Prager: A nonequilibrium surplus-production model 



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Figure 3 



Estimated trajectories of relative biomass and relative fishing mortality rate from two production model 

 analyses (including proposed yields from 1992 through 1996) loosely based on swordfish, Xiphias gladius, in 

 the North Atlantic Ocean. These analyses are illustrative and are not intended as an assessment of sword- 

 fish. "Relative biomass" is the stock biomass divided by B MS y the biomass at which maximum sustainable 

 yield (MSY) can be obtained; "relative fishing mortality rate" is the fishing mortality rate (F) divided by the 

 rate (-P^jgy) that yields MSY when the stock is at S MSY - Production models estimate these relative quantities 



more precisely than the corresponding absolute quantities. Trajectories ( ) are shown with approximate 



80% confidence intervals (— ) from the bootstrap. Model 2 differs from Model 1 in being tuned to a hypotheti- 

 cal index of abundance. Panels (A) and (B), estimates from Model 1; (C) and (D), estimates from Model 2. 



cise, but because they are correlated, the correspond- 

 ing estimates of MSY and optimum effort can none- 

 theless be quite precise. 



The estimate of B p the starting biomass in the first 

 year, is usually quite imprecise even when normal- 

 ized to S MSY . It is also my impression that it can be 

 biased for some data sets, although this does not sig- 

 nificantly affect relative biomass estimates beyond 

 the first few years. I would therefore not recommend 

 using a production model to draw any inferences 

 about the population biomass during the first few 

 (perhaps 2 to 4) years, unless auxiliary information 

 is available. Such information might comprise a bio- 

 mass index (for tuning) or knowledge to support us- 



ing an assumption of the type B 1 = sK, where s is a 

 proportionality constant known a priori. Punt, 1990, 

 provides an example. This indeterminacy in produc- 

 tion modeling is similar to the inability of sequential 

 population (age-structured) analyses to say much about 

 population dynamics in the most recent years unless 

 auxiliary information is used. In practice, it does not 

 seem to degrade the estimates of MSY and optimum 

 effort when a reasonably long time series is used. 



Validity of bias corrections and 

 confidence intervals 



Bootstrap confidence intervals are approximations, 

 and bias-correction methods can at times worsen the 



