Logistic Model with Harvesting If the growth of a population follows the logistic model bu...

Logistic Model with Harvesting If the growth of a population follows the logistic model but is subject to “harvesting” (such as hunting or fishing), the model becomes

where h(t) is the rate of harvesting.

(a) Show that when the harvest rate h is constant, a maximum sustainable harvest hmax is rL/4, which occurs when the population is half the carrying capacity. HINT: Set y′ = 0 and use the quadratic formula on r(1 − y/L)y − h = 0 to find hmax.

(b) For constant h, create the phase line and a sketch of solutions. Show how the graphical information relates to the computation in (a), and tell what it implies with respect to policy decisions regarding hunting or fishing licensing. Compare with the case of no hunting.

Logistic with Harvest

Experiment with the harvesting rate, and watch out for extinction!