## Optimising Animal Foraging – An Exciting Challenge

Miriam Slattery, University of Adelaide

I heard about the AMSI Vacation Research Scholarship while in my second year of my Mathematics degree and I was incredibly keen to delve into research. When searching for a topic I asked several lecturers for inspiration. One lecturer, Giang Nguyen, who became my supervisor for the project, suggested the topic of my research: optimal animal foraging in a two-dimensional world. This was very exciting for me because I had no idea where to even start.

I was quite interested to read about how so many animals (fruit flies, spider monkeys, albatross, jackals, reindeer etc.) have been observed to follow similar patterns of movement when foraging for food. Using this assumption, the aim was to find out how to make this way of movement most efficient in the search for food in unknown locations. The reasoning behind this was that we assume that animals will have evolved through the process of natural selection to move in such a way as to maximise the efficiency of finding food. So, if we want to understand and predict how animals move, solving this problem is a good place to begin.

I did a lot of research into the maths that people have done for similar topics to this. I found that there was already a known solution to this problem for an animal in one-dimensional space. This means that the animal is moving along only a straight line. While this is not very realistic, it was a good way to simplify the problem. I wanted to have a look at a more relevant version in which the animal can move in two dimensions. I decided to run some computer simulations for the one-dimensional case so that I could compare my solutions with the known solutions and make sure my simulations were working well. I then could use the same idea for simulations in two dimensions. My research required a lot of computer programming skills for doing these simulations that I had to learn which was challenging and enjoyable.

I also explored the detailed solution for one dimension. This involved a lot of new mathematical concepts and notation that I hadn’t come across before but, with the help of my supervisor, I was able to understand it. I wanted to try a similar method for two dimensions, but it was very complex and I didn’t have enough time do it.

I really enjoyed this whole project and I learned so many new skills and concepts in maths and programming. I think I really flourished in research and had a lot of fun working with other people to solve big problems.

Miriam Slattery was one of the recipients of a 2017/18 AMSI Vacation Research Scholarship.