RICKER, W. E. 



1975. Computation and interpretation of biological statis- 

 tics offish populations. Fish. Res. Board Can., Bull. 191, 

 382 p. 



Stevens, W. L. 



1951. Asymptotic regression. Biometrics 7:247-267. 



nSHERY BULLETIN: VOL 77. NO, 4 



TOMLINSON, P. K., AND N. J. ABRAMSON. 



1961. Fitting a von Bertaleinffy growth curve by least 

 squaresincludingtablesof polynomieds. Calif Dep. Fish 

 Game, Fish Bull. 116, 69 p. 



APPENDIX 



This appendix contains FORTRAN subroutines 

 required by BMD07R to fit models corresponding 

 to the five hypotheses in Table 3. These sub- 

 routines evaluate /x(<„ ) and its partial derivatives. 

 To use these subroutines, the following three in- 

 structions need to be understood. 



1. The variable NG must be set equal to the 

 number of populations to be compared. 



2. The first NG variables of the data input must 

 be "design variables," followed by age. That is, the 

 first NG variables for observation /„ must consist 



774 



of NG-1 zeros and a single one, the one occurring 

 in the ith position; followed by age (^y ). Next comes 

 length and statistical weights (if weighting is 

 used). 



3. The parameters to be estimated are refer- 

 enced in the order all / ,'s first, all K's second, and 

 all t„'s last. Relative positions of /,'s, /^'s, and t^ 's 

 amongst themselves are simply the order of popu- 

 lation number. It should be noted that the 

 number of parameters fitted under the five 

 hypotheses of Table 3 are 

 H„i,H„2.H„3: (2xArG)+l; H^4; 3. 



Hi,: SxNG; 



