Question

4) Based on the Lotka-Volterra predator-prey model, we would wxpect the number of prey to --- and the numbwr of predators to---.

5) Explain your answer for question #4 by ahowjng mathematically the conditions for predator-pret coexistence; and use your graph to explain why current abundaces od prey and predator you indicated in #4 indicate cowxistence or not

4) Based on the Lotka-Volterra predator-prey model, we would expect the number of prey to (10pts) and the number of predators to (10pts). Pisocline a. increase; increase b. increase; decrease C. decrease; increase d. decrease; stay the same Predator abundance (P) N isocline Im ba Prey abundance (N) 5) Explain your answer for question #4 by showing mathematically the conditions for predator- prey coexistence; and use your graph to explain why current abundances of prey and predator you indicated in #4 indicate coexistence or not (20pts).

I know the answer to #4 is that they both increase. I'm not sure how to do #5

Answer 1

answer

part 5: '

The Lotka–Volterra model is frequently used to describe the dynamics of ecological systems showing interaction between two species, one a predator and one its prey.The characteristic of this model is that the population change of the predator and the prey are explained in terms of each other. This model assumes that the prey consumption rate by a predator is directly proportional to the prey abundance. This means that feeding of the predator is limited only by the amount of prey in the environment. While this may be realistic at low prey densities, it is certainly an unrealistic assumption at high prey densities where predators are limited, for example, by time and digestive constraints.

• First consider the prey (N): Prey in the absence of predators:
• dN/dt = rN ,
• Where N = prey (victim) population,
• r = intrinsic rate of increase Prey in the presence of predators (P)
• dN/dt = rN - αNP ( Where αNP is the loss to predators)

Loss to predators is calculate by the product of predator and victim numbers (assuming that the predators and prey move randomly through the environment) and the capture efficiency, α which is also measure of the effect of the predator on the per capita growth rate of prey.

• Here αN also represents the functional response of the predator.
• Equilibrium N (number of prey needed to maintain a constant population of predators) = m/ba
• Number of prey needed depends on the ratio of the death rate of predators to the conversion efficiency of predators

here is the grapgh indicating coexistence :

.P abundant N scarce PEN decrease Pisocline Pan abundant pincreases N decreases - - Predator abundance (P) • Nisodline - m/ba Pscarce N scarce Nrecovers • Psearce precovers Nincrease Prey abundance (N)

hope this helps!