Length-dependent fishing selectivity for trawlers fishing for the Patagonian toothfish (Dissostichus eleginoides) on the Heard Island Plateau (Division 58.5.2) was modelled as a 3-segment linear model, which has ascending lower and descending upper arms corresponding to lower and upper fishing selectivity and a plateau section in between for the length range where fish are assumed fully selected. Using random length frequency (LF) data collected from each of trawlers and longliners for fishing seasons 2003-2005 the upper arm of the gear selectivity function for trawlers is estimated using a two-stage process. In the first stage I estimate a parameter for each 40 mm wide length bin from the fit of a binomial generalised linear mixed model (GLMM) to the number of fish in the bin using a logit link function and binomial sample size defined as the number of fish in that bin or greater. I combine the data for length-bins and fit the GLMM to this combined dataset since the binomial counts are conditionally independent. A forward-calculated continuation ratio (FCR) is the probability of a fish being in a length bin compared to that of being in a greater length bin and the logit link function allows the predicted log of these ratios or odds to be obtained directly from the GLMM. The ratio of the odds for trawl to that of longliners when this odds ratio is less than one gives the trawl gear selectivity for that length bin assuming fish in this bin are fully selected by longlines. To account for different availabilities of length classes with fishing depth I simultaneously fit length bin by depth interaction terms in the GLMM. In the second stage, the upper arm of the selectivity function was obtained as a linear fit through these ratios for the subset of bins where this ratio is less than one. The fitted linear decline in selectivity begins from near 800 mm and declines from a selectivity of 1 to 0 at 1731 mm length. Adjusting for gear type, the GLMM predicts the availability of large fish increases with increasing fishing depth.
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