790 



Fishery Bulletin 100(4) 



six different back-calculation equations and their use. 

 Ricker ( 1992) later commented on the conclusions of Fran- 

 cis ( 1990) to suggest yet another variation on the method. 

 Further variation exists on exactly which combination of 

 annuli to use. Standard method suggests the use of all 

 available annuli within the otolith to increase sample size. 

 However, recent literature (Vaughan and Burton, 1994), 

 as well as older reports (Ricker, 1973), have suggested 

 that only the most recently formed annuli should be used. 

 A review of the literature on age and growth shows that 

 a variety of techniques are in use today and that there is 

 no real agreement on a definitive method. The purpose of 

 this study was to examine how well the various back-cal- 

 culation techniques accurately estimate lengths at previ- 

 ous ages and to examine the biases associated with each 

 technique. 



Methods 



Model structure 



I simulated somatic and otolith growth using a bioener- 

 getics model. A detailed description of the model is pre- 

 sented in Schirripa and Goodyear (1997). The life history 

 and growth parameters were calibrated to fit, as closely 

 as possible, to reported estimates of striped bass growth 

 (Bason'); however the model is not intended to be a striped 

 bass model per se. Because of the commercial and recre- 

 ational importance of striped bass, a great body of litera- 

 ture from the field and laboratory work is available. One 

 of the most studied populations of striped bass is that of 

 the Chesapeake Bay system (Cohen et al., 1983; Coutant 

 et al., 1984; Goodyear, 1984, 1985; Tuncer, 1988; Coutant 

 and Benson, 1990; Secor, 1992; Brandt and Kirsch, 1993; 

 Rose and Cowan, 1993; Rutherford and Houde, 1995; 

 Secor and Houde, 1995). Biological and environmental 

 parameters reported for the populations of this system 

 were used whenever possible. The growth model used an 

 individually based framework, but rather than following 

 every fish of the cohort singly, "cells" offish with identical 

 attributes were followed instead (Rose et al., 1993). A total 

 of 250 cells, each with eleven attributes, were modeled. 

 Attributes examined included age, length, biomass, daily 

 food ration, food conversion efficiency, otolith weight, oto- 

 lith radius, maximum length attained, maximum biomass 

 attained, brain weight, condition factor, and number of 

 fish that the cell represented. 



The term "population" is used to define those fish that 

 remained alive for the entire simulation, unaffected by 

 either natural or fishing mortality. The term "catch" re- 

 fers to the entire group of fish that were susceptible and 

 killed due to fishing mortality, and "sample" refers to a 

 subsample of individuals from the catch, selected on the 



1 Bason, W. H., S. E. Allison, L. O. Horseman, W. H. Keirsey. P. 

 E. LaCivita, R. D. Sander, and C. A. Shirey. 1976. Ecological 

 studies in the vicinity of the proposed Summit Power Station 

 January through December 197.5. Vol. 1, Fishes, .392 p. Ich- 

 thyological Associates, hhaca, NY. 



basis of length and frequency within the catch. Frequency 

 in the catch was a function of the selectivity of the gear 

 under consideration and frequency in the population. For 

 the purposes of this study, gear was considered nonselec- 

 tive. Annulus formation within the otolith was assumed to 

 occur at the end of every growth year and to be measured 

 without error. 



The specific somatic growth rate of an individual fish was 

 calculated by a balanced energy equation. Equations for 

 rates of consumption, respiration, egestion, and excretion 

 generally followed those given by Hewett and Johnson. ^ 

 The otolith growth model used was a modification of the 

 equations presented by Mosegaard.'^ Fish formed an otolith 

 when they reached 90 mm in length. Daily change in otolith 

 weight (O,,,) was modeled as a function of daily change in 

 either brain weight (B^^ ) or brain length (B,). In the case of 

 brain weight, weight specific brain growth rate was mod- 

 eled as a function of the somatic growth rate as follows 



Growth. Brain = Growth. Somatic x a.,, 



(1) 



where a., = less than 1, denoting that brain gi-owth rate is 

 slower than somatic growth rate. 



The change in B^^ then was calculated as 



dBJdt = Growth. Brain x B^^,. (2) 



The daily change in otolith weight was then calculated as 



dO^yldt = a, X Brain. weight x temp"' 



(3) 



where a_, = the conversion factor from brain weight to oto- 

 lith weight (see below); 

 temp = the average temperature for the day in degrees 

 centigrade; and 

 «i = 0.77, which is used to determine the overall 

 size of the otolith. 



Otolith radius, O^, was then calculated from O^^ assuming 

 a spherical shape as 



O. 



0„ 



:(3/4;r)" 



(4) 



' SpD 

 where SpD = 2.5 and is the specific density of the otolith. 



Assuming a spherical shape resulted in a unique radius 

 for a given weight (i.e. a sphere made it unnecessary to 

 consider otolith length). 



When brain length was used to model otolith radius, B^^, 

 was calculated as in Equation 2 and B, was calculated as 

 the cube root of B,„: 



- Hewett, S. W.. and B. L. Johnson. 1992. Fish bioenergetics 



model 2. Sea Grant Institute, Technical Report WIS-SG-92-250, 



79 p. University of Wisconsin, Madison, WI. 

 ■' Mosegaard, H. 1994. A model of otolith and larval fish growth. 



In ICES. Report of the working group on recruitment processes, 



CM. 1994/L:12, p. 34-38. 



