Question
Consider a model for the numbers ofprey x (t) and predators y (t) inacertain region at time t The model equations are: dx = k1x k2x2 k3x y, dy = dt kay (1-%) + ksry: For i = 1,2.- 8 6, match the parameter ki 2 Owith its biological interpretation below: i=1 [Choose ] Birth rate of prey Carrying capacity for predators Birth rate of predators in the absence of prey Death rate of prey due to predation Rate of increase of predators due to prey consumption Death rate of prey in the absence of predator
Consider a model for the numbers ofprey x (t) and predators y (t) inacertain region at time t The model equations are: dx = k1x k2x2 k3x y, dy = dt kay (1-%) + ksry: For i = 1,2.- 8 6, match the parameter ki 2 Owith its biological interpretation below: i=1 [Choose ] Birth rate of prey Carrying capacity for predators Birth rate of predators in the absence of prey Death rate of prey due to predation Rate of increase of predators due to prey consumption Death rate of prey in the absence of predators [Choose ] i-2 j=3 i=4 [Choose ] i=5 [Choose ] i=6 Choose
Answers
For each predator-prey system, determine which of the variables, $ x $ or $ y, $ represents the prey population and which represents the predator population. Is the growth of the prey restricted just by the predators or by other factors as well? Do the predators feed only on the prey or do they have additional food sources? Explain.
(a) $ \frac {dx}{dt} = -0.05x + 0.0001xy $
$ \frac {dy}{dt} = 0.1y - 0.005xy $
(b) $
\frac {dx}{dt} = 0.2x - 0.0002x^2 - 0.006xy $
$ \frac {dy}{dt} = -0.015y + 0.00008xy $
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