Question

1. Suppose the graph below represents the population of minke whales where is the stock of whale population at time t, and F(X) is the net biological growth (births - natural death) in the population. (For those of you that are mathematically curious, the general logistic growth function is represent by a function of the form: F(X.) = gx:(1-)) Growth in Whale Populatuin (F(Xt)) o a. Minke Whale Population (tons) On the graph above mark the point that represents the carrying capacity of the marine system and label it K. Is K a stable equilibrium? Why or why not? (8 pts) b. Mark the point that represents the minimum viable population and label it K. Is Ka stable equilibrium? Why or why not? (8 pts) c. Define Maximum Sustainable Yield (MSY). Mark the point that represents the stock level that will enable maximum sustainable harvest of whales and label it XMSY (4 pts)

Answer 1

Consider the diagram below -

Growth in sy F G C Xm) GX) Resowe stock k XMSY xi csºseanneclith-GamScanne k

a.)

K represents the carrying capacity of the marine ecosystem. This is a stable equilibrium, because if the stock of whales reduces below this point, then inmigration and birth will be more than outmigration and death and hence the stock will be restablished, and if the stock of population increases above this point, then inmigration and birth will be less than outmigration and death and, the stock will be restablished

b.)

K_ is the minimum viable population, which is the minimum required to maintain the whale species and prevent it from extinction. This is an unstable equilibrium. Below this level, the whale species would not come back to a stable equilibium, it will perish and become extinct.

c.)

Maximum sustainable yeild is the point on the growth curve where the growth is the maximum. At this point, if the harvested amount is the same as the MSY, then the stock will regenerate and we will be able to harvest the same amount again, i.e., equal to MSY, after such a time as is required for regeneration of the species.