The testing and selection of recruitment distributions for North Atlantic fish stocks

Abstract The lognormal recruitment model has been widely applied as a description of the recruitment phenomenon. Despite its widespread use, recent work has suggested that a variety of distributional shapes might be expected to be descriptive of the available recruitment data. This paper applies randomization and goodness-of-fit tests to a hundred previously published North Atlantic fish stock recruitment data series as a means of establishing the suitability of the exponential, lognormal and Weibull distributions as descriptions of recruitment data. Randomization tests are required to establish the independence of data observations and act as a screening device for goodness-of-fit tests. Results of the testing procedure confirm that a variety of distribution models are often statistically adequate descriptions of the available recruitment data series. The Weibull model, however, best describes the largest number of data sets. The lognormal model best describes the remaining data sets and the exponential model is a poor description of the recruitment data. There were no patterns in the statistical suitability of any of the recruitment models on either a stock or species basis. No broad geographic patterns within the serially correlated data sets were found, however, the proportion of stocks displaying serial correlation was influenced by freshwater discharges or ocean current mixing. The results imply that recruitment should be viewed as a stock-specific attribute linked to life-history and environmental influences. Furthermore, managers should be made aware of the errors resulting from the inappropriate use of the lognormal recruitment assumption and the possible implications it might have on the development and implementation of fisheries management and exploitation policies.