Alternative error distribution models for standardization of catch rates of non-target species from a pelagic longline fishery: billfish species in the Venezuelan tuna longline fishery

Alternative error distributions were evaluated for calculating indices of relative abundance for non-target species using catch and effort data from commercial fisheries. A general procedure is presented for testing the underlying assumptions of different error distributions. Catch rates, from an observer program, of billfish caught mainly as bycatch in a pelagic tuna longline fishery in the Western Central Atlantic were standardized. Although catches of billfishes are not common in pelagic tuna longline fisheries, these fisheries are one of the main sources of fishing mortality for these stocks in the central Atlantic due to the magnitude and spatial extent of longline fishing effort. Billfish CPUE data are highly skewed with a large proportion of zero observations. Delta distribution models can accommodate this type of data, and involve modeling the probability of a non-zero observation and the catch rate given that the catch is non-zero separately. Three different Delta models were compared against other error distributions, including the lognormal, log-gamma, and Poisson. Diagnostic checks and deviance table analyses were performed to identify the best error distribution and the set of factors and interactions that most adequately explained the observed variability. The results indicated that the Delta-lognormal model (a binomial error distribution for the probability of a non-zero catch and lognormal error for the positive catch rates) complied best with the underlying characteristics of the data set. Analyses of catch rates for blue marlin, white marlin and sailfish confirmed the spatio-temporal nature of their distribution in the central Atlantic and Caribbean Sea. Also, the analyses indicated that catch rates of billfish differed among fishing vessel types; larger vessels had a higher probability of catching blue marlin, the more oceanic-oriented species, and lower probabilities of catching the more coastal-oriented species white marlin and sailfish. Standardized catch rates indicated in general a lower relative abundance for blue and white marlin in the most recent years, although estimated confidence intervals overlap through the years especially for white marlin.