THEILACKER: CHANGES IN BODY MEASUREMENTS OK I.AKVAI. NOKTHERN ANCHOVY 



ble 3). In larvae 6 mm SL or less, maximum 

 shrinkage (19^r) occurred after 5-10 min treat- 

 ment in the net; larvae were usually dead at the 

 end of the treatment. Older larvae shrank 

 throughout the 20-min period and were often alive 

 at the end. For example, 18-22 mm larvae were 2*^ 

 smaller after 5 min and S-W/e smaller after 20 min 

 in the net. Further net treatment of larger larvae 

 caused an additional 1-2*^ shrinkage. Figure 5 



■O.C '2 14-0 16 

 LIVE ST4NDAHD LENGTH (mml 



Figure 5. — Ten-minute net-treated shrinkage of standard 

 length as a function of size for northern anchovy larvae. Dots are 

 means of 10 larvae. Circles represent individual fish. 



shows that measurable shrinkage decreases for 

 older, larger larvae, and that the ratio (R ) of the 

 size of net-treated iX^ ) to live (L ) size larvae rises 

 rapidly from about 0.7-0.8 at 4 mm SL to 0.9 by 

 11-12 mm SL. Although shrinkage appears nearly 

 constant for larvae from 12 to 22 mm (Figure 5), I 

 measured few older, larger larvae. Conceptually, 

 shrinkage is probably related to the degi'ee of os- 

 sification; ossification of northern anchovy verte- 

 brae begins at 14 mm SL and is complete at trans- 

 formation, about 35 mm (E. H. Ahlstrom"*). At 

 transformation, shrinkage should be negligible or 

 zero, and the ratio should approach an asymptote 

 of one. To characterize this relationship, I used the 

 equation 



R ^exp[{-f,)exp(-f^X,)]. 



(1) 



Equation ( 1) may be transformed so that the dou- 

 ble logarithm of i? is a linear function of size, X^, 

 i.e. 



ln[-ln(i?)] = In/; -f.^X^. 



(2) 



For standard length measurements, the parame- 

 ters of Equation (2) were estimated for each of the 

 four net-treatment periods as shown below: 



"•E. H. Ahlstrom, Senior Scientist, Southwest Fisheries Center 

 La Jolla Laboratory, National Marine Fisheries Service. NOAA, 

 RO. Box 271, La Jolla, CA 92038, pers. commun. December 1978. 



The logarithm of/!, is linear with net-treatment 

 time, i.e. 



4 = s,t^^. 



(3) 



while/*! shows no trend. Combining these two rela- 

 tionships, i.e., R with size (Equation (D) and f.2 

 with time (Equation (3)), and inverting the equa- 

 tion to solve for live size in terms of treated larvae, 

 the resultant relationship is 



InL = InXj +Pj exp(-P2XjX/') 



(4) 



X, is 



where L is live size, Pj =fi,P.2 ^fiSi'P^ ^ S-z 

 treated size, and X.^ is time it) in minutes. Equa- 

 tion (4) was then fit directly using a nonlinear 

 fitting procedure (Conway et al. 1970 ) to obtain the 

 final parameter estimates. The same procedure for 

 estimating parameters and fitting equations was 

 followed for shrinkage of head length and body 

 depth. All equations gave a good fit to the observed 

 data (Figure 6, Table 3); estimates of the parame- 



30 

 20 



10 



E 

 _E 



LlJ 



> 



ro 



0.1 



STANDARD 

 LENGTH 



HEAD 

 LENGTH 



BODY 

 ^ DEPTH 



I I I I I I I I I 



I I I 1 1 I i_ 



0.1 1.0 10 20 30 



10 MINUTE NET TREATMENT (mm) 



Figure 6. — Fit of models (Equation (4)) describing net- 

 treatment shrinkage of larval northern anchovy body parts. 

 Estimates of parameters for models are given in Table 4. Models 

 predict live size from net-treated size. 



689 



