The following formula (Abramowitz and Stegun, 1970, equation 26.2.23) provides a closed-form approximation solution, accurate for four significant digits, for FNOW:
and c0 = 2.515517, c1 = 0.802853, c2 = 0.010328, dt = 1.432788, d2 = 0.189269, and d3 = 0.001308
This paper summarizes the recent development and use of reference points for fisheries management and their current contribution to precautionary fisheries management. Reference points are only relevant in the management context if they are incorporated into harvest control laws which form the basis for management action. They need to be reconciled through discussion and negotiation among managers, fishers and the fishing industry, since the risk that a particular fishing strategy will be precautionary depends on the overall performance of the fishery as a system and not just on the precision of the reference point. Reference points are only one component of a precautionary management system; precisely formulated reference points as part of a fisheries control law will be ineffectual in the absence of industry's agreement to act when the limit reference points are approached or exceeded or in the absence of prompt and effective surveillance to detect infringements. The review looks mainly at reference points that could be of particular use for developing countries' fisheries and shellfish resources or for oceanic resources such as tuna, where conventional approaches used in north-boreal shelf fisheries may not be applicable because of lack of data on age structure and recruitment. Consideration of the use of multiple reference points based on different criteria is suggested. Where data is scarce, precaution is even more necessary, but reference points may have to be partly empirical. Emphasis is placed on describing a number of options to be explored further through simulation and later through practical trials. Attention is given to different ways in which reference points could be combined in control laws within a fisheries management system.