Statistical inference about fish abundance, an approach based on research survey data

Abstract

Trawl research surveys for groundfish populations provide an important source of information for estimating the size of the population. The surveys usually provide an estimate of the size of a component of the population, called trawlable abundance. In this thesis we consider how to efficiently estimate trawlable abundance, and how to construct precise confidence intervals for this quantity. The mobility of the population and other aspects of the survey design motivate us to pursue a model-based approach for inferences. Another advantage of the model-based approach is the relative ease in which scientific knowledge can be incorporated into inferences. We demonstrate that this can have important consequences on the precision of inferences.

We propose a mixture-model approach for the analysis of trawl survey data. With such data it is common that extremely large catches occasionally occur. While most catches vary smoothly in terms of spatial location and depth, these large catches are quite different. In some years large catches do not occur, but it still seems likely that the dense fish aggregations that produce these catches exist. These aggregations are not sampled simply due to the small probability of sampling a very dense aggregation. Simple habitat-selection theory suggests that it is reasonable to expect different trends in abundance at favorable and less favorable locations. This is because animals tend to move to more favorable sites as space becomes available. This is the basis for our mixture-model. We use a smooth mean-function model for most trawl catches (type I's) in terms of spatial location and tow depth. For the rare large catches (type II's) we use a simple constant mean model, where the mean of the large catches is constant over time. The mixture-model combines the models for type I and type II catches. Habitat-selection is accommodated because the mean for type II catches can remain high while the mean for type I catches declines. We apply these methods to trawl research survey data for cod on the Southern Grand bank of Newfoundland.

We used a variety of graphical procedures for model building purposes. They suggest a nonparametric approach for modelling type I catches is useful. The approach we take is local likelihood estimation. A concern in model building is which covariates to include. We propose a nonparametric variable selection procedure for this purpose. We do not know exactly which catches are type II a priori, so robustness is an issue. For this we develop a robust nonparametric Negative Binomial smoother, to identify type II catches and for "robustified" variable selection. The Negative Binomial distribution is the stochastic model we use for trawl catches. We show that the mixture-model is an improvement over the model commonly used to analyze trawl survey data. We suggest approximate pivotal methods for confidence intervals for total type I and type II abundance, and use the profile likelihood to compute confidence intervals for total type I + type II abundance.

Our estimates show less interannual variation than traditional methods for estimating abundance. We feel the mixture model estimates are more consistent with the survey data. Our confidence intervals are also considerably shorter in some years than those based on +2x the design-based standard errors.