permutations of the data and then averaged Akaike weights across permutations.

S8. Temporal patterns To investigate for temporal trends in body mass (disregarding phylogeny) we calculated ordinary least-squares regressions for mean mass (loge) against four different measures of taxon age: minimum possible geologic stage, maximum possible geologic stage, radiometrically adjusted mean age range in Ma, radiometrically adjusted actual age (mean of minimum Ma-maximum Ma). For binned iterations (stage estimates), we normalized stage data by assigning rank values. Only values for taxa whose age uncertainty spans more than one stage bin vary between minimum and maximum stage iterations. In instances where more than one taxon of the same subclade had the same estimated, minimum/maximum stage, or actual age (Ma), we logged the mean of body mass data for that age.

Increasing BM is correlated with geologic time in all three subclades tested (table 1; figure S7). Although all three approaches to age estimation for coelurosaurian taxa registered p-values at or < 0.1, regressions based on both maximum possible geologic stages and actual age data against smoothed (mean) mass were significant (p < 0.05) for Therizinosauria and those based on actual age against both individual and smoothed (mean) mass for Oviraptorosauria. Temporal trends in BM data are weaker in Ornithomimosauria with only actual age data against individual mass data registering near significance at p = 0.055.

Figure S7. Significant iterations of ordinary least squares regressions on natural log-transformed mass in the herbivorous theropod clades Ornithomimosauria, Oviraptorosauria, and Therizinosauria against geologic time (Ma). Significant correlations were recovered for Ornithomimosauria with actual Ma age data and individual mass data; for Therizinosauria using both maximum possible geologic stages and actual Ma data against smoothed (mean) mass; and for Oviraptorosauria using actual Ma against both individual and smoothed (mean) mass for Oviraptorosauria.

S9. Ecological/taphonomic effects on body mass sampling If sampling of body mass is subject to ecological selection or taphonomic effects (or both) we expect to see parallel patterns in body mass change over time in sympatric members of different herbivorous clades. Our test is restricted to Asian therizinosaurians and ornithomimosaurians, as these are the only clades with sufficient diversity across a range of formations to allow for statistical analysis. We identified five localities/formations that preserve at least one ornithomimosaurian and therizinosaurian: Liaoning Fm., China, Early Cretaceous; Huren Dukh, Shinekhudag Fm., Mongolia, Early Cretaceous; Bayshin Tsav, Bayanshiree Fm., Mongolia, Late Cretaceous, Iren Dabasu Fm., China, Late Cretaceous; and Nemegt Fm., Mongolia, Late Cretaceous) (table S4). Unpublished data obtained for the Huren Dukh therizinosaurian (Y. Kobayashi pers. comm.). Mean body mass was calculated for localities/formations preserving more than one species of either subclade (e.g., Iren Dabasu). Body mass over time curves were compared with cross correlation in the software PAST (Hammer et al. 2001) to determine whether the observed fit between curves is significantly better than other possible curve fits. We note that the temporal sampling of the formations is uneven, however, which does not strictly fit the assumptions of the analysis. Table S4. Estimated mean body mass loge (kg) for Ornithomimosauria and Therizinosauria species from various localities/formations in the Cretaceous of Asia. Body mass estimates follow Christiansen and Fariña (2004). formation/locality age Ma Ornithomimosauria

mass loge (kg) Therizinosauria mass loge (kg)

Huren Duhk 131 4.88 4.17 Sihetun 125 2.48 3.3 Bayshin Tsav 94 4.58 6.77 Iren Dabsu 75 4.04 4.75 Nemegt 68 7.73 8.8

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