Size, growth, temperature and the natural mortality of marine fish

The natural mortality of exploited fish populations is often assumed to be a species-specific constant independent of body size. This assumption has important implications for size-based fish population models and for predicting the outcome of size-dependent fisheries management measures such as mesh-size regulations. To test the assumption, we critically review the empirical estimates of the natural mortality, M (year-1), of marine and brackish water fish stocks and model them as a function of von Bertalanffy growth parameters, L8 (cm) and K (year-1), temperature (Kelvin) and length, L (cm). Using the Arrhenius equation to describe the relationship between M and temperature, we find M to be significantly related to length, L8 and K, but not to temperature (R2 = 0.62, P <0.0001, n = 168). Temperature and K are significantly correlated and when K is removed from the model the temperature term becomes significant, but the resulting model explains less of the total variance (R2 = 0.42, P <0.0001, n = 168). The relationships between M, L, L8, K and temperature are shown to be in general accordance with previous theoretical and empirical investigations. We conclude that natural mortality is significantly related to length and growth characteristics and recommend to use the empirical formula: ln(M) = 0.55 - 1.61ln(L) + 1.44ln(L8) + ln(K), for estimating the natural mortality of marine and brackish water fish.