I Attended a Seminar by Helen Christodoulidi on 19th November Titled ‘Lotka-Volterra Systems: Dynamics and Applications’
I attended a seminar by Helen Christodoulidi on 19th November titled ‘Lotka-Volterra Systems: Dynamics and Applications’ which provided an insight what Lotka-Volterra equations are and how they can be applied in the real world.
The model is a dynamical system, meaning that it changes over time. Interestingly, it was introduced as a predator-prey model independently by Alfred J. Lotka and Vito Volterra and has now been developed and linked to many real-world applications in Ecology, Biology and Finance.
Most famously used in ecology, the Lotka-Volterra model describes the relationship between two species: a predator and a prey. It uses first-order non-linear differential equations to do this. We can take, for example, rabbits and foxes. The model shows that without any foxes interacting with the rabbits, the rabbit population increases exponentially. However, the growth rate decreases as the fox population increases as more rabbits are eaten. In contrast, the number of foxes declines exponentially without any rabbits, but then increases as the rabbit population increases as there is a greater food source. This can be expressed visually in the below figure:
[1]
In Biology, the model has applications in epidemics. The ‘prey’ in this case is the population of people susceptible to the disease with the ‘predator’ being the infected population. The number of susceptible individuals declines as the infected population increases as susceptible become infected. The infected population naturally reduces as they recover naturally or possibly die, but they increases as susceptible become infected. Figure [2] represents this as a graph (focusing on red and blue lines) which has also been seen using real life from Gov.uk Coronavirus cases from 1st April onwards [3].
[2]
In Finance, there are many uses of Lotka-Volterra with competing companies or mother and subsidiary banks interacting. The model can also be used to represent the relationship between wage share and employment rate. This was studied by Goodwin and represents employment rate as the ‘prey’ and wage share as the ‘predator’. High employment rate will lead to workers demanding higher wages so the wage share increases. This then results in falling profits for the businesses and so lower investment and employment rate drops in a cyclic pattern, very similar to predator-prey relationships. According to Goodwin, Lotka-Volterra can be “helpful in the understanding of the dynamical contradictions of capitalism” [4].
In addition to the above examples with 2 variables, the seminar concluded with going into detail about how Lotka-Volterra models can include 3, 4 or even more variables to show the relationships between the populations. In some cases, all species in the model can co-exist, in some not all species survive.
This is a great example of how mathematics can be applied to real-world contexts such as Biology and Finance, as we don’t usually get to see links between these areas.
[1] MyLearning, “Ecological Cycle: Predator and Prey,” MyLearning, 2025. [Online]. URL: https://www.mylearning.org/resources/ecological-cycle-predator-and-prey
[2] Korotkov, Standard Routine Techniques of Modeling of TickBorne Encephalitis. [Online]. URL: https://www.researchgate.net/publication/346515479_Standard_routine_techniques_of_modeling_of_tick-borne_encephalitis
[3] UK Health Security Agency, COVID19: Respiratory Virus Dashboard. [Online]. URL: https://ukhsa-dashboard.data.gov.uk/respiratory-viruses/covid-19
[4] R.M Goodwin, A Growth Cycle, presented at the First World Congress of the Econometric Society, Rome, 1965
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Structure of report is nicely formatted and well written, consider opening with a more engaging statement or question. Discussed all core topics both in depth and breadth, and correctly stated the name and date of the seminar. A variety of references shows external research and a good grasp of the subject, however does not include the references specifically given in the slides of the seminar. For example: specific diagrams were given that model the population of the predators and prey, and a specific paper was given that modelled this system in 4D which was mentioned however the reference was not given.
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Presentation
Date, title, and speaker: Clearly stated in the introduction: “Helen Christodoulidi on 19th November titled ‘Lotka-Volterra Systems: Dynamics and Applications’.” Grammar and English: Overall, the grammar is good and the language flows well. There are two minor issues: “but they increases as susceptible become infected” should read “but they increase as the susceptible become infected.” A comma is recommended after “wages” in the sentence: “High employment rate will lead to workers demanding higher wages so the wage share increases.” Spelling: “subsidiary” should be corrected to “subsidiary.” Score: Good. Content
Coverage of seminar content: The notes accurately summarise the seminar and explain the key concepts, including the historical background and real-world applications in ecology, biology, and finance. Accuracy: References are correctly cited, and the explanations align with established research. Score: Excellent. Context
Societal and research relevance: The piece effectively connects Lotka-Volterra models to broader contexts such as biology, epidemiology (with COVID-19 examples), and financial systems. This demonstrates strong awareness of both modern research and practical applications. Score: Excellent. Style
Accessibility and engagement: The tone is clear and suitable for a lay audience. Complex mathematical ideas are explained in an understandable way, and the inclusion of diagrams strengthens comprehension. Score: Excellent. External Sources
References and quoted opinion: All references are relevant, appropriate, and correctly cited. The inclusion of Goodwin’s quotation adds depth and authority to the discussion. Score: Excellent. Final Review
This is a well-structured and informative piece that successfully explains the Lotka-Volterra system and its diverse applications. It demonstrates strong contextual awareness and uses examples that make the topic relatable to readers outside mathematics.
Suggested improvements:
Correct minor grammar and spelling errors. Add a few more commas for clarity in longer sentences. Overall impression: A clear, engaging, and accurate summary that effectively conveys the seminar’s content and relevance to real-world contexts.