A competitive-hunter model: trout and bass
Imagine two species of fish - trout and bass - in the same body of water competing for the same limited resources. Let represent the number of trout, and represent the number of bass.
In the absence of competition, the population of each each species would increase at a rate proportional to its size. In this dynamic figure, the initial trout growth rate is set at 5% and the initial bass growth rate is set at 4%. You can change these to other reasonable rates and explore what happens.
The model for this scenario is and .
However, the two species are in competition. Each will decrease at a rate proportional to the frequency with which the two species interact, which in turn is proportional to , the product of the two populations. In the interactive figure, the model is initially set so that the trout population decreases at a rate of and the bass population decreases at a rate of .
The revised model taking into account this interaction rate is
and
Explore this model by setting parameters and then dragging the blue point in the plane that represents the initial population of trout and bass.
Developed for use with Thomas' Calculus, published by Pearson.