Moving Away From Delta-GLM Indices in the Safmc Sedar Process: Use of a Zero-Inflated Negative Binomial Model to Develop a Fishery-Independent Index of Gray Triggerfish Abundance

Traditionally fishery-independent indices of U.S. South Atlantic fishes were generated based on the observed catch rate (e.g. catch*hr^-1) and standardized with respect to covariates using a delta-GLM approach.  A drawback of delta-GLM models is often a poor fit to the assumed positive model error distribution because of frequent relatively small catches (<5) and constant soak time.  Here we propose basing the index on observed catch using a zero-inflated discrete error distribution with effort (soak time) as an offset term.  We evaluate this approach using fishery-independent data on catch of gray triggerfish in chevron traps (1990-2011).  Covariates included in the model were latitude, depth, bottom temperature, and season.  We also provide a method for estimating the annual index of abundance (i.e., the year effect) and associated uncertainty measures.  Diagnostic tests suggested a zero-inflated negative binomial model was superior to a delta-GLM approach for constructing a gray triggerfish abundance index.  The index suggests abundance decreased from highs in the late-1990s to near series lows in recent years.  We suggest evaluating indices based on catch data assuming discrete and possibly zero-inflated error distributions in concert with traditional delta-GLM approaches using catch rate data.  Such evaluations will avoid using models with misspecified error distributions.