Mandging a sustainable fishery. We are interested in the economics of a commerci

Question

Mandging a sustainable fishery. We are interested in the economics of a commercial fishery. To model the fish population in ocean region under our regulation we are assume that the "logistic equation" holds. That is, if N(t) denotes the total fish population of the commercially-fished species that we are concerned about, then it will evolve according to the differential equation dN/dt = rN(1 - N/K) - qN, where r is the natural reproduction rate of the species (without competition), and K is the carrying capacity of the fishery. The extra term. - qN, is included to take account of the fishing itself, and qN equals the rate at which fish are drawn from the existing population N per unit time. Thus, q is interpreted as the "fishing effort" coefficient, and it has the units of (time)^-1; in other words, q is the fraction of the fish population that is harvested per unit time. Given r,q, K, find the equilibrium states, N*, of this simple model, and determine the stability (or instability) of each equilibrium. For fixed r and K, consider small q and large q and discuss the essential distinction between these cases. Moreover, identify the critical value, q_cr, at which the behavior for small q changes to the behavior for large q; that is, for q q_cr there is no equilibrium and the population N(t) is eventually depleted (goes to zero) due to overfishing. For q

Explanation / Answer

http://www.fao.org/docrep/009/a0212e/A0212E14.htm

There are four population parameters. However, under the stable equilibrium point the dominant eigenvalue of the population matrix is 1. Therefore, the number of free population parameters is three under the equilibrium point without fishing mortality, and consequently the fertility rate at the equilibrium point was chosen to be varied as a function ofm, s and p.

Further kindly refer:

http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0034556

Related Questions

Navigate

• Browse (All)
• Browse M
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.