So for foxes, we have.Įquations (3) and (4) together, are a system of first order differential equations called the "Lotka-Volterra" equations (or simply, predator-prey equations). Thus for the poor bunnies.įor the predators, we would expect the change in their population to be boosted in proportion to the number of encounters since they now have a food source ( ). So we would expect their population growth to be slowed in proportion to the number of encounters, expressed as. Unfortunately, for the prey that means being eaten by the predators. Obviously this is very simplistic, but what this means is the number of encounters depends on the number of either species. So let the number of encounters be the product of the number of foxes by the number of rabbits. Let's now bring predator and prey together so they start encountering or "interacting" with each other. Now, assuming there are no predators around, and they have indefinite lives, and infinite resources and space in which to thrive, the growth in the population of rabbits can be modeled by natural growth (aka exponential growth), or the equation.įor foxes, assuming they have no food supply (no prey) we would expect their population, denoted by F to naturally decline (aka exponential decay) according to the equation. Suppose we have a prey species (for example: rabbits) that serves as a food source for a predator species (for example: foxes).įirst, let the number of rabbits (i.e. So I thought we could explore this model a bit further and develop the logic behind it. A few days ago posted a fascinating article: " The mathematics behind medieval battles" and mentioned that the model is connected to the Predator-Prey equations. Let's take a peek into a more advanced area of study in the field of differential equations.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |