FISHERY BULLETIN VOL. 72. NO. 1 



These two curves are plotted in Figure !.'■♦ 

 Their intersection at (X*, K*) denotes bio- 

 economic equilibrium. The direction of the 

 arrows describes the qualitative dynamic 

 changes of a point in ])hase space. Figure 1 rep- 

 resents the general case of exploitation. When 

 (15) is combined with (14), however, we can 

 simulate either nonexploitation (Figure 2) or 

 extinction as a possible dynamic result (Figure 

 3).'-'' The state of the fishery — exploited, unex- 

 ploited, or extinct — depends upon the para- 

 meters a. b, r, /3, TT, and a and their interrela- 

 tionships. This completes our general model of 

 how a fishery functions. Now let us turn to a 

 specific application of the model. 



AN EMPIRICAL CASE STUDY: 



THE U.S. INSHORE 

 AMERICAN LOBSTER EISHERY 



The U.S. inshore American lobster fishery — 

 principally located off the coast of Maine — 

 represents a good case study for a number of 

 reasons. First, the American lobster is consid- 

 ered a high quality seafood item and is a popu- 

 larly consumed species for which demand has 

 been increasing rapidly (Bell, 1972). Second, be- 

 cause of intensive fishing pressure, the resource 



''• In steady state, the reader should be aware that we 

 have not constrained the population stock to its initial 

 size or any other size. Using the Schaefer model (i.e., 

 steady state), the stock size varies inversely with fishing 

 effort, T. Even in a dynamic context, the biomass would 

 asymptotically approach the steady -state solution. 



'■' It should be pointed out that Schaefer (1954) discuss- 

 es economic transitional states which are very similar 

 to the bioeconomic model presented in this paper. He 

 states: 



"To arrive at a particular function to describe the 

 change of the intensity of fishing with the size of the 

 population, we may consider that the incentive for new 

 investment is proportional to the return to be expected, 

 in which case there will be a linear relation between 

 the percentage rate of change of fishing intensity and 

 the difference between the level of fish population and 

 its economically critical level, b. This function will, 

 then, be 



dF 



where k-^is a constant." 



b) 



(11) 



has shown signs of overexploitation."' Third, the 

 inshore lobster fishery is one of the few grounds 

 for which enough data are available so that 

 some rough measures of needed biological and 

 economic ])arameters can be derived. Fourth, 

 according to Dow (1961),'^ the inshore lobster 

 fishery is a relatively closed population as our 

 production model assumes. Last, we believe 

 that over the long run the American lobster 

 population has not had a great divergence 

 from the steady-state model employed in our 

 analysis. The gross divergence from the 

 steady-state assumption is significant only 

 when fishing effort changes dramatically from 

 period to period. For modest changes in fishing 

 effort, the steady-state assumption will not 

 yield biased estimates. A check on the fishing 

 effort series for the American inshore northern 

 lobster fishery reveals a steady and gradual 

 increase. The alternative methods of Pella and 

 Tomlinson (1969) do yield biased parameters 

 due to nonlinear fitting methods. Gulland's 

 (1961) method yields bia.sed parameters since 

 effort is averaged and then used as an indepen- 

 dent variable. Therefore effort in period t is not 

 indei)endent of effort in period t -\- 1 which 

 violates classical statistical assumptions under- 

 lying least squares. Also the predictive value 

 (using the steady- state assumption) or goodness 

 of fit is certainly at an acceptable level, R"^ = 

 0.962 (infra). Our discussion will be subdivided 

 on the basis of production-related and demand- 

 related estimates. 



The Production Eunction and 

 the Supply of American Lobsters 



There are four parameters on the supply side 

 for which initial estimates are required: a, b, r. 



His process of transitional states is implicit in our dia- 

 grams in Figure 3 since adjustment (i.e., transitional 

 states) will occur anywhere in phase space to the equilibri- 

 um values where X = and K = 0. 



"* U.S. landings of trap-caught American lobsters in- 

 creased from approximately 23 million pounds in 1950 

 to a peak of over 29 million pounds by 1957. Since 1957 

 landings have fallen off, reaching a low of 22 million 

 pounds in 1967. In 1969 lobster production had recovered 

 to 26.9 million pounds. Despite the poor performance 

 of production over the 1950-69 period, the number of 

 lobster traps fished per year (i.e., a proxy for fishing 

 effort) has increased secularly from approximately 579,000 

 in 1950 to over 1,060,000 in 1969. Because of these past 

 events, several bills have been presented in the Maine 

 Legislature to apply some sort of stringent licensing 

 scheme to limit entry. 



'^ Dow, R. 1971. Effort, environment, supply, and yield 

 in the Maine lobster fishery. Unpublished manuscript sub- 

 mitted to the U.S. Fish and Wildlife Service, Washington, 

 D.C. 125 p. (May be obtained from Sea and Shore Fish- 

 eries, Maine.) 



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