Punt: Managing West Coast groundfish resources through simulations 



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Table 3 



The performance statistics used in the present study. For consistency with the definition of recovery used by the Pacific Fishery 

 Management Council, "recovery by year x" is defined as the spawning output being larger than OABq at or before year x. Some of 

 the statistics are based on the "actual" (i.e. operating model) spawning output and others are based on the "assessed" (i.e. assess- 

 ment model) spawning output. 



Abbreviation 



rec 

 °decl 



5%D/50%D 



AAV 



Description 



The fraction of the simulations in which the stock is assessed to be overfished at the start of the first 

 projection year that actually recover by the maximum possible recovery year determined from the 

 rebuilding analysis conducted in projection year 1. 



The median year in which the actual spawning output first reaches QABg. 



The proportion of simulations in which the spawning output is assessed to be below 0.25Bq (i.e. overfished) 



at the start of projection year 1. 



The lower 5th and median of the distribution of the actual spawning output in projection years 20 and 60 



expressed in relation to the actual pre-exploitation spawning output, Bq. 



Average annual absolute change in catch evaluated after 20 and 60 years, i.e. 



where C^ is the catch during yeary. 



Average annual catch over projection years 1-20 and 1-60. 



The fraction of simulations in which actual spawning output reached 0.4Bo sometime between projections 



years 1 and 20 and between projection years 1 and 60 (but may have dropped below 0.4Sq again). 



being conducted and their being used for management 

 purposes. 



The performance statistics 



A variety of performance statistics are considered (Table 3). 

 These consider both the performance of the management 

 procedure in terms of the behavior of the rules used for 

 management (statistics F^^^, Y^^^, and P^g^^) and of satis- 

 fying the goals established by the SFA in relation to the 

 status of the population and the fishery (statistics 5%D, 

 50%D, C, AAV, and P^J. The choice of years 20 and 60 

 in the definitions of the latter five statistics is meant to 

 capture "short"-term and medium-term considerations. For 

 instance, recovery should have occurred by year 60 in most 

 cases and the population should be well above 0.25Bq after 

 20 years. The catch and catch variability statistics for the 

 first 20 years provide an indication of the likely impacts of 

 recovery on the industry. 



The need to examine aspects of the behavior of the man- 

 agement rules can be understood from Figure 3, which 

 shows results for four simulations for the combination of 

 a PFMC management procedure and an operating model 

 variant. The solid lines are the "true" time-trajectories of 

 spawning output (expressed in relation to the pre-exploi- 

 tation level) and the dotted lines reflect the estimates of 

 this ratio each time an assessment is conducted (every 

 third year for the analyses shown in Fig. 3). The up ar- 

 rows indicate when the assessment first indicates that the 

 population is overfished (based on the model estimates of 

 spawning output) — note that a population may be identi- 

 fied to be overfished more than once during a given simula- 



tion. The down arrows indicate the years in which recovery 

 is predicted by the rebuilding analysis software (with the 

 estimates from the assessment) to occur with 60% probabil- 

 ity. The solid bar parallel to the j:-axis indicates the years in 

 which management is based on the rebuilding plan (rather 

 than the 40-10 rule). The bar will stretch from the up ar- 

 row to the down arrow unless the population is assessed 

 to have recovered to 0.4Bq (when management reverts to 

 being based on the 40-10 rule). 



There are several possible impacts of the difference 

 between the perceived and true state of the system. For 

 example, the population can erroneously be assessed not 

 to be overfished in the first projection year (e.g. simulation 

 1 in Fig. 3). The statistic Pj^^, is designed to capture the 

 frequency of this possibility. Even if the population is as- 

 sessed to be overfished, there is no guarantee that it will 

 recover with the expected probability and in the "correct" 

 year. For example, for simulation 1, the stock assessment 

 indicates that recovery occurs in year 71 (the solid bar con- 

 sequently stops in year 71) even though the true population 

 size is less than 30% of fig at that time. The statistic F^^^ 

 attempts to capture whether the rebuilding analysis per- 

 forms as expected given that the population is assessed to 

 be overfished at the start of the first projection year. 



There are other aspects to evaluating the behavior of the 

 management rules in relation to the perceived and true 

 state of the system (e.g. the difference between the true 

 and estimated biomasses and recruitments). Although it 

 is straightforward to evaluate these aspects (e.g. Patter- 

 son and Kirkwood, 1995; Punt et al., 2002), they are not 

 considered in detail in this paper to reduce the volume of 

 results presented. 



