A nonparametric-monotone regression model and robust estimation for paired-tow bottom-trawl survey comparative fishing data

Abstract

Long survey time series tend to produce better stocks assessments; however, over a long time-period it will often be necessary to replace vessels and even survey gears as technology and the objectives of the survey evolve. In this case, survey catchability (Q) may change and comparative fishing experiments are often conducted to provide information about the relative change in Q (i.e. ρ) for the new survey protocol compared to the old one. In this paper we develop a smooth monotone nonparametric regression model for ρ as a function of fish length. Nonparametric regression approaches provide a generic advantage because they can account for a wide range of ρ behavior which is useful when analyzing the many species that are often caught in surveys. However, these models are prone to over-fitting due to sampling variability in data. A monotone nonparametric regression will be less prone to this problem and an improvement, provided the monotone assumptions are warranted. We also apply robust estimation methods to further limit the impact of outliers on estimates of ρ. This includes a simulation analysis to guide specific choices for robust estimation. We apply our methods to three flatfish species and data collected in comparative fishing experiments conducted by Fisheries and Oceans Canada in 1995. We also compare our methods with the approach of Miller (2013) to estimate change in Q. Our main conclusion is that the monotone approach fits about the same as the Miller model but the monotone approach provides more realistic extrapolations and improved precision of ρ at larger lengths that were poorly sampled.