FISHERY BULLETIN: VOL. 84, NO. 4 



Intensive Fishing 



Length Frequency 



© 



Systematic Survey 

 of Relative Abundance 



Otoliths 



Time Series 

 Length Frequency 



I 



Yield and Relative 

 Spawning Stock Equations 



f MSY j 



Figure 1.— Schematic of the yield assessment approach. A more general approach to fishery 

 assessment which includes a treatment of catch and effort data as well is given in Munro (1983); 

 our Figure 1 represents a detailed subset of Munro's figure 1 (1983). 



and Holt 1956). For a series of L c values at inter- 

 vals beginning with the smallest L c and going up to 

 L^, there will be a corresponding set of I values. 

 By solving the ZIK equation above for I as a func- 

 tion of L c , the following relationship is obtained: 



T = LJ(Q + 1) +L c (0/(0 + 1)). 



Thus, regressing a sequence of I values on the cor- 

 responding L ( values will produce estimates for the 

 slope and intercept which can be solved for esti- 

 mates of L x and ZIK (Wetherall et al. in press). 



Once an estimate of L has been obtained by this 

 method, otolith data and/or a time series of length- 

 frequency data can be fit to the von Bertalanffy 

 growth curve to estimate the growth coefficient K. 

 Estimation of L^ from length-frequency data was 

 used for the Marianas bottom fish data because a 

 large length-frequency sample was available and 

 otolith readings were difficult to interpret for old 

 stages of growth. With an estimate for K, the total 

 mortality rate, Z, can then be estimated as the pro- 

 duct of K and the ratio of ZIK obtained in the 



previous step. Alternatively, one can estimate Z 

 from a catch curve constructed from a length- 

 frequency sample which has been corrected for 

 nonlinear growth and converted to an age-frequency 

 sample (Pauly 1983). 



If these techniques are applied to unexploited or 

 lightly exploited resources, the estimate of Z pro- 

 vides an estimate of the instantaneous rate of 

 natural mortality (Af ). However, if fishing mortal- 

 ity is believed significant, an equation to estimate 

 M as a function of K, L^, and mean annual water 

 temperature (T) (in °C) has been developed as 

 follows (Pauly 1983): 



log 10 M = -0.0066 - 0.279 log 10 L^ 



+ 0.6543 log 10 K + 0.4634 log 10 T. 



Given estimates of K, M, and age of entry to the 

 fishery (t c ), the Beverton and Holt (1957) yield per 

 recruit (Y/R) equation can be used to compute the 

 ratio of equilibrium yield to unexploited recruited 

 biomass as a function of fishing mortality (F). The 



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