The world is a complex place. Whether man-made or natural, many complex systems are active every day. Most of these systems, if not all of them will interact with each other to some degree. Of course, looking at the world as a whole is a daunting and impossible task. Looking at the smaller systems that make up the world we live in is similarly a formidable task.
With so many factors to consider all at once, it is very common to approximate systems by breaking them down into their core components. Just as we can break the world down into fundamental systems, we can break down these systems into core components and forces that make it work and then understand it better.
This is where Mathematics comes in. Mathematical models can be used to analyse and appreciate the most prominent factors of the system.
Immunology is one area that already uses mathematical modelling extensively. These models can emulate the spread of pathogens or treatments in order to predict ahead of time what may be optimal for medical purposes: the dosage, where the targeted treatment is applied etc.
Evolutionary biology is one of many areas that would benefit greatly from extensive mathematical modelling. With so many factors deciding the evolutionary path a species may take, many evolutionary biologists theorise continually about what factors have a defining role in the evolution of certain aspects in a species.
With Mathematics we can model various theories and see how truly these theories hold. We might find that changes in the environment might not have as big a role as suggested by theories, or that increased predation is by far the leading cause for some evolutionary pathway. The results are often not obvious, and because of the timespans necessary for evolution to occur it would be impossible to test these theories with real life experiments!
We looked into an area of sexual conflict that deals with how male interests and female interests aren’t always the same and might clash. How these come together might not even be beneficial for the species. If a male wants to kill off all competition, not only does that reduce female’s choice in mates, but it is definitely not sustainable for the population as a whole. In economics this phenomenon is often referred to as the ‘Tragedy of the Commons’.
Conflict between males as well as infanticide in primates was where we focused our attention. In our model we found that the most stable populations were when males would always defend their partners. However, over time we found that males would eventually become very passive and try to avoid conflict. This meant that more aggressive males could potentially devastate the population making this passive state very unstable. With more modelling we can investigate this further.
How well will this trend hold in general? We will have to dig deeper into the model.
Nicholas Fazio was a recipient of a 2018/19 AMSI Vacation Research Scholarship.