In conclusion, northern Loligo opalescens popu- 

 lations form large spawning schools and deposit 

 massive egg capsule masses similar to those ob- 

 served in the Californian populations. 



Acknowledgments 



We thank the directors of the Bamfield Marine 

 Station and the Friday Harbor Laboratories for 

 the use of the respective facilities. Two anonymous 

 reviewers provided helpful suggestions. 



Literature Cited 



COUSTEAU, J.-Y, AND R DIOLE. 



1973. Octopus and squid: the soft intelligence. Double- 

 day, Garden City, N.Y., 304 p. 

 FIELDS, W. G. 



1965. The structure, development, food relations, repro- 

 duction, and life history of the squid Loligo opalescens 

 Berry. Calif. Dep. Fish Game, Fish. Bull. 131:1-108. 

 HOBSON, E. S. 



1965. Spawning in the Pacific Coast squid, Loligo opales- 

 cens. Underwater Nat. 3(3):20-21. 

 HOCHBERG, F G, AND W. G FIELDS. 



1980. Cephalopoda: The squids and octopuses. In R. H. 

 Morns. D. R Abbott, and E. C. Haderlie (editorsi, Interti- 

 dal invertebrates of California, p. 432-444. Stanford 

 Univ. Press. Stanford. 

 MCGOWAN, J. A. 



1954. Observations on the sexual behavior and spawning 

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RONALD L. SHIMEK 

 DAVID FYFE 

 LEAH RAMSEY 

 ANNE BERGEY 

 JOEL ELLIOTT 

 STEWART GUY 



Bamfield Marine Station 

 Bamfield. British Columbia 

 Canada VOR 1B0 



or exponentially as 



ARITHMETIC VERSUS EXPONENTIAL 

 CALCULATION OF MEAN BIOMASS 



Mean biomass (B) within a time interval (t) is 

 used in the Ricker method of estimating yield per 

 recruit and can be calculated either arithmeti- 

 cally as 



(i) 

 446 



B< 



B t + B t+1 



(ii) 



B t 



B t (e G t~Zt- 1) 

 G t -Z t 



(Ricker 1975). The choice of calculation method 

 may influence the yield estimates and con- 

 sequently the determination of optimal levels of 

 exploitation. 



Ricker (1975) and Paulik and Bayliff (1967) al- 

 luded to the importance of the difference in mag- 

 nitude between instantaneous growth and total 

 mortality rates (G t - Z t ). They indicated that if 

 the difference was small, arithmetic and exponen- 

 tial calculations approached one another. Ricker 

 suggested using small intervals if the rates are 

 rapidly changing. In this paper we 1) examine the 

 difference in the two estimates of mean biomass as 

 a function of the instantaneous rates of growth 

 and mortality, and 2) reexamine the consequences 

 of the choice of mean biomass estimates on esti- 

 mates of equilibrium yield per recruit using data 

 previously employed by Ricker (1975) and Paulik 

 and Bayliff (1967), showing that under many con- 

 ditions, exponential estimates of mean biomass 

 are preferable. 



The difference between arithmetic and expo- 

 nential estimates of mean biomass increases 

 rapidly as G t - Z t increases in a positive direction, 

 but diverges less rapidly when G t - Z t increases in 

 a negative direction. When B t is arbitrarily taken 

 in unity, the relationship is satisfactorily rep- 

 resented by a polynomial regression (Fig. 1). 



With many fisheries it is only possible to esti- 

 mate instantaneous fishing mortality (F t ) on an 

 annual basis. Thus, a large interval must be used. 

 The larger the interval, the more likely it is that 

 G t - Z t is of a magnitude that would cause sig- 

 nificant differences in estimates of B t calculated 

 arithmetically and exponentially. Also, in heavily 

 exploited fisheries there may be a large difference 

 between growth and mortality rates within an 

 interval especially at older ages. 



We employed Ricker's (1975:242-243, table 10.3) 

 example of bluegills from Muskellunge Lake to 

 illustrate the difference between the two methods 

 of computing mean biomass. This set was chosen 

 because Ricker's data have been used previously 

 as a historical data set and are readily available 

 through his text. Mean biomass was computed 

 arithmetically in the text example and also by 

 Paulik and Bayliff (1967), who used the same data 

 to introduce their computer program. We used the 

 data in two separate runs to compute yield per 



FISHERY BULLETIN: VOL. 82, NO. 2, 1984. 



