Mathematical Contest in Modeling: Honorable Mention

Lampreys play a complicated role in their ecosystems. Their ability to adjust their sex ratio in response to food availability and possibly other factors adds much complexity to understanding their behavior and how this can affect their ecosystem, which presents a unique challenge for researchers. This underscores the need for a comprehensive understanding of these adaptive mechanisms, as they play a pivotal role in shaping the broader ecological landscape.

In this year’s MCM competition, our team developed a probabilistic model to simulate the population dynamics of lampreys in a specific habitat. We assert that the population of male and female lampreys can be effectively modeled using a system of differential equations whose variables depend on several parameters, including birth rate, mortality rate, and the probability of a newborn being female. These parameters, in turn, are influenced by external factors such as water temperature, predator abundance, and food availability within the habitat.

Utilizing our model, we conduct extensive simulations to analyze the long-term population dynamics of lampreys. Our investigation delves into the intricate interactions between male and female lampreys, examining their effects on predator numbers and food availability within the habitat. To gauge the model’s robustness, we subject it to sensitivity analysis by adjusting environmental parameters and introducing random conditions to simulate real-world variability.

Lastly, employing our model, we contrast the population dynamics of species with a flexible sex-determination mechanism against those with a fixed sex ratio. We simulate the population dynamics of different species through 100 different simulations with changing habitat conditions. Our findings indicate that although species capable of adjusting their sex ratio experience advantages such as increased food availability and reduced predator numbers, they tend to exhibit lower birth rates and higher mortality rates. Consequently, this results in an overall lower population level compared to species with a fixed sex ratio.

On a higher level, we conclude that lampreys’ capacity to alter sex not only enables swift adaptation to local conditions, leading to increased food availability, but also creates ecological space, enhancing the potential for symbiotic relationships and stability among coexisting species.

Award: Honorable Mention