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.

中文翻译：

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一个影响大小统计框架，用于调查非禽类恐龙和其他已灭绝的类群中的性二态性

尽管有报道说灭绝的类群存在两性异形，但在过去十年中，非禽类恐龙中的这种说法很少见，并且经常受到批评。由于双态性在当今的有性生殖生物中很普遍，因此文献中的报道不足可能暗示方法上的缺陷，或者表明这一多样性群体表现出高度不同寻常的生殖生物学。单变量显着性检验（尤其是对于双峰检验）无效且容易产生假阴性。因此，可能不需要物种识别和相互的性别选择假设来解释整个年级假定的性别二态性缺失（II型错误）。取而代之的是，有多种证据支持性选择和与次要性特征相符的结构变异，强烈暗示了非禽类恐龙的性二态性。我们提出了一个研究化石中性二态性的框架，重点研究可能的次要性状，并使用多条证据对所有替代假设进行化验。我们使用适合于低样本量的效应大小统计数据（而非显着性检验）来分析性状中生长曲线的潜在差异，并限制双态程度的估计。在许多情况下，对性别变异的估计可能是相当准确的，并且改善性别分配和解释性内变异的方法的进一步发展（例如混合模型）将提高准确性。比较数据集之间双态性的大小和支持程度的估计要好于二分法拒绝或无法拒绝单个物种中的单态性，从而更好地研究系统发育和时间上的性选择。我们用包括恐龙在内的模拟和经验数据为我们的方法辩护，表明即使在许多情况下，即使简单的方法也可以得出相当准确的性变异估计，从而可以比较支持性变异的物种高低。