Abstract:
While you may not enjoy maths, or think that it is necessary, it plays a vital role in how we understand and look after our environment. Mathematical ecology is a field of maths which puts the applied in applied math, using the strengths concept ODE’s, optimization, and deep learning neural networks to good use. Maths is helping us to help the world. Maths is awesome.
When I tell people that I study maths they usually raise their eyebrows, say something along the lines of ’better you than me’, then make some statement about how they really don’t like maths, or didn’t think maths was necessary at school.
You might not think that maths is very helpful, or helpful at all and that what you learned or are learning in high school mathematics is doing you no good. I am here to tell you that a lot of good comes out of high school math- ematics, especially from those really fundamental concepts. In particular, I am talking about how the applications of those differential equations help a lot when we are trying to understand and help the world we live in, particularly when we are trying to understand ecology. Ecology is the study of the relationship between organisms and their environment [5]. Ecologists investigate how species interact with each other within ecosystems and attempt to categorise and un- derstand species interactions. Ecologists are also interested in how ecosystem populations change in space and time so that they can study the direct and in- direct impacts of species reintroductions, invasive species management, habitat restoration, climate change, and predict how species behave when faced with natural events like fire, floods or cyclones.
So how does maths come into all this? Mathematics, particularly the study of the theory of dynamics, has played an important role in simplifying the complexity of ecosystem dynamics. Mathematical models are important be- cause they allow us to simulate complex ecological dynamics helping ecologists study ecosystem behaviour. The first substantial use of maths in ecology was in the early 1900’s by two mathematicians, Alfred Lotka and Vito Volterra, who developed the Generalised Lotka-Volterra model for species population in ecosystems, a basic ecological model for competition and predation [3]. Their model attempted to model the population of species within an ecosystem over time using a linear growth term and species interaction. Since then, many other models have been developed to improve on our predictions. If you want more on that, check out my report.
Maths has not just been used for ecosystem populations. Applications of deep learning for predicting animal movement, mathematical models for coral bleaching dynamics, and predicting the spread of infectious disease within ani- mal populations are just some examples of how mathematics can be so beneficial to ecology [1], [2], [4]. So the next time you feel the need to express negative opinions about math- ematics, maybe stop and remember this blog post. Maths is awesome.
References
[1] Kaitlyn Brown et al. Coral Bleaching Dynamics on the Great Barrier Reef: New Insights from a Mathematical Model. Rochester, NY, Oct. 31, 2024. DOI: 10.2139/ssrn.5006023. URL: https://papers.ssrn.com/abstract= 5006023 (visited on 02/28/2025).
[2] Scott W. Forrest et al. Predicting animal movement with deepSSF: a deep learning step selection framework. Pages: 2025.02.13.638055 Section: New Results. Feb. 17, 2025. DOI: 10.1101/2025.02.13.638055. URL: https://www.biorxiv.org/content/10.1101/2025.02.13.638055v1 (visited on 02/28/2025).
[3] Kevin S. McCann. Mathematical Ecology. obo. May 23, 2012. URL: https://www.oxfordbibliographies.com/display/document/obo-9780199830060/ obo-9780199830060-0004.xml (visited on 02/26/2025).
[4] Robin H. Miller et al. “Ecological Niche Modeling to Estimate the Distribution of Japanese Encephalitis Virus in Asia”. In: PLoS Neglected Tropical Diseases 6.6 (June 19, 2012), e1678. DOI: 10.1371/journal.pntd. 0001678. URL: https://pmc.ncbi.nlm.nih.gov/articles/PMC3378598/ (visited on 02/28/2025).
[5] Lauren G. Shoemaker et al. “Writing mathematical ecology: A guide for authors and readers”. In: Ecosphere 12.8 (2021). eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/ecs e03701. ISSN: 2150-8925. DOI: 10.1002/ecs2.3701. URL: https://onlinelibrary. wiley.com/doi/abs/10.1002/ecs2.3701 (visited on 02/26/2025).
Ben Cicchini
Queensland University of Technology
