# N

Depleted

Population size N

Figure 6.6. The acronym soup. Over the years, various reference points other than MSY (see Connections for more details) have developed. A stock is said to be in the range of optimal sustainable population (OSP) if stock size exceeds 60% of K, and to be depleted if stock size is less than 30%-36% of K.

V Effort

### Optimal effort

Figure 6.7. Steady state economic analysis of the net revenue from the fishery, which is composed of income pY(E) and cost cE. When these are equal, the bionomic equilibrium is achieved; the value of effort that maximizes revenue is that for which the slope of the line tangent to the parabola is c.

V Effort

### Optimal effort

Figure 6.7. Steady state economic analysis of the net revenue from the fishery, which is composed of income pY(E) and cost cE. When these are equal, the bionomic equilibrium is achieved; the value of effort that maximizes revenue is that for which the slope of the line tangent to the parabola is c.

model catch per unit effort (CPUE) is proportional to abundance and is thus commonly used as an indicator of abundance. This is based on the assumption that catchability is constant and that catch is proportional to abundance, neither of which need be true (see Connections) but they are useful starting points. In Figure 6.6, I summarize the variety of acronyms that we have introduced thus far, and add a new one (optimal sustainable population size, OSP).

This multi-part exercise will help you cement many of the ideas we have just discussed. We focus on two stocks, the southern Gulf of St. Laurence, for which r — 0.15 and K — 15 234 tons, and the faster growing North Sea stock for which r — 0.56 and K — 185 164 tons (the data on r come from Myers et al. (1997a) cited above; the data on K come from Myers et al. (2001)). To begin, suppose that one were developing the fishery from an unfished state; we use the discrete logistic in Eqs. 6.8 and write

where C(t) is catch. Explore the dynamics of the Gulf of St. Laurence stock for a time horizon of 50 years, assuming that N(0) — K and that (1) C(t) — MSY, or (2) C(t) — 0.25N(t). Interpret your results. Now suppose that the stock has been overfished and that N(0) — 0.2K. What is the maximum sustainable harvest Cmax associated with this overfished level? Fix the catch at 0, 0.1 Cmax, 0.2Cmax, up to 0.9Cmax and compute the recovery time of the population from N(0) — 0.2K to N(trec) > 0.6K. Make a plot of the recovery time as a function of the harvest level and try to interpret the social and institutional consequences of your plots. Repeat the calculations for the more productive North Sea stock. What conclusions do you draw? Now read the papers by Jeff Hutchings (Hutchings 2000, 2001) and think about them in the light of your work in this exercise.