Stock, recruitment and moderating processes in flatfish

A difficulty that frequently arises when stock-recruitment relationships are fitted to historical data of fish populations is the high degree of variation in recruitment so that the relationship is difficult to identify with any precision. The purpose of this paper is to describe refinements that can be made to the model by incorporating information on parallel environmental factors that also affect recruitment. The identification of the stock-recruitment relationship can be made with greater precision because of the reduction in the unexplained variability. Many investigations on the effects of environmental changes on recruitment have been published in the fisheries literature. It is, however, comparatively rare for the simultaneous effects on recruitment of environmental factors and stock size to be analysed. Here we describe the formulation of an appropriate mathematical relationship to describe these effects. The framework of this formulation is F.E.J. Fry's classification of environmental factors into one of five kinds: controlling, limiting, lethal, masking and directive, following the work of Neill et al. (1994) [Neill, W.H., Miller, J.M., Van der Veer, H.W, Winemuller, K.D., 1994. Ecophysiology of marine fish recruitment: a conceptual framework for understanding interannual variability. Neth. J. Sea Res. 32, 135–152.]. An examination of some of the theory underpinning stock-recruitment relationships indicates how independent experimental evidence on the effects of environmental factors on recruitment can be incorporated into the relationship in an appropriate mathematical form. A method is described for the graphical illustration of the relationship between, on the one hand, stock and recruitment allowing for the effects of environmental factors and, on the other hand, the relationship between environmental factors and recruitment allowing for changes in stock levels. The method is based on the idea of partial residuals (or adjusted variables) derived from statistical regression methodology. The scatter of the adjusted variables around the fitted relationship is often considerably less than that of the raw data. The method is illustrated by two examples of flatfish stocks, plaice ( Pleuronectes platessa) in the North Sea and English sole ( Pleuronectes vetulus) in the Hecate Strait off the coast of British Columbia.