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Concept
Sexual dimorphism refers to the phenotypic variations between male and female members of species. Examples include differences in morphology, size, ornamentation and behaviour. Sexual dimorphism, a by-product of sexual selection, is prominent across all categories of living organisms. For instance, peacocks display vibrant plumage colours in an attempt to attract and copulate with their female counterpart, the peahen. This form of temptation is defined as intersexual selection, the process in which female or male specimens choose among potential mates. However, some groups of species acquire a mate by the means of competitively engaging in an aggressive confrontation among others, whereby the victor is entitled to its significant other, a concept coined as intrasexual selection.

Sexual dimorphism and dinosaurs
Examining fossils of dinosaurs in search of sexually dimorphic characteristics requires the supply of complete and articulated skeletal and tissue remains. As terrestrial organisms, dinosaur carcasses are subject to ecological and geographical influence that inevitably constitutes the degree of preservation. The availability of well preserved remains is not a probable outcome as a consequence of decomposition and fossilization. Some paleontologists have looked for sexual dimorphism among dinosaurs using statistics and comparison to ecologically or phylogenetically related modern animals.

Examples of sexual dimorphism in dinosaurs
The following are academic researches conducted by palaeontologists, Roy Chapman and Paul Penkalski. Although these studies aren't conclusive in providing factual information, they do provide an insightful perspective.

Apatosaurus and Diplodocus

Females of the Apatosaurus and Diplodocus species, comprise of an interconnected caudal vertebrate that allows them to keep their tails elevated to aid in copulation. Discovering that this fusion occurred in only 50% of the Apatosaurus and Diplodocus skeletons and 25% of the Camarasaurus skeletons, indicated that this a sexually dimorphic trait.

Theropoda

Male theropods contain a retractable penis, a feature similar to the modern day crocodile. Crocodilian skeletons were examined to determine whether there is a skeletal component that is distinctive in both genders, hence, providing an insight on the physical disparities between male and female theropods. Findings revealed that male crocodiles consisting of the caudal chevron, used to anchor the penis muscles, had significantly larger than the female chevron. There are criticism that disapprove this discovery but it remains a subject of debate among advocates and adversaries.

Ornithopoda

Studies of sexual dimorphism in hadrosaurs have generally centred on the distinctive cranial crests of the Hadrosauridae, which would provide a fantastic signal for sexual display. A biometric study of 36 skulls showed sexual dimorphism in the crest of 3 species of hadrosauria. The crests were categorized as full (male) or narrow (female) and may have given some advantage intrasexual mating.