The mathematics of evolution

Every so often you think about a moment, and this sounds quite cliched, but it’s a moment that changed your life, but you didn’t realise that it did. For me one of those moments was in year 10. Prior to that year, I was a bit cheeky at school. I was always getting into trouble and I wasn’t that interested. And I think it was because I was bored, really.

I had the option to move up into the advanced maths class, but my teacher at the time said all sorts of ridiculous rabble, like people like me don’t do maths, so I would struggle if I moved up. Because I am very head strong, I essentially told her to go get stuffed and moved up anyway. And because I’m very competitive, I made it my goal to beat everyone in the class – and I did that too.

I went to Oxford University and started investigating the evolution of sleep. Sleep as a behaviour, when you think about it from an evolutionary standpoint, makes very little sense. Why would such a vulnerable state evolve?

I submitted a paper, focusing on sleep, and one of the reviewers made a very good point; how do we distinguish sleep from rest? We need to talk about information collection if we’re to make that distinction. That then led me to thinking about how and when organisms are collecting information about their environment and when they’re not.

Have you heard of the grandmother hypothesis? I went on to look at the evolution of post-menopausal longevity. The grandmother hypothesis posits that post-menopausal grandmothers may increase the reproductive success in their children, and so indirectly their own fitness.

But significant post-menopausal representation (as opposed to viability) exist only in us humans and the toothed whales. I used a lot of game theory to show that in fact there are some very good reasons why you would expect it to be rare. Now, I’m asking other questions, because while I really quite like the grandmother hypothesis – I think it’s very elegant – it’s also very hard to test.

So, for example, if grandmothering is so great, at what point do the benefits of it stop, in terms of increasing life span.

I moved from Oxford to Melbourne to be closer to family. Even just being in the same time zone as my family made a really big difference. I’m on a McKenzie Fellowship which gives you an uncommon amount of freedom, for a young academic.

Mathematics can tell us a lot about the world and behaviours. There are famous studies from the 90s investigating the motivations of behaviour around risk. Say you give a bird two options – it may be water with different amounts of sugar in it or it may be food. On average, the reward is the same, but the variances are different. If I starve the bird, will the bird go for the more risky option? If I make sure the bird has full energy reserves, will they be more conservative?

We need to reassess the classic studies of behaviour, because they mostly assume that the experimentalists and the experimental subject had the same frame of reference. But I would argue that in most cases, that’s not true. I was able to show using some very simple mathematics that we need to be really cautious about the conclusions we draw from those experiments. You can show that, in a finite period of time, they will never agree that the expected rewards are the same.

My work now is looking at traditional Indigenous marriage rules. These are rules for who can marry whom; I’m thinking about the mathematics of these rules and the evolutionary consequences of them. One reason I’m interested is for very personal reasons, because it is my culture. And I strongly believe we must be keepers of our own knowledge.

But the other reason is that at the turn of the last century a lot of people were studying these rules, but they were sort of swept aside as cultural artifacts, not having much utility or reasoning behind them.

Indigenous marriage rules are actually quite clever systems to prevent a lot of diseases from spreading. I can show, just with pen-and-paper mathematics, that by following the marriage rules, the entire population of the Gamilaraay Nation (where I’m from) – which extends from New South Wales to southern Queensland – would have to reduce to 24 individuals for people to be as closely related as first cousins when marrying. That’s 24 people, over a landmass that is the size of France.

In the 1850s, the upper crust in England were doing this on purpose. Charles Darwin married his first cousin.

I would argue that this is science. Although Indigenous marriage rules may not be couched in modern scientific terms, to understand these things is to very closely observe, using intense longitudinal studies. This is science.

There are only around five Indigenous mathematicians in the country, and most of them have left academia because of racism. I decided to apply to the ABC’s Top 5 Media Residency Program because I’m hoping that being a little more visible might encourage other black people to dive into maths.

There are very few of us out here saying “I’m a black mathematician” or “I’m a black scientist”. I think, maybe, that’s because we need reminding that not only are we capable, but we’ve always been capable.

- As told to Dr Daryl Holland