Suppose that in the absence of foxes, a rabbit population increases by 15% per year; in the absence of rabbits, a fox population decreases by 25% per year; and in equilibrium, there are 1,000 foxes and 8,000 rabbits.
(a) Explain why the Volterra-Lotka equations are
dR/dt = 0.15R - 0.00015RF
dF/dt = -0.25F + 0.00003125RF
(b) Suppose we introduce an element of "harvesting," detrimental to the rate of growth of both prey and predator, so that the equations are modified as follows:
dR/dt = 0.15R - 0.00015RF - 0.1R
dF/dt = -0.25F + 0.00003125RF - 0.1F
Determine which population is most affected by this harvesting strategy. by calculating the new equilibrium point.