Statistical estimation of mean values of fish stock indicators from trawl surveys

Abstract

The mean or average value of a measure or indicator variable used to monitor a fish population can be defined in various ways, each with a correspondingly different statistical estimator for use in the context of a trawl survey. When, as is typical for many species, fish are heterogeneously clustered space, then scooped in clusters from restricted localities using a trawl, these different estimators can produce different sample mean values with con- trasting variations time, possibly leading to different inferences about the fish population. Two mean parameters and their intuitive estimators, the mean over fish, and the mean over stations, are discussed and found to present contrasting statistical properties. A third estimator based on fitting a mixed model is proposed which has intermediate properties based on the within-haul correlation. The three estimators are applied illustratively to length data for cod caught in the North Sea by the English groundfish survey from 1992 to 2007. The time series of the mean stations was smoothest, that for the mean fish much more variable, and the mixed mean fell between in all years. Variance estimators derived from the fitted mixed model are also put forward. Estimates made from the example suggested that the mixed mean is most efficient. The type of estimator used for the mean should always be considered carefully and mentioned when reporting indicator studies.