Sexual dimorphism is difficult to spot among remains of dinosaurs, but in a new paper, published Thursday in the Biological Journal of the Linnean Society, scientists argue that just because something is subtle, or hard to spot, doesn't mean it's not there.

When fossil records are sparse, determining if differences between specimens are the result of differences in species, age, sex or natural variation is especially challenging, researcher say.

However, new research suggests traditional methods for identifying the presence of sexual dimorphism have underestimated the phenomena.

Traditionally, paleontologists rely on a statistical method called significance testing to determine whether size and structural variation among a group of fossils is the result of sexual dimorphism.

"Significance testing attempts to determine the probability that the observed data could be obtained by pure chance if a particular null hypothesis is true," Evan Saitta told UPI in an email.

"The lower the probability, the more inclined we are to reject the null hypothesis in favor of another," said Saitta, a research associate at Chicago's Field Museum and the lead author of the new paper.

For most studies, the null hypothesis is that there was no variation between males and females within a specific dinosaur species.

"This leads to black-or-white dichotomous thinking that an effect -- e.g., dimorphism -- is either present or absent," Saitta said. "This is a major problem when data is scarce, such as in some fossils -- it might require a massive degree of sexual dimorphism to trigger a positive result in favor of dimorphism."

To solve this problem, Saitta and his colleagues turned to a different statistical method called effect size statistics. The method attempts to estimate the size of the effect, as well as the uncertainty in that estimate.

"Since many sexual dimorphisms are subtle in magnitude, it is better to think in terms of the magnitude of sexual variation and attempt to constrain the uncertainty in that estimated magnitude, rather than blankly rejecting the possibility of dimorphism," Saitta said.

For their analysis, researchers developed effect size statistical simulations and uploaded measurements of dinosaur fossils. Their analysis showed effect size statistics can estimate the level of sexual dimorphism present within a species or fossil data set.

"There is no need to absolutely declare 'no dimorphism' or even 'no evidence of dimorphism' in a fossil dataset, but instead you can report your estimate of sexual variation and the range in which you might confidently expect the true value to lie -- which might include zero differences between the sexes," Saitta said. "A small dataset of a species with minimal dimorphism will yield a small estimated magnitude of sexual variation with wide error bars on that estimate relative to a large dataset of a species that is highly dimorphic."

The new statistical analysis still won't be able to help scientists determine whether any one individual was male or female, but it can help researchers estimate the prevalence of sexual dimorphism, which could be useful for paleontologists and other scientists trying to answer a variety of questions in the field of evolutionary biology.

"It is important because sexual selection is a major driver of evolution," Saitta said. "By studying trends in the magnitude of sexual variation we can examine how sexual selection affects long-term evolutionary processes in the fossil record."

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