Assessing mortality changes from size-frequency curves

The relationship between the instantaneous mortality rate (Z) and the instantaneous change in length-frequency distribution of organisms per unit of animal size (μ_L) takes the following form: Z = μ_Lk(L∞ - L) + k, where k and L∞ are coefficients of the von Bertalanffy equation, and L is organism size (length). Z and μ_L change coherently when they are measured for a specific size or age class. Therefore, observations of μ_L can provide information on the relative changes in mortality. This is useful when no precise information about animal growth is available and growth curve is assumed to be invariable. This method was tested on a heavily exploited population of St Peter's fish (mango tilapia) Sarotherodon galilaeus in Lake Kinneret, Israel, where large fluctuations in the size structure of the catch have occurred over the past few years. Analysis of the changes in the length-frequency distributions showed that the changes in μ_L over multiple years estimated for fully exploited fish reflected the respective changes in Z.