Can maths pick a dinosaur’s sex?

Palaeontologists show that using a different statistical model to analyse differences between dinosaur sexes may provide more accurate estimates.

This short article and associated resources are well suited to maths and biology students in years 5, 7, and 10 who are learning about, or interested in, the features of animals, statistics and identifying dinosaur fossils.

See the downloadable student activity for more detail about the statistics involved in this research.


Word Count: 523

scale of the size of dinosaurs compared to an average human
Credit: Gamma 124/Wikimedia Commons, CC BY-SA 3.0

How do you tell if dinosaur fossils are male or female?

Different sizes? Maybe one was just younger than the other.

Different bone structures? Maybe they’re different species.

Different physical features? Unfortunately when all you’ve got to go from is fossilised bones, you can’t see those distinctive features. After all, male lions typically have manes, and male peacocks have long tail feathers – but we don’t get that information from looking at their bones.

That’s the problem that palaeontologists face: it’s hard to tell if dinosaurs with different features were just varied in a way that had nothing to do with sex.

But now some researchers from the US have used a different kind of statistical analysis to find which differences in fossils are likely to be due to sexual variation, and which aren’t. Their analysis has been published in the Biological Journal of the Linnean Society.

“It’s a whole new way of looking at fossils and judging the likelihood that the traits we see correlate with sex,’ says Evan Saitta, who led the research at Chicago’s Field Museum.

Normally, palaeontologists have used “significance testing” to look for differences between sexes. They collect data points and then calculate the probability that those results could have happened by pure chance rather than due to an actual cause.

That’s fine when you have big datasets. But when it comes to fossils, “they’re usually pretty bad”, says Saitta. There’s not usually all that many bones to study, and those scientists have can be poorly preserved, incomplete, or sometimes just mislabelled. And that means that significance testing finds a lot of false negatives – the model can’t work out if the difference is due to sex or something else.

Maiasaura, one of the dinosaurs analyzed in the study, was estimated to have substantial variation in adult sizes, possibly indicating males and females, with relatively low uncertainty compared to other species. Credit: James Ormiston

Instead, Saitta used effect size statistics. Effect size is better for smaller datasets because it is a way of quantifying the size of the difference between two groups, rather than simply finding if there is a statistical difference or not.

For instance, Saitta and his colleagues found that in the dinosaur Maiasaura, adult specimens vary a lot in size. The analyses show that these are likelier to correspond to sexual variation than differences seen in other dinosaur species.

One problem is that while the current data suggest that one sex was about 45% bigger than the other, they can’t tell if the bigger ones are males or females.

The researchers also compared three dinosaur species – Maiasaura, Psittacosaurus lujiatunensis, and Tyrannosaurus rex. They found, based on the data, that Maiasaura had a larger estimate of sexual variation than the others. They point out that it doesn’t mean that any one of those species does or does not show differences between sexes, but that Maiasaura had a larger estimated difference than the others.

While there’s a lot of work yet to be done, Saitta says he’s excited that the statistical simulations gave such consistent results despite the limits of the fossil data.

“Sexual selection is such an important driver of evolution, and to limit ourselves to ineffective statistical approaches hurts our ability to understand the paleobiology of these animals,” he says. “We need to account for sexual variation in the fossil record.”

Written by Ben Lewis, Content Development Manager at The Royal Institution of Australia.

Years: 5, 7, 10

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Biological Sciences: The Body, Genetics, Living Things

Additional: Careers, Maths, Technology.

Concepts (South Australia):

Biological Sciences: Diversity and Evolution, Form and Function