Male weaponry is well understood and extensively studied across taxa, while female weaponry remains understudied, and the reasons why females bear similar traits are still unclear. In the horned family Bovidae, males possess horns for sexual contests, but the presence and size of female horns vary considerably. Previous research has suggested that female weaponry may assist in intraspecific competition for territory and/or serve as an anti-predator defense in more exposed species. However, these studies did not fully explore how socio-ecological factors might influence variation in female horn length. In this study, we revisited the impact of socio-ecological factors on horn presence and conducted more robust tests of their effects on relative weapon investment (WQ). Our family-level comparative analyses (N = 115) reaffirmed that female territorial behavior and body size are the strongest predictors of female horn presence. For relative weapon investment, we found that among species where females bear horns, horn investment was positively correlated with larger body size and group size. In contrast, smaller-bodied, territorial, and monogamous species—such as klipspringers and dik-diks—tend to invest in relatively shorter horns. Although male horn investment did not significantly predict female horn presence, we observed that when females did bear horns, their size scaled positively with conspecific males. Our findings continue to support the idea that female horn presence is primarily driven by intraspecific competition for territories and/or anti-predator defense in larger-bodied species, while providing new evidence that social structure (monogamy vs. polygyny) influences female investment in mammalian weaponry.

Horn Investment

 Maximum female and male horn lengths (HL: in cm), shoulder heights (SH: in cm), and body masses (BM: in kg) were collected from the Bovids of the World field book (Castelló 2016). We chose to only use morphological data from this source to control for measurement consistency, and this book provided the most updated and detailed information on female horns. Our final dataset included 80 female horned species and 35 hornless species (Fig. 1).

We adapted a traditional method used to calculate relative brain size –  ‘encephalization quotient’ [EQ] (Boddy et al. 2012) to calculate investment in horn size or ‘Weapon Quotient’ [WQ] for each sex. This method has recently been adapted to estimate relative weapon investment for tusks, horns, and antlers (Lopez et al., 2024). We first ran phylogenetically corrected linear regressions across all species separately for each sex: log₁₀ HL vs log₁₀ BM. We pruned the Upham et al. (2019) DNA-based consensus mammal-wide tree to include our 115 species (Fig. 1) and performed phylogenetic generalized least squares tests using the ‘pgls’ function in the R packages ‘caper’ and ‘ape’ (Orme 2013; Paradis 2019).  To account for phylogenetic uncertainty and ensure statistical robustness, we repeated our analyses across 300 phylogenetic trees (Upham et al. 2019). The coefficient for log₁₀FHL ~ log₁₀FBM averaged 0.697 (SD = 0.097) and coefficient for log₁₀MHL ~ log₁₀MBM averaged 0.480 (SD = 0.0220), with all trees (100%) yielding significant results at both α = 0.05 and α = 0.01.

We used the average corrected ẞ (slope) and b (intercept) estimates to calculate the predicted HLs for each sex for each species (i) based on BM (Table 2): HL_i(predicted) = 10^b(HLvsBM) × BM_i^ẞ(HLvsBM). We then calculated WQ_i for each sex and species as HL_i(measured)/HL_i(predicted), where a WQ above 1.0 would represent a relatively larger horn, a WQ below 1.0 would be a relatively smaller horn, and a WQ of 0 would represent hornless species.

Habitat Openness & Exposure

A species’ habitat openness was scored based upon the relative cover it provides and how far away the prey can be seen by a potential predator. Following many previous studies (Stankowich and Caro 2009; Stankowich and Campbell 2016; Stankowich and Stensrud 2019; Caro et al. 2021) , using the IUCN Red List database (IUCN, 2020), each species’ presence and suitability in each of the 30 possible IUCN habitat types was scored as one of the following: 3= suitable and of major importance, 2= suitable but not of importance, 1.5= unknown, 1=marginal, and 0=not found.  Marine, Artificial Marine, and Caves/Subterranean biomes were not included in the data analysis. Because some species had more than five possible habitats reported, to emphasize the habitats each species primarily lives in rather than where they can potentially be found we used the Handbook of Mammals of the World (Wilson and Mittermeier 2011)** and Bovids of the World (Castelló 2016) to extract the three primary habitat types listed for each species and pruned the IUCN habitat list accordingly. Open habitat types (e.g., tundra, desert) were scored as near 1, while closed habitat types (e.g., tropical rainforest) were given scores near 0 (e.g., Temperate Grassland (0.8), Rocky areas (0.5), Temperate Forest (0.25)). We then calculated a weighted species-average habitat openness score by summing the products of the presence/suitability score (0-3) by habitat openness (0-1) for each habitat the species lives in, and divided that by the sum of weight presence/suitability scores (see equation below; Caro et al., 2021):

\text{Species Weighted Avg Habitat Openness} =

\frac{

\sum_{i=1}^3 |\text{HabitatSuitabilityScore} \times \text{HabitatOpennessScore}|

}{

\sum_{i=1}^3 \text{HabitatSuitabilityScore}

}

We estimated visual exposure to predators for each species and sex as the product of the sex-specific log₁₀ transformed shoulder height and habitat openness score. 

Body Size, Sociality & Territoriality Behavior

General social/group structure and intraspecific behavior (territoriality) were primarily collected from Bovids of the World (Castelló, 2016). Missing or incomplete sociality data were supplemented and/or verified using Handbook of Mammals of the World Vol. 2 (Wilson & Mittermeier, 2011) and other published literature  (Roberts and Dunbar 2000; Vervaecke et al. 2005). 

For sociality, we converted numeric group size to an ordinal sociality score: ‘1’ (socially bonded pair), ‘2’ small (<10 individuals), ‘3’ intermediate (11-39 individuals), and ‘4’ large (40+ individuals). In few accounts, females are described to perform a range of territorial behaviors from simple scent marking to aggressive fighting with or running off intruders with their mated male (Roberts 1994; Roberts and Dunbar 2000; Wilson and Mittermeier 2011; Castelló 2016). There were insufficient details on these behaviors, and it rarely described the use of horns in territorial defense, thus female territoriality was generally scored as present “1” or absent “0”. We found 24 species accounts that explicitly described females to be territorial – mostly within the subfamily, Cephalophinae (duikers, klipspringers). Additionally, there was a lack of detail on female dominance hierarchy behavior (besides stating it has been seen in female herds) to divide them into ordinal categories. A few reports suggest horn size can be a determining factor of hierarchy status (e.g., Vervaecke et al., 2005), but hornless females are also described to established hierarchies (Castelló, 2016; Wilson & Mittermeier, 2011), so we did not include explicit female hierarchal behavior in our study.

Bayesian Hurdle Models

We log₁₀ transformed all body metrics and scaled all continuous variables (shoulder height, body mass, exposure score, habitat openness score). Categorical variables (territoriality score and sociality score) were left unscaled. Because some species do not possess horns, we added 1 to all species’ average horn lengths prior to log transformation to account for hornless species with 0 cm horn lengths.

We then performed hurdle models to test for the strongest predictor of female horn presence and horn size using the Bayesian function ‘brm’ in the package ‘brms’(Bürkner 2017). Hurdle models are used for zero-inflated datasets (Feng 2021) and for our study females of 34 species were hornless (i.e., WQ = 0). The first component of the hurdle model estimates the binary probability (hu). If the outcome is non-zero, it passes the hurdle, and the model then fits the non-zero data separately. In our study, this first stage identifies which factors predict whether a female has horns (0 = absent, 1 = present). Importantly, a negative estimate (β) indicates a lower probability of being in a ‘zero’ state, meaning the trait is more likely to be present (non-zero). The second part tells us which factors are strongly predictive of horn size when horns are present (i.e., WQ is non-zero). We specified the ‘family’ as ‘hurdle_gamma’ to model distribution for positive continuous values and all models were performed across 4 chains with 2000 iterations per chain (Bürkner 2017).

Model Reduction

We performed model reduction by generating all possible subset models and compared LOO (leave-one-out cross-validation) scores (Vehtari et al. 2017). The importance values represent how often each variable appears across the averaged models, weighted by model probabilities (Galipaud et al. 2014). We tested if female horn presence and size are most explained by (1) predation risk, (2) intrasexual competition, or (3) conspecific male weaponry by including the following variables: (1a) body mass, b) shoulder height, (1c) habitat openness, and (1d) exposure (shoulder height x habitat openness), (2a) territoriality score, (2b) sociality score, and (3) male horn investment (MWQ). After testing all model combinations of our 7 variables, we used LOO cross-validation for model comparison (Vehtari et al. 2017). Our model selection method calculated variable importance as the sum of model weights for models containing each variable and provides model rankings (Galipaud et al. 2014). We then pruned models that included “BM” and “SH” together as they both represent a body size metric, and we removed models that included “Expo” and “SH” or “HS” because “Expo” is a product of SH and HS. Our final pruned model combinations included 64 models. Using LOO scores and model weight (k), our best fit and biologically relevant model (LOO = 211.8) is: FWQ ~ log10(Body Mass) + Territoriality + Sociality + MWQ (Table 2). We ran additional ANOVAs and Tukey tests to test differences in horn investment among categorical group sizes (Table S1) among female horned species (N=80 species). We used the function ‘aov’ and ‘TukeyHSD  in the package ‘stats’ (R Core Team 2021).

Female horns appear to have evolved independently multiple times across the Bovidae (Stankowich & Caro 2009; Fig 1a); thus, we suspect different factors may influence female horn presence and investment across different lineages. We conducted tribe-level hurdle analyses on groupings with the most species: Group 1 (N=40; Caprini, Alcelaphini, Hippotragini), Group 2 (N=18; Cephalophini, Oreotragini), Group 3 (N=28 species; Antilopini, Neotragini), and Group 4 (N=18; Bovini, Tragelaphini). Due to smaller sample sizes, Reduncini (N=9), Aepycerotini (N=1), and Nesotragini (N=1) were excluded from tribe-level comparisons. For Group 2, sociality score and territoriality score were not analyzed because all species are territorial and form socially bonded pairs. In our supplement, we performed multivariate (Tables S3-S6) and single-variable subfamily hurdle models (Table 7). We ran additional ANOVAs and Tukey tests to test differences in horn investment among tribe groupings among female horned species (Table S2; N=80 species). We used the function ‘aov’ and ‘TukeyHSD  in the package ‘stats’ (R Core Team 2021).