Harvesting Models Labs Launch Harvesting Models Lab Background Consider a population of I say , fish , with a growth rate of 18% in an environment with a carrying capacity of 50 , 000 . We take a standard simple modelof population growth , the logistic model ( see the section on population models ) . We then consider different ways of harvesting the fish , with a goal ofmaximizing the long – term yield ( that is we want to harvest the largest number of fish without driving the population to extinction ) . We will*experiment with this numerically and then analyze the situation graphically to find the optimum harvesting . It is worth noting that while we couldsolve the differential equations exactly , it will be easier to find the answer to the question of optimum harvesting from the geometric analysis withoutexplicitly solving the equation .There are two standard approaches to harvesting from a population . We can harvest a set number of individuals every time ( constant harvesting ) , orwe can harvest a set percentage of the population every time I proportional harvesting ) . The basic model of the unharvested population isP’ = 18 P (1 – P 150.0100 )where ? is the population and the derivative is taken with respect to time & . If we harvest A units of fish every unit of time , we get the constantharvesting modelP’ = 18 P (1 – P /50.000) – 17In the other model , if we harvest a fraction*E of the population every unit of time , we get the proportional harvesting modelP’ = 18 P (1 – P/50.000) – EPYou should think about how the final terms in the two harvesting models reflect the different harvesting strategies . You will be asked to explain thisin your lab reports .In real life , constant harvesting can be enforced by setting a quota on all harvesters and then counting the harvest . Proportional harvesting is often*enforced by limiting the number of days that harvesting is permitted , with the assumption that in a fixed period of time it is only possible to catch acertain percentage of the fish available . Another way to enforce proportional harvesting is to do a periodic census , and then adjusting quota values*for harvesters according to the current population figures .