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The mathematics of why grannies exist



4 March 2015

I love reading student projects. It always impresses me how much someone can learn and the sophistication of what they can investigate just a couple of years after finishing high school. So I came across Jared Field's honours thesis from October 2014 - an independent project he embarked on four years after his HSC under the supervision of our very own Dr Peter Kim from the School of Mathematics and Statistics. Title: 'A McKendrick-von Förster type equation for the Grandmother Hypothesis'. What?!

The question: if our species is built on procreation and survival of the fittest why do women live well beyond reproductive age? This has been happening for much longer that the medical and lifestyle advances that push us all into living vibrant retirements. Compared with other great apes, who do not share this affliction, we also have shorter intervals between births and a later age for first birth. Any other animal share these traits? So far all we know of is Killer whales. Interesting.

Here's what we need to think about. Life is risky business and our young are so dependent on us for such long periods that it means there's more chance of orphaning and therefore hindering your child's survival. So why not have womenlook after their grandchildren who still carry one quarter of their geneticmaterial? With you - an older woman - as a significant helper, your children's children will have a better chance of healthy survival and your children canalso get on with having more children quicker. This is called 'allomothering' and is widespread in mammals and birds, and especially so in primates such as monkeys and, of course, us.

Allomothering is an example of the evolutionary results of kin selection,which is a type of natural selection where animals benefit from 'caring' behaviour that advantages their genetic relatives. Charles Darwin first wrote about kin selection as an evolutionary strategy in his 1859 book 'On the Originof Species'.

To test these ideas that invoke such long time scales of global communities,the only appropriate tool is a mathematical model. Jared's first step was to deconstruct our human population into the following tiers: unweaned, weaned,independent, fertile, infertile, and frail. He then used mathematics to analyse equations describing how each of these groups would evolve generation aftergeneration.

And what did Jared's mathematics unearth? Well first it confirmed that grandmothering reduces reproductive stresses within a population as well as interbirth intervals. But more interestingly what came out in the wash was that grandmothering leads to an increased population growth rate. And then that grandmothering drove the evolution of the longevity of our species. The greatest of the mathematics then came as the same equations confirmed the data for Killer whales who can also live past their nineties even though their reproduction ceases in their forties.

Go and give your grandmother a big hug straight away!

Jared ends histhesis with a quote from famous physicist Richard Feynman: "To those who do notknow mathematics it is difficult to get across a real feeling as to the beauty,the deepest beauty, of nature."

Dr Clio Cresswell
Dr Clio Cresswell

Clio Cresswell is a Senior Lecturer in Mathematics at the University of Sydney and has recently been appointed as our official Mathematics Spokesperson. Communicating mathematics is her field and passion. Clio has appeared on panel shows commenting, debating and interviewing; authored book reviews and opinion pieces; joined breakfast radio teams and current affair programs; always there highlighting the mathematical element to our lives. She is author of Mathematics and Sex.