Sexual size dimorphism is biased towards males in most mammalian species. The most common explanation is precopulatory intra-male sexual selection. Large males win fights and mate more frequently. In artiodactyls, previous tests of this hypothesis consisted on inter-specific correlations of sexual dimorphism with group size as a surrogate for the intensity of sexual selection (Is). However, group size is not a proper measure of sexual selection for several reasons, as is largely recognised in other mammalian taxa. I conducted an inter-specific test on the role of sexual selection in the evolution of sexual dimorphism using variance in genetic paternity as a proxy for the Is. I reviewed the literature and found 17 studies that allowed estimating Is=V/(W2), where V and W are the variance and mean number of offspring per male, respectively. A phylogenetic generalised least squares analysis indicated that dimorphism (Wm/Wf) showed a significant positive regression with the intensity of sexual selection but not group size (multiple r2= 0.40; F3,17 = 12.78, p = 0.002). This result suggest that sexual selection may have played a role in the evolution of sexual size dimorphism in Artiodactyla. An alternative hypothesis based on natural selection is discussed.

I conducted a literature search during July-September 2019 using Web of Knowledge to locate genetic paternity studies in artiodactyls species. I identified a total of 34 publications for 17 species. From these studies, I selected those that either provided an estimate of Is or the necessary data to estimate this measure. The final data set included Is estimates from 17 studies that represent 17 species (Table 1). When multiple estimates of variance were available from one study (e.g., estimates derived from different methods or with different levels of confidence), I used the most conservative estimate or the method defined as preferable by the authors. Both peccary species were assigned a value of Is = 0 because the studies did not provide sufficient information to estimate Is. Nevertheless, the studies found that: (i) reproduction is randomly or evenly distributed among males in Pecari tajacu (Cooper et al. 2010) and (ii) there are no significant differences in the number of young sired per year among Tayassu pecari males (Leite et al. 2018). I defined size dimorphism as the ratio of mean male adult body mass (kg) to mean female adult body mass (kg). Most body mass values were obtained from Perez-Barbería and Gordon (2000), who performed an extensive bibliographic search to derive a dataset of body mass (kg) that comprises as much information as possible about population and subspecies variability for the artiodactyl species used in the analyses. They did not provide information for the following species, so I searched for alternative sources: Lama pacos (Bonavia 2008), P. tajacu (Cooper et al. 2011 mentioned the lack of dimorphism), Sus scrofa (Tack 2018) and T. pecari (Leite et al. 2018 mentioned the lack of dimorphism). Most data regarding group size were obtained from the PanTHERIA 1.0 database (Jones et al. 2009). Data not available in this database were obtained from www.ultimateungulate.com for: Capreolus capreolus (Marchal et al. 1998), Rangifer tarandus (Alendal et al. 1979), Muntiacus crinifrons, Ovis Canadensis, Capra ibex and T. pecari.