If someone was to mention modelling (simulating) the interactions between the populations of several animals
If someone was to mention modelling (simulating) the interactions between the populations of several animals your mind would almost certainly jump to computer simulations, but the concept of modelling is just as important (and goes back much further) in mathematics. A branch of these mathematical models was discussed by Dr Helen Christodoulidi in her seminar “Lotka-Volterra Systems: Dynamics and Applications” on the 19th of November 2025.
Dr Christodoulidi starts off with one of the most widely known models the Lotka-Volterra model (the name doesn’t give much of a hint as to its purpose). This is a very simple model for the competition between a predator species (such as foxes) and a prey species (such as rabbits). The model gives the number of members of each species over time. There are many arguably too many assumptions required for this model. Some of these are [1]:
- The only factors influencing the species are the populations of the two species themselves
- The prey species has access to unlimited resources
- Both predator and prey populations react immediately to the change of the opposite population
It would be extremely hard to come up with a model for these populations directly. Instead, a common method in mathematics, and especially physics, is to instead think of the rate of change of the populations over time. There are two ways in which the population of either species can change: birth or death of animals. We’ll stick with imagining the predators as foxes and the prey as rabbits for simplicity. For the rabbits, the birth rate depends only on the number of rabbits already alive (as their food source is unlimited). The higher this is, the faster the population will grow. The death rate depends on both the number of rabbits and the number of foxes. Either more rabbits or more foxes will increase the rate at which rabbits die. The foxes effectively the opposite. The birth rate of them depends on both the number of foxes and the number of rabbits, with the death rate depending only on the number of foxes already alive [2]. Hopefully by thinking about this for a few moments you can see why this is true.
Unfortunately, we have traded an impossible problem for an extremely difficult one turning these two rates of change back into an exact description of the two populations over time is not easy. There are, however, ways to do this, and in doing so you find a whole range of possibilities. The solutions generally follow a pretty simple pattern. Starting with a high number of rabbits, the fox population starts to grow. This causes the rabbit population to decrease which, in turn, then causes the fox population to decline as well. Finally, the rabbit population rises back up again. This continues indefinitely. There are additionally two stable positions: either both animals are extinct (not great), or the two animals have very specific balanced populations in which the reduction in population caused by death is exactly matched by the growth due to birth.
Increasing the number of species any higher than three creates even more difficulties. The rates of change of each of the populations are easy enough to write, but in trying to solve them we come across an issue. Any case in which all species survive is chaotic. That means that it is impossible to come up with equations for the populations of the species over time they can only be determined numerically using computers.
These types of mathematical models aren’t just limited to simulating ecosystems though. They have many uses including simulating the spread of an infectious disease the SRI (Susceptible, Infectious, Recovered) model [3, pp. 10251044]. This was obviously a fairly important topic a few years ago as scientists were trying to predict just how much of an issue the COVID-19 pandemic was going to be. All of that is to say mathematical modelling is a cornerstone of research which is often overlooked by the public is favour of computer models these are often based on mathematical models anyway!
[1] GeeksforGeeks, “Lotka-Volterra Model of Predator-Prey Relationship.” Accessed: 2025. [Online]. Available: https://www.geeksforgeeks.org/biology/lotka-volterra-model-of-predator-prey-relationship/
[2] E. W. Weisstein, “Lotka-Volterra Equations.” Accessed: 2025. [Online]. Available: https://mathworld.wolfram.com/Lotka-VolterraEquations.html
[3] A. S. Mata and S. M. P. Dourado, “Mathematical modeling applied to epidemics: an overview,” vol. 15, no. 2, pp. 10251044, Dec. 2021, doi: 10.1007/s40863-021-00268-7.
15100
Engaging start and good ending line. It has a clear example with a good amount of detail, and a clear description of the graph shape. For a couple of extra marks, you could add an example for the 3 or more species model.
Overall, it has a good amount of detail and an easy-to-understand writing style. Well done.
90561
Great readability with the mix of lay terms and higher level reading. Approachable structure is nice with things like the bullet point helping a lot. Overall very concise while keeping scientific. Nice job!
62451
1, Blogs overall presentation: The overall layout is really clear and well thought out, the title, name of speaker and date are all mentioned throughout the introduction, which was a nice way to do it instead of just writing them at the top of the page and then continuing the essay. However, there was no title for the blog itself. There is also good grammar throughout as well. 2/3
2, Accuracy of reporting the seminars take home message: The message that Helen was trying to get across through the seminar has been clearly and thoughtfully explained through this blog. 3/3
3, Accuracy of contextualisation for the research: The accuracy for the contextualisation is well done for the research and shows that the writer knows the research behind the topic however the social contextualisation could be more in depth and added to a bit more. 2/3
4, Additional research and use of external sources: There is additional research done in this blog however there was no use of a direct quotation. 2/3
5, Writing style and level for audience: The blog is written in a way for people who have minimal knowledge to be able to understand and then gain some sort of understanding of the topic while also giving more advanced detail to those who wanted more knowledge. 3/3
Overall: 12/15, very well written blog with a few minor adjustments through it.
42890
This blog is accurate and written well. It is suitable for a lay audience and despite not having a direct quote, reads fluently and is engaging.
82157
The article is very engaging to the reader by using real world examples to help portray the concept of the Lotka -Volterra model. You haven’t included any equations which I believe to be a good thing as it shows that you understand the audience of the blog post, which is supposed to be layman.
Overall gets the message across clearly to a wide range of audiences and flows well!