Abstract
Catch-rate data are traditionally used to index abundance in fishery science. An objective of this research was to evaluate the bias in the assumption of linear proportionality between the catch-rate, characterized as the number of fish hooked per 100 hours trolling (HPUE), and the abundance, for the U. S. recreational billfish fishery. To investigate the relationship between HPUE and abundance a mathematical model of the general fishing process was first developed. Then the modular BLLSIM (BiLLfish SIMulation) model was constructed, using the northeastern Gulf of Mexico as the study area. Starting with a fixed initial abundance, both the boat and the fish would move throughout the spatial grid as the fishing day progressed. Spatial data were defined for three possible scenarios that represented the environmental quality (EQ). Fish movement was accomplished by the MOVEFISH algorithm which used the Circular-Normal distribution with the concentration parameter serving as a proxy for the EQ gradient. Hence, fish had a statistically induced preference to continue to move in the direction of higher EQ. The stochastic model dynamics of BLLSIM allowed for the determination of whether a fish and boat were in proximity, then if a fish in that proximity was raised to the bait, and then if a raised fish was hooked. Simulations were repeated at varying levels of abundance, and the functional relationship between HPUE and abundance was derived using nonlinear regression techniques. Results were found to be similar to those of the mathematical model. Relationships were significantly nonlinear and could be conservatively estimated with HPUE being proportional to the square-root of abundance. The bias in the assumption of proportionality was tabulated in terms of estimated percentage decrease in abundance for a given decrease in HPUE. Statistical power was estimated via a Monte Carlo simulation routine, ESTPOWER. This generated the probability of detecting various decreases in abundance at different relative levels of HPUE. Results indicate strong ramifications to this fishery because, for example, at acute low levels of HPUE a 20% decrease in HPUE indicates an approximate 34% decrease in abundance with a probability of being detected of 49%.