Sizing Up Swords: Correlated Evolution of Antlers and Tusks in Ungulates

Most sexual weapons in sexual combat and visual displays of dominance (e.g., antlers, horns) show positively allometry with body size for both growth during development and evolution across species, but allometry in species with more than one sexual weapon is unstudied. We examined the allometric relationships between body size and tusks (pure combat weapons) and/or antlers (both a visual signal and combat weapon) from forty-three artiodactyl species including the muntjaks (Muntiacinae), which uniquely have both antlers and tusks. We found that in Muntiacinae antler length scales positively allometrically with skull length, whereas tusk size scales isometrically suggesting greater energy investment in antlers as signals over tusks as combative weapons when both are present. Interspecically, we found that species who possess only one weapon (either solely tusked or solely antlered) scaled positively allometrically with body mass, and the latter relationship levels off at larger body sizes. In our tusk analysis, when we included Muntiacinae species the positive allometric trend was not conserved resulting in an isometric relationship suggesting the possession of antlers negatively affect the energy investment in tusks as weapons. Overall, our ndings show that species that possess dual weapons unproportionally invest energy in the development and maintenance of their multiple weapons.


Introduction
Sexual weapons are used in physical combat to secure mating opportunities; victorious males typically have larger body size and larger sexual weapons as a direct result of intrasexual selection (Geist 1999;Emlen 2008; McCullough et al. 2016; Sol et al. 2020). Structures that serve as intrasexual signals and weapons (e.g., ungulate antlers and horns) typically exhibit positive allometry in both developmental growth and evolution: As individuals grow and species evolve larger body sizes, they grow and evolve disproportionately larger ornaments than smaller individuals and species (Gould 1974 Larger, stronger individuals invest more energy into these presumably honest signals of strength in order to avoid costly or injurious ghts (Barrette 1977;Emlen 2008). Pure sexual weapons (e.g., tusks, claws, rhinoceros beetle horns), however, have evolved to provide advantages during intrasexual ghts, are only used in combat, and thus provide little signaling value (McCullough et al. 2016; Rico-Guevara and Hurme 2018; Sol et al. 2020). Few studies, though, have examined static allometric growth or allometric evolution of these pure, non-signaling, sexual weapons, and even fewer examine these allometric relationships in species with multiple sexual weapons. In this study, we investigate the allometric relationships that in uence the growth and evolution of tusks and antlers as sexual weapons within and among the artiodactyl families Tragulidae, Moschidae, and Cervidae, and among the Muntiacinae, the only ungulate group with both sexual weapons.
Sexual weaponry is a result of intrasexual selection (Emlen 2008), and weapons can vary in size, shape, and purpose across several classes of animals (McCullough et al. 2016). Sexual ornaments range between pure sexual weapons (e.g. beetle horns and mandibles) to pure sexual signals (e.g. eye stalks in ies). Weapons that fall in the middle of this continuum, such as ungulate antlers and ddler crab claws, can serve both functions (McCullough et al. 2016). Beetle horns, for example, increase with body size and usually become the stronger strategy for attaining mates through physical combat rather than other non-combat sexual mating strategies ( (Vanpe et al. 2007). While antlers (and horns in bovids) are the more common sexual weapon among artiodactyls, tusks are the sole weapon in several groups and grow along with antlers in the Muntiacinae (muntjaks and tufted deer). This presence of dual weaponry in ungulates provides an opportunity to understand how selection may prioritize growth and maintenance of one weapon over the other and whether there are constraints on the size of such structures.
Possession of tusk-like canine teeth is the ancestral state for all Artiodactyls, with antlers, horns, and pronghorns evolving later in the cervids, bovids, and antilocaprids, respectively (Cabrera & Stankowich, 2018). Tusks were retained in the mouse deer and chevrotains (Tragulidae: three genera Moschiola, Hyemoschus, and Tragulus; Wilson and Mittermeier 2011), which are nocturnal and live in dense forests (Prothero 2007). Adult males use their large upper canines to attack in a sideways slashing motion targeting the neck and head of their opponent (Matsubayashi et al. 2003); these ghts are likely often fatal (Prothero 2007). As ungulates evolved larger body sizes and moved into more open habitats, large tusks were lost with the evolution of antlers, horns, and pronghorns, but were re-evolved as the sole combat weapon in the Chinese water deer (Cervidae: Hydropotes; Fig. 1C) and musk deer (Moschidae: Moschus; Fig. 1D), both of which lack antlers but possess very large upper canines that reach 10 cm in length (Aitchison 1946;Fennessy 1984; Cabrera and Stankowich 2018).Living a "slinker" lifestyle in closed, forested environments favors the evolution of smaller "duiker"-like bodies for easier maneuverability (Geist 1999; Cabrera and Stankowich 2018), makes close-range combat essential for territory maintenance (Wilson and Mittermeier 2011), and favors the evolution and retention of tusks as the primary combat weapon in Artiodactyls (Cabrera and Stankowich 2018), where larger tusked males hold the best territories (Cooke, 2019). This lifestyle also likely results in minimal sexual selective pressure favoring an additional visual signal of dominance (i.e., antlers; Cabrera & Stankowich 2018). Open grassland habitats, on the other hand, favor visual displays of dominance rather than physical combat, which should result in larger ornamental weapons like antlers and horns and shorter tusks, which are limited in their ability to signal dominance from longer distances (Emlen 2008).
Within the cervids, the Muntiacinae (Muntiacus (Fig. 1A) and Elaphodus (Fig. 1B)) are very primitive deer that possess both tusks and antlers, and their antlers may have evolved in parallel with other cervids rather than being shared by their common ancestor (Groves and Grubb 1990). Males use large 2-4 cm upper canines, which begin emerging as early as ve months and reach their maximum length around year ve (Cooke, 2019), in physical combat to maintain control of access to mates (Fennessy 1984;Geist 1999 Gould (1974) found that the massive extinct Irish Elk (Megaloceros giganteus) violates this physical constraint explanation in cervids as their antlers are on the same positively allometric trajectory as smaller cervids. Whereas the equally large moose (Alces spp) fall well below this trajectory and likely drive the appearance of physical constraints on larger antlers in large extant cervids (Gould 1974). Tusks have evolved independently across multiple mammalian taxa (e.g., whales, elephants, ungulates), but their static and evolutionary allometric growth patterns are not well understood. Tusk girth, weight, and length in male narwhals (Monodon monoceros) all had positively allometric relationships with body length (Gerson and Hickie 2011). It is unknown how the presence of both a pure weapon and a weapon/ornament in the same species will alter allometric relationships.
Here, we analyze the relationship between overall body size (shoulder height, body mass, and skull length) and sexual weaponry among only tusked, both tusked and antlered, and only antlered ungulates. In our static allometry tests, we hypothesized that the growth of larger body sizes favors the growth of disproportionately longer antlers and longer tusks when they are the sole sexual weapon available (i.e., positively allometric), however tusks are not generally visual signals of size (i.e., pure weapons) and may not scale positively allometrically. When both types of weapons are present, however, we hypothesized that larger body sizes favor disproportionately larger antlers but not tusks as larger antlers make for stronger signals and may be advantageous in ghts. Evolutionarily, we hypothesized that evolving larger body sizes favors disproportionately larger weapons, regardless of whether one or two types of weapons are present, but that dual-weapon species may invest less in each weapon relative to single-weapon species of similar size. We examined these relationships both within several species of tusked adult ungulates, and between species of tusked and antlered deer using linear regression and phylogenetic generalized least squares (PGLS) analyses respectively.

Data Collection
Two-hundred and ninety-seven adult male skull specimens were measured from four museums: National Museum of Natural History (NMNH), Natural History Museum of London (NHML), American Museum of Natural History (AMNH), and the Field Museum of Natural History (FMNH) (All data and specimen catalog numbers available in Online Data Supplement). We measured twenty-eight species from seven genera of tusk-bearing cervids: Muntiacus (110), Elaphodus (21), Hydropotes (16), Hyemoshus (5), Tragulus (127), Moschus (12), and Moschiola (6). Skulls varied in completeness, with some missing premaxilla or tusks, and others were just skullcaps with antlers (i.e., most of the skull was missing).
We used digital calipers to measure skull, antler, and canine features to the nearest 0.01mm. If available, both the right and left values of all measurements were collected, and measurements were not taken on tusks, antlers, or skull lengths if that feature was broken. We measured Skull Length from the anterior tip of the premaxilla to the most posterior point of the skull (typically the occipital crest) (Fig. 2). Because tusk-like canine teeth are mesiallydistally curved structures, two measurements of the longest intact tusk were averaged to obtain Canine Length (1) from the most mesial point on the buccal surface where the tooth emerges from the skull to the tooth tip, and (2) from the most distal point on the buccal surface where the tooth emerges from the skull to the tooth tip ( Fig. 2A).
For Muntiacinae species, which have substantial bony pedicels that are often more than half of the total weapon length, we calculated Total Cranial Weapon Length as the sum of the pedicel length and antler length of the longest antler on the skull (used in intraspeci c analyses only). Pedicel length was measured along the medial surface of the antler bone from the coronal suture (between the frontal and parietal bones) in the notch between the antler bone and cranium to a nodule on the medial midline of the burr (antler/bone complex). True Antler length was then measured from this same nodule to the most distal tip of the antler (Fig. 2B).
We took photographs of each skull from the dorsal view and both lateral views using a Nikon D3100 camera.
Because many skulls were broken or missing teeth, we had many missing measurements for individual specimens, especially Skull Length. In order to estimate the missing skull lengths, we used a combination of morphometrics and Bayesian methods. We rst used ImageJ (Schneider 2012) to plot 20 universal landmarks on all photographed skulls (7 from the dorsal view and 13 from the lateral view; Fig. 2C,D). We calculated 23 euclidean distances (mm) between these points. We separated our dataset into three groups: 1) smaller-tusked tragulids, 2) larger tusked cervids (Hydropotes inermis and Moschus moschiferus), and 3) the dual-weaponed Muntiacinae (Muntiacus species and Elaphodus cephalophus). For each group, we created an additional data subset that contained 10 of the 23 distances that were complete for most of the specimens (i.e. the fewest NA's).
We then used the "pcaMethods" package (Stacklies W 2007) in R (R_Core_Team 2019) to conduct a principal components analysis using Bayesian methods to use these known values to estimate missing skull length values in both datasets (full and reduced) for each of the three groups.
All data were centered prior to the estimation analyses, then were uncentered after estimation to re ect original measurements. We ran Pearson correlation analyses between the full 23-distance dataset and the limited 10distance dataset for each group and found estimated values were highly correlated (R > 0.9 for all three groups), suggesting the estimates were robust and consistent. We used the 10-distance estimations of skull length for specimens with missing skull lengths in subsequent analyses.
We obtained antler lengths and male body masses for thirty-one other species of cervids from Plard and colleagues (2011) and antler length data of the extinct Irish Elk (Megaloceros giganteus) from Gould (1974). For these species, Antler Length was measured as the main beam without the pedicel, which is typically very short and makes up less than 10% of overall weapon length. We obtained most body masses and shoulder heights from For all static tests of weapon length on skull length, a slope ( ) of 1 indicated isometry, we used 95% con dence intervals of the slope estimates to assess deviation from isometry, and we deemed either linear or quadratic models as the best t if the difference in AIC values was greater than 2 (Burnham and Anderson 2004) Table 1 Summary of intraspeci c allometric analyses for Muntiacinae. SkL = total skull length; CL = maximum canine length; CWL = maximum pedicel + antler length. For all tests, isometry is predicted as = 1. For quadratic tests, results for the quadratic (x 2 ) and linear (x) terms of the model are separated by a "/". Skull sample size (N), regression slope ( ), t-statistic (t), p-values (p), AIC scores. Statistically signi cant allometric relationships are indicated: Isometry (I) and Positive Allometry (+  showed that comparing allometric relationships of sexually selected traits with a trait that should not possess any signaling power (reference trait) con rms positive allometric relationships of signaling traits. Similarly, we natural log transformed all tusk and antler lengths of the species described above, standardized them, and ran OLS analyses. We then used the length of M 2 molar measured from lateral images in ImageJ as the reference trait and conducted identical allometric analyses with skull length. We found that amongst tusked species, generally all weapons (tusks and/or antlers), scaled qualitatively higher than the reference trait, M 2 , except in Muntiacus muntjak (both weapons) and Elaphodus (tusks). Due to limited sample sizes, however, there were no statistically signi cant differences between any weapon and its corresponding reference trait; we therefore focus our results and discussion on traditional static OLS analyses. Full results from these tests, including 95% con dence intervals of regression slopes, can be found in the Online Supplement.

Evolutionary Allometric Analyses
We were interested in how tusks and antlers evolve with body size across many taxa. We grouped species in several ways to compare relative allometric relationships of tusks and antlers depending on the presence/absence of the other type of weapon. These included "Only Tusked" (Tragulus, Moschus, Hydropotes), "All Tusked" (Tragulus, Moschus, Hydropotes, Elaphodus, and Muntiacus), "Only Antlered" (all cervid species except Hydropotes, Elaphodus, and Muntiacus), and "All Antlered" (all cervid species except Hydropotes). For our "All Antlered" analyses, we used our own measured Antler Lengths (i.e., not including the pedicel length) for Full results from these tests, including 95% con dence intervals of regression slopes, can be found in the Online Supplement.  (Table 4) and provide the AIC scores for each model. In addition, we also report Phlya RMA (Revell 2012) results in the Online Supplement  Fig. 3). The quadratic model for canine length in M. reevesi was the best t. This model showed a positively allometric relationship for smaller skull sizes, before leveling off at large sizes (Table 1, Fig. 4). For cranial weapon length on skull length, the linear and quadratic models performed equally well in both M. muntjak and M. reevesi, and both showed positively allometric relationships (Table 1, Figs. 3,4). In Muntiacus vaginalis, however, we found no relationship between either canine or cranial weapon length and skull length ( Table 1).
The allometric relationship between canine length and skull length were analyzed in six species of tragulids (Table   2). Datasets for Hyemoshcus and Moschiola were insu cient to run species-level analyses. Among the four tragulid species examined, only Tragulus kanchil showed a positively allometric relationship between canine length and skull length with quadratic regression model as the best t ( Table 2; Fig. 5). We also found a trend towards a positively allometric relationship in T. javanicus, and the ts of the two models were similar, but the effects in neither model reached statistical signi cance (linear: p-value = 0.067; quadratic: p-value = 0.13; Table 2; Fig. 4). Non-signi cant relationships in T. nigricans and T. javanicus (N = 14) may have stemmed from low sample sizes, but T. napu showed no indication of an allometric relationship despite a large sample size (N = 75).
Hydropotes and Moschus did not show any statistically signi cant allometric relationships between canine length and skull length (

Evolutionary Allometric Relationships
To examine interspeci c allometric relationships, although we conducted non-phylogenetic linear and quadratic regressions for comparisons with older studies (Table 3), we base our main conclusions on the results of phylogenetically corrected models (Table 4). Phylogenetic signal (λ) was mostly weak and near zero in tusk analyses and variable (but greater than zero) in antler analyses (Table 4). Only Tusks First, we tested how canine length scaled against skull length, body mass, and shoulder height within solely tusked species (i.e., lacking antlers; N = 9; "Only Tusks"; Table 3). Our PGLS linear regression analyses support a signi cant positively allometric relationship between tusk length and skull length (Fig. 7). The quadratic model was the best t model to support signi cant relationships between canine length with shoulder height in "Only Tusked", and it was supported by the PGLS linear regression model. The linear model was the best t model supporting a positively allometric relationship between canine length and body mass, but this relationship was not statistically signi cant in the PGLS analysis.

All Tusks
Second, we analyzed how canine length scaled across all tusked genera (i.e., "All Tusks" = "Only Tusks" plus Muntiacinae; N = 14; Table 4, Fig. 7). Though our OLS models across all tusked species indicated that canine length scaled isometrically with skull length and shoulder height, they were not supported after controlling for phylogeny in the PGLS analyses (Table 3) All Antlers Next, we tested how antler length in "All Antlered" species (N = 29), including Muntiacinae, scales with body mass and shoulder height. In our PGLS, we found that antler length scaled positively allometrically with both shoulder height and body mass ( Table 5). The linear models provided the best t with shoulder height, and the quadratic models provided the best t for body mass. The latter suggests that antler length scales positively allometrically with body mass at small to moderate body masses, before leveling off in the largest species (Fig. 8). Only Antlers Lastly, we tested how antler length in "Only Antlered" (N = 23) species, excluding Muntiacinae, scales with body mass and shoulder height. In our PGLS analysis, we found that antler length scaled positively allometrically with both shoulder height and body mass s ( Table 6). The linear models provided the best t with shoulder height. For body mass, the quadratic PGLS model provided the best t, suggesting that antler length scales positively allometrically with body mass at small to moderate body masses, before leveling off in the largest species.

Intraspeci c Static Allometric Relationships
Intraspeci cally, amongst the dual weapon-bearing genera, there were different results for each species. Muntiacus muntjak tusks scaled isometrically with skull length (Fig. 3), while M. reevesi showed a positively allometric relationship (Fig. 4). We found positively allometric relationships between antler length and skull length in both M. muntjak and M. reevesi (Fig. 3, 4), with the latter also showing this relationship levels off in larger individuals. Elaphodus and M. vaginalis showed no signi cant relationships between skull length and tusk or antler length. Within solely tusked species (Tragulus, Moschus, and Hydropotes) we found no static allometric relationships, except we found positively allometric relationships between tusk length and skull length in both T. javanicus and T. kanchil (Fig. 5, 6), with the latter also showing this relationship levels off in larger individuals. These inconclusive results may be due to lack of su cient sample size, issues with tusk preservation, or possible physical constraints on weapon size as body mass increases. Together the data suggest that (1) antler length in Muntiacinae predictably scales with body size up to a certain point before leveling off, and (2) there might be an upper limit on selection favoring longer tusks: i.e., tusks grow with age up to a point, but having longer tusks at larger sizes either provides no advantage or makes the tusks physically weaker.
Contrary to the predicted positive static allometric relationship between tusk length and skull size (Geist 1999) within solely tusked species, only two of the six species showed positive allometry (although three of these species suffered from low sample sizes; N = 10-16). The mixed results in this group are di cult to interpret.
Tragulids are small and similar in ecology and behavior, but the allometric slopes varied from 0.5-2.1. Reference trait analyses (see Methods, O'Brien et al 2018) also showed that the allometric slopes of tusks were greater than those of the second molar but did not reach statistical signi cance. The taxonomy of this family is unclear, and species and subspecies names are frequently being revised, suggesting that some specimen identi cation labels may be incorrect and the individual belongs in another group, contributing to the varied results. There was no relationship between canine growth and skull size in Hydropotes and Moschus. Compared to the Tragulids (1-3  Therefore, it is unsurprising that we failed to nd strong positive allometric growth of this pure weapon, contrary to the ndings of Kodric-Brown and colleagues (2006) that allometric exponents for sexual weapons are "almost invariably" positive (typically 1.5-2.5). There are also two alternative, non-biological explanations. Fifth, the canine teeth of these larger genera are typically loose or separate from the skull in museum collections (especially Hydropotes), and after placing them back into the skulls, their relative positional depths during measurement may not have been consistent, confounding the results. Sixth, museum collections emphasize adult specimens and we may have seen allometric growth if our samples included smaller and juvenile members of each species.
Our intraspeci c allometric analyses for the Muntiacinae provided contradicting results when it came to canine length. In Elaphodus, there was no detectable relationship between canine length or antler length with skull size. The antlers are rudimentary, however, and tusks likely remain as the primary sexual weapons. Like the solely tusked species, there may be little positive selection favoring (or even negative selection disfavoring) tusks above a certain size due to risks of breakage; although their tusks are noticeably thicker and more robust than any other tusked species we measured. Unlike Elaphodus, Muntiacus muntjak tusks grew isometrically, and cranial weapons (antler + pedicel) grew positively allometrically with body size, similar to other intraspeci c studies of antler allometry in cervids (Gould 1974;Vanpe et al. 2007). M. reevesi tusks and antlers both scaled positively allometrically with skull length; although the former did level off with increased size (quadratic relationship: Fig. 4). A hint of the same trend is visible in M. muntjak tusks (Fig. 7), but the linear model was the best t. Behaviorally antlers in muntjacs are used to knock an opponent off balance before stabbing the neck, face, and ears with their sharp tusks (Barrette 1977). This suggests that both weapons are critical to victory but that (1) strong, long antlers are more critical for generating opportunities to quickly stab with the tusks, which don't need to be great in size to do signi cant damage, and (2) antlers do stop increasing in length with greater body sizes.
Interestingly, the permanent bony pedicel in Muntiacinae makes up most of the cranial weapon length (much more than other cervids), and the deciduous antler tip is very short compared to other cervids. Limiting the energy required to regrow the full length of the antler every year may allow these species to divert more energy to growing and maintaining their tusks, which other cervids don't have (except the antlerless Hydropotes). Comparison of the allometric growth rates of two sexual weapons in the same species provides great insight into (1) the relative energetic investment into the two weapons and (2) why progressively longer antlers might be more important to winning ghts and provide greater tness bene ts than progressively longer tusks.
Interspeci cally, among solely tusked species (excluding Muntiacinae) we found that tusk size scaled positively allometrically with head size (Fig. 7) and shoulder height. These relationships appeared isometric in when including all tusked species (including Muntiacinae), but no relationship at all was detected using phylogenetically corrected analyses. This difference in scaling relationship between solely tusked and all tusked species suggests a decreased investment in larger tusks in the antler-bearing Muntiacinae. As has been found previously (Gould 1974;Vanpe et al. 2007), antler length scaled linearly positively allometrically with both shoulder height and body mass but levels off in larger species (Fig. 8). Interestingly, the Muntiacinae all showed smaller than predicted antler lengths for their body size (Fig. 8), suggesting investment in antlers is reduced when tusks are still used in sexual combat. Overall, as deer-like Artiodactyls evolved larger body sizes, their primary weapon shifted from tusks to antlers (Cabrera & Stankowich 2019), and the primary weapon increased in size disproportionately faster than the body (this study).

Evolutionary Allometric Relationships
We generally saw that tusks have a positively allometric relationship among solely tusked species. This positively allometric evolutionary relationship between relative body size and one sexual combat weapon is seen in weapons in other taxa, such as the mandibles of Stag beetles (Odontolabis) (Kawano 2009), weevil rostrums (Somjee et al.

2021)
, bovid horns (Gould 1974), and antlers of cervids (Gould 1974;Lemaitre et al. 2014; This study). In addition, rhinoceros beetle horn length is strongly correlated with ghting ability; therefore smaller horned males resort to other behavioral methods, such as sneaking behavior, suggesting smaller horns possess weaker signaling power Also, species with greater breeding group sizes (i.e., more polygynous with greater malemale competition) have larger antlers for a given body size compared to species with smaller breeding group sizes (Plard et al. 2010). This greater signaling opportunity and stronger sexual selection on males favored antlers to grow to immense size, which led to increased e ciency of honest signaling from longer distances between opposing males and possibly with females assessing male body condition (Vanpe et al. 2007).
Our nding that antler length evolutionarily scales positively allometrically with both shoulder height and body mass con rms that antlers are both weapons and exaggerated sexual signals that are expensive to grow and regrow annually. As body mass increases, there is a general transition from tusks to antlers in ungulates, commonly accompanied with the transition from dense forested habitats to more open habitats (Cabrera and Stankowich 2018). Antler growth amongst solely antler-bearing species, including the enormous Irish Elk had previously been shown to scale positively with shoulder height with = 1.74 in non-phylogenetic studies (Gould 1974 (Simmons et al. 2007). In our study, tusks showed positively allometric relationships with body size in solely tusked species (Table 3; Fig. 5). This positive relationship was not conserved, however, when we included Muntiacinae in our analyses (Table 4)  In dung beetles and eye stalked ies, males with exaggerated weapon lengths suffered compensation in secondary traits for ight performance through reduced wing traits (Swallow et al. 2000). In the present study, we uniquely examined static and evolutionary allometric relationships in two independent weapons in Muntiacinae and found that antlers nearly always grew and evolved with positive allometry with body size, while tusks showed mixed static allometric relationships and no evolutionary allometric growth. This nding, combined with the stronger evidence for positive evolutionary allometry in solely tusked species, suggests moderate secondary sexual trait compensation whereas dual-weapon species increase in size, they invest more in their signaling weapon than their combat weapon (Tomkins et al. 2005).
Our dataset did suffer from two major limitations. First, many of the skulls available were broken or incomplete.
These imperfections limited our ability to take direct skull measurements of skull length, and we relied on digital imaging, morphometrics, and principal component analyses to generate predicted skull length values when missing, based on existing skull landmarks. While this does generate some uncertainty in the skull length data, the same analyses were able to predict the skull lengths of the complete skulls to a high degree of precision. Second, we were unable to collect enough data to analyze allometric relationships from many other tusked species not reported here; these data would have strengthened our ndings. In all, we took measurements from 14 tusked species, but we had measurements from fewer than 10 skulls for Hyemoschus aquaticus, Moschiola memmina, Moschus berezovski, Muntiacus truongsonensis, and Muntiacus vuquangensis. This particularly affected our interspeci c Muntiacinae analyses, as we only had six species with at least 10 measurements to generate species averages to use in the interspeci c analyses. A greater sampling of the rarer species of muntjacs might have allowed us to make stronger conclusions about the evolution of tusk and antler allometry within this unique clade.
Declarations Figure 1 Taxidermy mounts of several tusked deer. A) Muntiacus; B) Elaphodus; C) Hydropotes; D) Moschus.   The scaling relationships of (A) antler length and (B) canine length with skull length in Muntiacus reevesi. The lled circles (•) represent natural log transformed canine measurements and the red triangles represent natural log transformed antler measurements (▲). The black curved line represents the quadratic relationship between tusks and skull length. The red solid line represents the positive linear relationship between antler length and skull length ( =1.44).
Page 28/32 The scaling relationship of canine length with skull length in Tragulus javanicus. The lled circles (•) represent natural log transformed canine measurements. The black dashed line represents the suggestive positive linear relationship between canine length and skull length. The black curve represents the quadratic regression model of canine length and skull length.