1. Sharks, Mullet, and Mathematical Ecology
Using ODEs to model predator-prey relationships
Chandler Shaeffer

2. Lotka – Volterra Equations
Imagine you have a closed system with a predator population and a prey population
With the logistic map equation, you have a set number of rabbits for each year. However, this isn’t realistic!
Predator and prey populations influence each other – how do you model this?
Lotka – Volterra Equations
dx / dt = αx – βxy
dy / dt = -γy + δxy

3. Let’s say we have 100 lemon sharks and 400 mullet.
dx / dt = αx – βxy
dy / dt = -γy + δxy
Where
x represents the number of mullet
y represents the number of sharks
α represents the growth rate of the mullet population
β represents the rate of predation upon the mullet
γ represents the rate of loss of the predator population
δ represents the growth rate of the predator population
Use fourth-order Runge-Kutta method to solve ODE system (adapted code from labs and homework)

5. All models are wrong, but some are useful
Lower γ
Lower α
Higher β

6. Refine model by introducing competition
Model intraspecific competition w/ new parameter c*x^2
Model interspecific competition by adding new ODE