Interaction Between Stock Area, Stock Abundance, and Catchability Coefficient

Abstract

The relationship between commercial catch-rates and population density upon which many stock assessment models depend assumes that stock area (A) is constant and independent of population abundance. Starting from a theoretical demonstration that the catchability coefficient (q) is inversely proportional to A, we establish the empirical basis of this relationship through comparisons of q and A of various Northwest Atlantic herring (Clupea harengus harengus) stocks and, in more detail, for Fortune Bay herring. For these stocks the relationship was of the form q = cA−b. For Atlantic herring stocks, levels of b were in excess of 0.80. In Fortune Bay herring, reductions in abundance were accompanied by proportional reductions in A, which in turn was inversely correlated with changes in q. School size, measured as catch per set, also declined as population levels declined but the change was not proportional. Published findings indicate that pelagic stocks in particular, and fish stocks in general, exhibit a common response of reductions in A with interactive increases in the q during periods of rapid population decline. We conclude that the conventional assumption of a constant stock area is usually violated due to the systematic interaction between A and population abundance which is reflected in an inverse relationship between stock abundance and q. Calibration of sequential population models should therefore be restricted to research vessel data collected in a standard manner and covering the distributional area of the stock.