Targets and Limits for Management of Fisheries: A Simple Probability-Based Approach

Abstract

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.

Sensitivity of yield-per-recruit and spawning-biomass-per-recruit models to bias and imprecision in life history parameters: an example based on life history parameters of Japanese eel (Anguilla japonica)

“…The reference points F max and F 0.1 can be regarded as boundaries in order to constrain harvesting below the level within which the fish population can produce maximum sustainable yield (United Nations, 1995), and they usually are used as limiting and precautionary indicators of growth overfishing, respectively; fishing mortality rates above F max indicate that fish are caught before they reach optimal size given the rate of natural mortality and their growth rate (Gabriel and Mace, 1999;Quinn and Deriso, 1999). Fishing mortalities at 30% and 50% of SPR, compared with SPR at F=0, are considered to be the limiting and precautionary levels for anguillid eels (ICES 1 ).…”

“…Because F cur and the F BRPs are not fixed constants, we applied composite risk analysis that allowed for the incorporation of the uncertainty in both indicator and management reference points (Prager et al, 2003;Jiao et al, 2005). By the discrete approach proposed by Jiao et al (2005), the composite risks were calculated as the expected probability of one random variable being larger than another.…”

“…In addition, the uncertainty (or multiplicative error) in the growth curve (ε GR ) is related to the imprecision in the lengths-at-age scatter at a given age. The current fishing mortality rate (F cur ) can be estimated from various methods (e.g., Seber, 1982;Quinn and Deriso, 1999; King, 2007) with both the mean and variance of high uncertainty (Chen and Wilson, 2002).It is essential to incorporate and quantify these uncertainties in the assessment of population dynamics (Hilborn and Walters, 1992;Peterman, 2004). Further, parameter uncertainties can be categorized into bias uncertainty and precision uncertainty.…”

“…Yield-per-recruit (YPR) and spawning-biomass-per-recruit (SPR) models, in which the total yield or spawning biomass of a cohort is standardized for the numbers of recruits, are commonly used in fisheries assessment (Beverton and Holt, 1957;Quinn and Deriso, 1999). They can be used to infer the total yield and spawning biomass of an entire population composed of different cohorts with an assumption of a steady state and with knowledge of equilibrium recruitment (King, 2007).…”

“…In addition, the uncertainty (or multiplicative error) in the growth curve (ε GR ) is related to the imprecision in the lengths-at-age scatter at a given age. The current fishing mortality rate (F cur ) can be estimated from various methods (e.g., Seber, 1982;Quinn and Deriso, 1999;King, 2007) with both the mean and variance of high uncertainty (Chen and Wilson, 2002).…”