(Adapted from Crawley, 1997) Denote plant biomass by V, and herbivore number by N. The plant–herbivore interaction is modeled as:
dV/dt = aV(1 - V/K) - bVN
dN/dt = cVN - dN
(a) Suppose the herbivore number is equal to 0. What differential equation describes the dynamics of the plant biomass? Can you explain the resulting equation? Determine the plant biomass equilibrium in the absence of herbivores.
(b) Now assume that herbivores are present. Describe the effect of herbivores on plant biomass; that is, explain the term −bVN in the first equation. Describe the dynamics of the herbivores—that is, how their population size increases and what contributes to decreases in their population size.
(c) Determine the equilibria (1) by solving dV/dt = 0 and dN/dt = 0 and (2) graphically. Explain why this model implies that "plant abundance is determined solely by attributes of the herbivore," as stated in Crawley (1997).