FOX: FITTING THE GENERALIZED STOCK PRODUCTION MODEL 



requires six points, while the equihbrium ap- 

 proximation approach with four significant year 

 classes will require, in general, seven points. 

 With a large number of significant year classes 

 in the fishable population or a relatively high age 

 at first capture, however, the major concern for 

 either approach is the likelihood of failure of 

 the transition state population assumptions. 

 The results summarized in Table 7 illustrate a 

 general shortcoming in simultaneously estimat- 

 ing a large number of parameters, i.e. large devia- 

 tions from model can be statistically reduced in a 

 least-squares estimation procedure at the expense 

 of the accuracy of certain "desired" parameters. 

 The transition prediction approach, fitting a 

 "free-form" type of curve with five parameters, is 

 relatively more susceptible than the equilibrium 

 approximation approach which fits a monotoni- 

 cally decreasing curve with only three parame- 

 ters. On the other hand, estimates from the 

 equilibrium approximation approach can be very 

 sensitive to the placement of one data point in 

 certain cases (e.g., a data point at an intermediate 

 level of fishing with clusters of points at both low 

 and high levels of fishing). 



Utilizing the production model approach for as- 

 sessing the effects of exploitation presents 

 significant problems in addition to choice of the 

 parameter estimation procedure or the length of 

 the data series. These additional problems are 1) 

 maintaining a constant catchability coefficient 

 throughout the data series, 2) assessing the effects 

 of changes in the constitution of the fishery, and 3) 

 assessing the effects of time lags in population 

 production processes. 



The basic components of the overall effective 

 catchability coefficient are 1) the relative ef- 

 ficiency of various types and classes of fishing gear 

 and 2) the manner in which the gear is employed 

 relative to the availability and vulnerability of 

 the population, and its subunits, to capture. 

 Heterogeneity in the efficiency of various gear 

 classes, or vessels, within a fishing season can be 

 alleviated by adjusting for their estimated rela- 

 tive fishing powers — currently the best method for 

 estimating fishing power is by analysis of variance 

 with the computer program FPOW (Berude and 

 Abramson 1972). The major problem remaining, 

 however, is adjusting for among-year changes in 

 efficiency of the standard gear. Rothschild (1970) 

 discussed and provided examples of problems as- 

 sociated with changes in the catchability 



coefficient related to areal deployment of the 

 fishing gear. The expansion of fishing across a 

 gradient of population density will increase or de- 

 crease the effective catchability coefficient de- 

 pending on the direction of the density gradient 

 and fishing expansion. Year-to-year shifts in the 

 population location and density relative to the 

 fishing effort deployment also could likewise 

 create trends in the catchability coefficient. 

 Age-specific differences in the catchability would 

 cause shifting of the overall effective catchability 

 coefficient with changes in fishing effort. For ex- 

 ample, if the catchability offish declined with age, 

 then the overall effective catchability of the 

 fishable population would increase with increas- 

 ing fishing effort since the relative proportion of 

 younger age groups would most likely increase. 



Alterations in the constitution of the fishery 

 probably are the most difficult problems to over- 

 come satisfactorily. Expansion of the fishery 

 across several stocks, either independent or with 

 some mixing, can result in rather large shifts in 

 the productivity estimates (Joseph 1970; Inter- 

 American Tropical Tuna Commission 1972). 

 Changes in the relative levels of fishing effort 

 exerted by different gear types which exploit dif- 

 ferent age groups of the population, either volun- 

 tarily or through a change in minimum size limit 

 regulations, can similarly have significant impact 

 on the shape of the production model curve (Le- 

 narz et al. 1974). The latter problem identifies a 

 major shortcoming of the production model ap- 

 proach; i.e., the impact on total yield by altering 

 the selectivity of fishing gear can not be assessed a 

 priori without considerable additional informa- 

 tion. 



The effects of time lags in population production 

 processes (e.g., reproduction, growth, and mortal- 

 ity, both density-independent and density- 

 dependent) can result in either overestimation or 

 underestimation of the population productivity, or 

 in population cycling which may never result in 

 reaching an equilibrium state (Wangersky and 

 Cunningham 1957; Walter 1973). 



In summary, both the equilibrium approxima- 

 tion and the transition prediction fitting methods 

 are useful, one or the other more so under condi- 

 tions outlined above. Application of the produc- 

 tion model to catch and fishing effort data is rela- 

 tively simple, the primary virtue of the approach. 

 The interpretation of the results and the formula- 

 tion of advice for managing the resource, however, 

 can be extraordinarily complicated by a variety of 



35 



