Effects of Size-Selective Mortality and Sampling Bias on Estimates of Growth, Mortality, Production, and Yield

Abstract

Size-selective mortality decreases or increases the actual and back-calculated lengths of an age-group, while at the same time altering the shape and variance of its length frequency distribution only slightly or not at all. An index of intensity of selection (r) can be calculated from the difference in computed length (d) between the penultimate annulus at age n and the terminal annulus at age n−1, together with the standard deviation in length (s); it is r = 1.349d/s, and represents the difference in mean instantaneous mortality rate between the two halves of the frequency distribution. Instantaneous rates of increase in weight can be computed from length data by multiplying the difference between the natural logarithms of length 1 year apart by the exponent in the weight–length relationship. When there is size-selective mortality, the difference between the rate (GX) based on observed weights in successive years differs from the true rate (G) based on the terminal length differences computed from scales. Similarly the instantaneous rate of decrease in numbers (Z) differs from the rate of loss of weight or ponderal mortality rate (ZW). It is found that G−GX = ZW−Z. "Lee's phenomenon" may be caused by selective mortality or by biassed sampling. Unlike selective mortality, biassed sampling produces only positive Lee's phenomenon (back-calculated lengths from older fish less than those calculated from younger fish), regardless of whether it is the smaller or the larger fish that are favoured by the sampling gear. The use of incorrect growth rates can lead to rather large errors in estimates of production of a stock. Errors in computation of yield, due to using numerical instead of ponderal mortality rates, tend to be much smaller.