## Selfish species: game theory and the ecosystem

### Introduction

I am studying for a PhD in Statistical Physics and Complex Systems at The University of Manchester. My research studies a system of many interacting species where the population of one species can facilitate or hinder the growth of another species. This relationship is determined by a specific interaction coefficient between the species. The interaction coefficients for the relationship between every pair of species are drawn randomly from a two-dimensional Gaussian distribution, and we use the parameters of this distribution to predict how the ecosystem behaves. We can then simulate these interacting species using a computer programme to check our predictions.

### In Depth…

I studied Mathematics and Physics for my undergraduate degree at The University of Manchester. I chose this degree because I enjoy understanding how the world works, and appreciate how bizarre and counter-intuitive our reality is. I had a fascination for quantum mechanics and relativity, higher dimensions, and sub-atomic particles. I really enjoyed learning about these concepts as well as being introduced to many other fascinating ideas. I enjoyed the lecture style of teaching but I also developed my ability for independent learning, I became really good at managing my own time, and absorbing information at my own pace from reading textbooks and lecture notes. The most useful skill I learned during my degree was how to computer programme, I learned how use Matlab, C++, and Python, and I learned how to write codes for simulations, data analysis, solving complicated equations, and optimization algorithms. I decided to do a PhD after my undergraduate degree because I really enjoy self-study and programming, and I am further developing these skills with new challenges every day.

I became interested in population dynamics after reading "The Selfish Gene" by Richard Dawkins, where he described behavioural evolution using ideas from Game Theory. He described how an animal’s behaviour, and the behaviours of the other animals it interacts with, would determine how successful the animal would be at surviving and passing on it genes. These successful behavioural strategies would dictate how the behaviour of the population as a whole would change over time, and evolve to an Evolutionary Stable Strategy which could be understood as stable Nash equilibria. During my degree I took the opportunity to study Game Theory further by writing my second year vacation essay on the topic. I researched many areas of Game Theory and went through a short online course. I discovered how it can be applied to statistical physics, in the Ising model for ferromagnets, and really enjoyed learning about how ideas from quantum mechanics could produce Quantum Game Theory, where a player could play multiple strategies at the same time. In my fourth year I undertook a project with my current PhD supervisor on a population of individuals who had the choice of two behavioural strategies to interact with. The population evolved by the number of individuals playing the more successful strategy increasing, but this model also considered the effect of time delay, such as a gestation period in nature. I really enjoyed my project with my supervisor and through this I continued onto a PhD with him.

### Going Further…

Here is a link to my supervisor’s webpage, if you are interested in my research you could look at his publications:

https://www.theory.physics.manchester.ac.uk/~galla/

Here are links to the undergraduate Mathematics and Physics courses webpages:

http://www.maths.manchester.ac.uk/https://www.physics.manchester.ac.uk/

If you are interested in game theory, here is a brief course:

https://www.youtube.com/watch?v=iZKErrvVMaY&list=PL76B0EB6DDFC42D02

If you are interested in “The Selfish Gene” here is a brief summary of the book, chapter 12 discusses game theory:

http://old.unipr.it/arpa/defi/econlaw/SELFISH%20GENE.pdf

and the full text can be downloaded here:

https://www.zuj.edu.jo/download/the-selfish-gene-r-dawkins-1976-ww-pdf/