FISHERY BULLETIN: VOL. 79, NO. 2 



parameters, even though group-specific pa- 

 rameters are implied.) 



In Model 1 we assume that the ratio of instan- 

 taneous growth rate, dL(u)/ du, to potential 

 growth, L^c - L(u), is K, a constant. Instead, we 

 may suppose generally that this ratio varies with 

 age. We considered one such situation. In this 

 model, Model 2, we assume that stresses due to 

 capture, handling, and tagging will initially re- 

 duce the growth rate of a tagged fish below its 

 usual level, but that as time passes the normal 

 grovvi;h process will be restored. Specifically, in 

 our analysis of Model 2 we assume the standard 

 model holds for untagged fish but that when a 

 fish is tagged its normal growth pattern is inter- 

 rupted, such that 



G{u) = K, 



0<u<t.. 



Giu) = Kl{l+aexp[-Piu-t.j)]] f..<u. 



We assume 7^2=0, (i>0, and a^O. Model 2 says that 

 following tagging the growth rate is immediately 

 reduced to a fraction (1 -I- a) "^ of its normal value, 

 K, and then returns to K asymptotically (Figure 

 1). Loc is assumed to be unaffected. 



Parameter Estimation 



20 



In the standard von Bertalanffy model as ap- 

 plied to tag recapture data, there are two pa- 

 rameters to be estimated, K and Lx- The usual 

 approach is to estimate them simultaneously, and 

 we did so using the FORTRAN program BGC 4 

 written by Tomlinson (1971). This routine finds it 

 andL X as those parameter values which minimize 



Figure l. — Standard von Bertalanffy growth model (Model 1), 

 and an extension (Model 2) incorporating a temporary reduction 

 in growth rate. Git), following tagging. The resulting growth 

 pattern, L(t), is altered. Time units are arbitrary. 



2 



[L^-(L„-L, )exp(-i<:A..)] 



ij 



where L2 ^ L(tij + Am). Since E{L2.) is a non- 

 ij ■' ■' ij 



linear function oi K, parameter estimates derived 

 using this procedure are prone to serious bias un- 

 less observations onL2.. are made over a wide 

 range of Li . and A,^. Tresumably, it is also 

 desirable that they be made uniformly in the 

 plane of these two variables. 



The parameters of Model 2 may also be esti- 

 mated jointly using nonlinear least squares 

 methods, but estimates of L^ and correlated 

 parameters suffer the same drawbacks as esti- 

 mates of the standard von Bertalanffy model 

 parameters derived from BGC 4 



An alternative approach in fitting both models 



is to estimate L^ and the other parameters 

 sequentially. Where the oldest members of the 

 population have been intensively sampled and an 

 upper asymptote to length is clearly demon- 

 strated in the data, a reasonable estimate of Lx is 

 the length of the largest fish seen in the catches, 

 or the average length of the largest specimens 

 observed. Which estimator to use depends on 

 one's conceptual model of the growth process — 

 Lx can be regarded as the mean of a distribution 

 of asymptotic lengths in the population, or 

 strictly as an upper bound to the length any fish 

 in the population can achieve. With the value of 



296 



