An effect size statistical framework for investigating sexual dimorphism in non-avian dinosaurs and other extinct taxa

Abstract

Despite reports of sexual dimorphism in extinct taxa, such claims in non-avian dinosaurs have been rare over the last decade and have often been criticized. Since dimorphism is widespread in sexually reproducing organisms today, under-reporting in the literature might suggest either methodological shortcomings or that this diverse group exhibited highly unusual reproductive biology. Univariate significance testing, especially for bimodality, is ineffective and prone to false negatives. Species recognition and mutual sexual selection hypotheses, therefore, may not be required to explain supposed absence of sexual dimorphism across the grade (a type II error). Instead, multiple lines of evidence support sexual selection and variation of structures consistent with secondary sexual characteristics, strongly suggesting sexual dimorphism in non-avian dinosaurs. We propose a framework for studying sexual dimorphism in fossils, focusing on likely secondary sexual traits and testing against all alternate hypotheses for variation in them using multiple lines of evidence. We use effect size statistics appropriate for low sample sizes, rather than significance testing, to analyse potential divergence of growth curves in traits and constrain estimates for dimorphism magnitude. In many cases, estimates of sexual variation can be reasonably accurate, and further developments in methods to improve sex assignments and account for intrasexual variation (e.g. mixture modelling) will improve accuracy. It is better to compare estimates for the magnitude of and support for dimorphism between datasets than to dichotomously reject or fail to reject monomorphism in a single species, enabling the study of sexual selection across phylogenies and time. We defend our approach with simulated and empirical data, including dinosaur data, showing that even simple approaches can yield fairly accurate estimates of sexual variation in many cases, allowing for comparison of species with high and low support for sexual variation.

Morphology and distribution of scales, dermal ossifications, and other non‐feather integumentary structures in non‐avialan theropod dinosaurs

“…Remarkable cases of possible sexual dimorphism have been reported in early-diverging avialans based on soft tissues [e.g. blade-like tail feathers in Confuciusornis (Hou et al, 1996;Martin et al, 1998); but see also Chiappe et al (1999Chiappe et al ( , 2008], whereas convincing evidence based solely on osteology has so far been elusive (Mallon, 2017;Saitta et al, 2020). Among living birds, sexual dimorphism is most commonly expressed by the males, which are larger (an osteological trait) and have more elaborate plumage (a soft-tissue trait) than the females (Møller & Cuervo, 1998).…”

Femora from an exceptionally large population of coeval ornithomimosaurs yield evidence of sexual dimorphism in extinct theropod dinosaurs

“…We then investigated the resulting dataset using Principal Component Analyses (PCA) and Gaussian Mixture (GM) modelling as clustering analyses. This clustering analysis calculates the number of Gaussian distributions present in a dataset by maximum likelihood estimations and has been demonstrated as a well-suited method for the identification of dimorphism (Godfrey et al, 1993;Dong, 1997;Fabre et al, 2014;Manin et al, 2016;Mallon, 2017;Saitta et al, 2020) Institutional abbreviation: ANG: Angeac-Charente Collection, Musée d'Angoulême, Angoulême, FR…”

“…Dimorphism has been reported in every major dinosaur clade and has often been attributed to sex-specific variation (Dodson, 1976; Chapman et al, 1997; Bunce et al, 2003; Padian and Horner, 2011; Knell and Sampson, 2011; Knell et al, 2013; Mallon, 2017; Saitta et al, 2020). However, recent studies have demonstrated that most of the documented cases of sexual dimorphism in extinct dinosaurs were most likely biased by ontogenetic changes, taphonomic deformations and small sample sizes, which substantially affect the representativeness of the inter- and intraspecific diversity, and undermine statistical analyses (Griffin and Nesbitt, 2016; Hone and Mallon, 2017; Saitta et al, 2020).…”

“…Dimorphism has been reported in every major dinosaur clade and has often been attributed to sexspecific variation (Dodson, 1976;Chapman et al, 1997;Bunce et al, 2003;Padian and Horner, 2011;Knell and Sampson, 2011;Knell et al, 2013;Mallon, 2017;Saitta et al, 2020). However, recent studies have demonstrated that most of the documented cases of sexual dimorphism in extinct dinosaurs were most likely biased by ontogenetic changes, taphonomic deformations and small sample sizes, which substantially affect the representativeness of the inter-and intraspecific diversity, and undermine statistical analyses (Griffin and Nesbitt, 2016;Hone and Mallon, 2017;Saitta et al, 2020). For example, a discrete and binary variation between gracile and robust morphologies of bone scars, mostly at the level of the lesser trochanter, has frequently been inferred, with more or less confidence, as sexual dimorphism in various ceratosaurian theropods and non-dinosaurian dinosauriforms (Colbert, 1990;Raath et al, 1990;Benton et al, 2000;Britt et al, 2000;Carrano et al, 2002;Piechowski et al, 2014).…”

Evolution of Hadrosaurs in the Campanian of Laramidia: New Information from the Skull Roof and Braincase

“…Analysis of Maiasaura bonebed material is compatible with dimorphism in body mass (Saitta et al 2020). However, sexual dimorphism in cranial anatomy has not been confirmed in any ornithischian dinosaur to date (Mallon 2017).…”