Size, growth, temperature and the natural mortality of marine fish Henrik Gislason 1 , Niels Daan 2 , Jake C Rice 3 & John G Pope 4 1 National Institute of Aquatic Resources, Technical University of Denmark, Charlottenlund Slot, DK-2920 Charlottenlund, Denmark; 2 Institute for Marine Resources and Ecosystem Studies, PO Box 68, 1970 AB IJmuiden, The Netherlands; 3 DFO Science Advisory Secretariat, Department of Fisheries and Oceans, 200 Kent Street, Ottawa, ON, Canada K1A 0E6; 4 Norwegian College of Fishery Science, University of Tromsø, N-9000 Tromsø, Norway Introduction 150 Materials and methods 150 Results 152 Discussion 153 Acknowledgements 157 References 157 Supporting Information 158 Abstract The natural mortality of exploited fish populations is often assumed to be a species- specific constant independent of body size. This assumption has important implica- tions 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, L ¥ (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, L ¥ and K, but not to temperature (R 2 = 0.62, P < 0.0001, n = 168). Temperature and K are signif- icantly correlated and when K is removed from the model the temperature term becomes significant, but the resulting model explains less of the total variance (R 2 = 0.42, P < 0.0001, n = 168). The relationships between M, L, L ¥ , 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(L ¥ ) + ln(K), for estimating the natural mortality of marine and brackish water fish. Keywords Asymptotic length, fish, growth, length, natural mortality, temperature Correspondence: Henrik Gislason, National Institute of Aquatic Resources, Technical University of Denmark, Charlot- tenlund Slot, DK-2920 Charlottenlund, Denmark Tel.: +45 33963361 Fax: +45 33963333 E-mail: hg@aqua. dtu.dk Received 13 Feb 2009 Accepted 7 Dec 2009 F I S H and F I S H E R I E S , 2010, 11, 149–158 Ó 2010 Blackwell Publishing Ltd DOI: 10.1111/j.1467-2979.2009.00350.x 149