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