This repository contains an excel spreadsheet, and a Jupyter Notebook (IPython Notebook) which illustrates the Lotka-Volterra model for predator-prey systems.
The Lotka-Volterra equations are a pair of first-order, nonlinear, differential equations that are used routinely to describe the dynamics of biological systems in which two species interact, one as the prey and the other as the predator.
The equations are given as shown:
Where:
- x = population of prey
- y = population of predators
- t = time
- \alpha = birth rate of prey
- \gamma = death rate of predators
- \beta = interaction term between predators and prey
- \delta interaction term between prey and predators
The Lotka-Volterra model has several assumptions, which decrease the accuracy of the model when applied to real world scenarios. These include the following:
- The prey population never runs out of food.
- The predators consume only the prey.
- The rate of change of populations are proportional to their size.
- The environment does not change in favour of one species, and genetic adaptation of offspring is negligible.
- Predators have limitless appetite.