Predicting Effort and Protected Species Bycatch Under an Effort Limit or Take Caps

Many production processes feature joint production of a desirable output with an undesirable byproduct. Producers and consumers of the desirable output mutually benefit at the expense of non-consumers, who bear external damage costs imposed by production of the undesirable byproduct. A standard approach to regulating such production activities is through the combination of a limit on allowable production effort in conjunction with a cap on the level of the undesirable output. The situation is greatly complicated when the production externality is a random function which depends on the level of production effort. In this case, capping undesirable output induces a random limit on the level of the production effort, assuming further production is prohibited once the undesirable output cap is reached. One situation which fits the above description is that of controlling protected species bycatch in commercial fisheries management. Because protected species are typically rare or endangered, and hence limited in population size and distribution, protected species bycatch is by nature a rare event, subject to random variation over time periods or areas where fishing effort occurs. A standard approach to protected species bycatch mitigation is to employ some combination of effort limit and protected species take caps within a given fishing season, in order to ensure that fishing effort ends before an unacceptably large number of protected species takes has occurred. Given the inherent randomness of protected species bycatch for a given level of fishing effort, a number of questions of interest arise in comparing alternative bycatch management regimes, including: 1. If effort reaches the regulatory limit, what is the likely range of variation in bycatch? 2. What is the likely range of effort under regulation by protected species take caps? 3. What is the effect on the allowable range of effort if take caps are simultaneously implemented for multiple protected species? 4. With multiple take caps and an overall effort limit, what are the probabilities for hitting each of the different possible caps or limit? A probabilistic framework is developed herein to address these and related questions. I use a Poisson distribution to model the probability distribution of bycatch conditional on a given level of effort. A Bayesian framework for deriving predictive distributions of bycatch conditional on fishing effort is used to obtain the stochastic effort limit for a given specified limit and take caps. The methodology is applied to observer data from the Hawaii-based longline fishery for swordfish in order to address the questions posed above.