Survey estimates of king crab (Paralithodes camtschaticus) abundance off Northern Norway using GLMs within a mixed generalized gamma-binomial model and Bayesian inference

A trawl survey provides information on number and biomass of introduced king crab ( Paralithodes camtschaticus) to the management of a fishery off the coast of Northern Norway; the annual catch quotas are largely set as a percentage of the survey estimate. A specially built sledge trawl was designed for the survey. It needs only small areas of trawlable bottom, performs well on a wide range of bottoms, and appears to have good catchability for benthic organisms. Many survey hauls catch no crabs and the non-zero catches have a highly skewed distribution. Data were therefore analysed with a compound model, in which separate predictors were fitted for the proportion of zero catches and for the catch size of the non-zero catches. The compound model was fitted by Bayesian methods using WinBUGS. The distribution of non-zero catches fitted well to a generalized gamma distribution, but with parameter values that made it approximate a lognormal distribution. Numbers of fishable crabs peaked in 2003, and total numbers in 2010 were about two-fifths of the 2003 maximum.