Precautionary fishery management requires that a distinction be made between target and limit reference points. We present a simple probability framework for deriving a target reference point for the fishing mortality rate (F) or biomass (B) from the corresponding limit reference point. Our framework is a generalization of one devised previously by Caddy and McGarvey (1996). Both methods require an a priori management decision on the allowable probability of exceeding the limit reference point; our method removes a major assumption by accounting for the uncertainty in the limit reference point. We present the theory underlying the method, an algorithm for solution, and examples of its application. The new procedure, like the old, requires an estimate of the implementation uncertainty expected in the following year's management, an estimate that might be obtained by a review of the effectiveness of past management actions. Either method can be implemented easily on a modern desktop computer. Our generalized framework is more complete, and we believe that it has wide applicability in the use of fishery reference points or, for that matter, in other conservation applications that strive for resource sustainability.
In 2011, a large multivessel survey was conducted to provide nearly synoptic sampling of Red Snapper Lutjanus campechanus throughout their reproductive season in the U.S. Gulf of Mexico. A total of 2,487 Red Snapper were caught with a female : male ratio that was approximately 1:1. The ovaries of 1,002 females were histologically examined. Females (n = 391) were found with spawning markers (postovulatory follicles and hydrated oocytes) throughout the study area, but primarily in outer shelf waters. Statistical models were developed to quantify and test the dependence of the proportion of females bearing spawning markers (spawning fraction) on female length and age, time of year, depth, gear type (vertical line or longline), or region (east or west of the Mississippi River). Most of the variance in spawning fraction was explained by the time of year; spawning fractions were generally low in spring, peaked in midsummer, and declined by fall. There was also strong statistical evidence of a positive relationship between spawning fraction and either age or length. The effects of region and gear type were not significant once time of year and size or age were accounted for. These results demonstrate the need to account for differences in the time of year and age structure of the population when the productivity of populations of Red Snapper are compared. For example, productivity has been hypothesized to be greater in the western Gulf than in the eastern Gulf, as evidenced by regional patterns of egg and larval abundance. Our results suggest that this regional difference is not due to any intrinsic difference in the biology of the fish, but simply a consequence of there being more large, old Red Snapper in the western Gulf. Recent stock assessments have indicated that Red Snapper are increasing in abundance and there is a need to continue monitoring to detect any possible compensation in reproduction.
Received November 25, 2014; accepted April 2, 2015
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