NOTE Hewitt and Hoenig: Estimating natural mortality from longevity 



435 



0) LU 



Absolute 



Percent 



i  i  i  : F^= 



1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 96 100 

 max 



Figure 2 



The absolute and percent difference between estimates of M from the 

 regression estimator (RE) and 3/i mM (3M). 



tation on the work of Alagaraja (1984), who provided 

 the mathematics of a method that Sekharan (1975) 

 used without description. Interestingly, Shepherd and 

 Breen (1992) rearranged Equation 3 to obtain the rule of 

 thumb based on the results of Hoenig (1983). This latter 

 presentation is provided in Quinn and Deriso (1999). In 

 all of these cases, the proportion of animals surviving 

 to £ max is assumed to be some arbitrarily small value, 

 typically 1% or 5%. 



The development and use of the specific form 3/t max 

 in blue crab work occurred altogether separately. Its 

 use began with an assessment for the Chesapeake Bay 

 stock, in which Rugolo et al. (1998) used an estimate 

 of M based on "the ICES [International Council for the 

 Exploration of the Sea] convention; that is, 5% survivor- 

 ship at maximum age following negative exponential de- 

 pletion." The approach is more explicitly denned in their 

 original document (Rugolo et al. 1 ) as M = (3/maximum 

 age). The report also states that "this convention ... is 

 widely used for many east coast finfish stocks (NMFS 

 [National Marine Fisheries Service]/NEFSC [Northeast 

 Fisheries Science Center], ASMFC [Atlantic States Ma- 

 rine Fisheries Commission])." Following its introduction 

 by Rugolo et al. (Rugolo et al. 1 ; Rugolo et al., 1998), the 

 3/£ max approach has been used in nearly all blue crab 



Rugolo, L., K. Knotts, A. Lange, V. Crecco, M. Terceiro, C. 

 Bonzek, C. Stagg, R. O'Reilly, and D. Vaughan. 1997. Stock 

 assessment of Chesapeake Bay blue crab (Callinectes sapi- 

 dus), 267 p. Report of the Technical Subcommittee of the 

 Chesapeake Bay Stock Assessment Committee of the National 

 Marine Fisheries Service, NOAA (National Oceanic and 

 Atmospheric Administration). NOAA Chesapeake Bay Office, 

 410 Severn Avenue, Suite 107, Annapolis, MD 21403. 



stock assessment work conducted on the east coast of 

 the United States (Miller and Houde 2 ; Miller, 2001; 

 Murphy et al. 3 ; Helser et al., 2002; Kahn 4 ). 



The references used by Rugolo et al. (1998) in support 

 of what they termed the "ICES convention" (Antho- 

 ny 5 ; Vetter, 1988) do not mention the 3/t max approach. 

 Rather than advocating a method for determining M, 

 Anthony 5 called for standardization of the range of ages 

 to include in the calculation of yield-per-recruit for a 

 stock; this range of ages was termed the stock's "fish- 

 able life span." He proposed that the fishable life span 

 should be defined such that the oldest age would be that 



2 Miller, T. J., and E. D. Houde. 1999. Blue crab target 

 setting, 167 p. Final report to the Living Resources Sub- 

 committee of the Chesapeake Bay Program. University 

 of Maryland Center for Environmental Science (UMCES) 

 Technical Series No. TS-177-99. Chesapeake Bay Program, 

 U.S. EPA (Environmental Protection Agency), 410 Severn 

 Avenue, Annapolis, MD 21403. 



3 Murphy, M. D., C. A. Meyer, and A. L. McMillen- 

 Jackson. 2001. A stock assessment for blue crab, Ca Uinectes 

 sapidus, in Florida waters, 56 p. FMRI (Florida Marine 

 Research Institute) Inhouse Report Series IHR 2001-008. 

 Florida Fish and Wildlife Conservation Commission, FMRI. 

 100 Eighth Avenue SE, St. Petersburg, FL 33701. 



4 Kahn, D. M. 2003. Stock assessment of Delaware Bay 

 blue crab (Callinectes sapidus) for 2003, 52 p. Delaware 

 Department of Natural Resources and Environmental Control. 

 Division of Fish and Wildlife, P.O. Box 330, Little Creek. 

 DE 19961. 



5 Anthony, V. C. 1982. The calculation of F 0-1 : a plea for 

 standardization, 16 p. Northwest Atlantic Fisheries Organi- 

 zation ( NAFO ) Serial Document N557, SCR 82/VI/64. NAFO 

 Secretariat, P.O. Box 638, Dartmouth, Nova Scotia B2Y 3Y9, 

 Canada. 



