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APPENDIX 



The estimation procedure of Conway et al. 

 (1970) is a least squares procedure which requires 

 only the definition of the functional relationship 

 and the first derivative with respect to each 

 parameter. Although not stated explicitly, con- 

 stant variance is assumed and, hence, the loga- 

 rithmic form will be used throughout. For a sin- 

 gle-cycle Laird-Gompertz curve the equations are 

 as follows: 



InF = InFo + A[l - Ex-p{-at)]/a 



■^0 



6lnF 

 A 



6\nF 



= [1 - Exp(-aO]/« 



= A[{at + 1) Exp(-aO - l]/a2 



For a two-cycle curve with the second cycle begin- 

 ning at t = t* the equations are: 



\r\F = InF,, + ^[l-Exp(«Ai)]/a 

 + B[l - Expi-0^2)]//3 



^^ ^ VF 



6Fo 



*1^ = [1 - Exp{-aA,)]/a 



dlnF 

 ba 



6lnF 

 h\nF 



b\nF 

 bt* 



where 



= A[(al, + 1) Exp(-aAi) - l]/a2 



= [l-Exp(-/8A,)]//3 



-yS[(y5A2 + 1) Exp(-/?A,,) - l]/yS2 



= [A Exp(-aAi) - B Exp(-^2)] 



Al = MlNitJ*) 



A, = MAX(^-r ,0). 



FORTRAN programs are available for fitting 

 single-cycle, temperature-dependent and multi- 

 cycle, temperature-dependent curves at SWFC. 



621 



