Predator-Prey modeling

1. Predator-Prey modeling • Learning about...

2. What Predator-Prey is a model system that seeks a dynamic equilibrium between two interacting populations. Why Most real systems are complex with sub-populations affecting each other. Economic theory is based upon these interactions, and accounting for these influences can improve the probability of successful statistical predictions. How Fundamental supply and demand factors are used to model future variations in population sizes.

3. population Consider a barn overrun by mice. Two cats move in. With so much prey, the cats breed and eat mice faster than the mice can replace themselves. With less food, the cats begin to starve and die, easing the pressure on the mice, whose population begin to recover. Over time, the two populations stabilise; the cats are not so numerous as to overhunt, and the mice can replace themselves at the same rate that they are preyed upon. Fundamental supply and demand factors are used to model future variations in population sizes.

4. dX/dt = aX - bXY dY/dt = cbXY - dY • The equilibrium is dynamic and complex for most situations. • To simplify the model, we must assume: • the system is closed; • there are no external factors - only the interaction of the two populations is considered. • there is no competition for food - the prey is vegetarian and the predators eat only the prey. The classic Predator-Prey model is summarised as a pair of equations: so, what does it mean?

5. dX/dt = aX - bXY dY/dt = cbXY - dY • where: X = size of the prey population Y = size of the predator population; a = number of offspring per prey per year; b = proportion of the prey population consumed by one predator per year c = conversion of one prey consumed into new predators; d = proportion of predator population dying per year