556 



Fishery Bulletin 100(3) 



29 months 

 n. =10 



47 months 



49 months 

 n =50 



~i 1 1 \ 1 1 1 1 1 1 1 1 1 1 1 r — 



280 300 320 340 360 380 400 420 440 260 300 320 340 360 360 400 420 440 280 300 320 340 360 380 400 420 440 



Total length (mm) 



Figure 6 



Male Gulf St. Vincent length-frequency histograms and fitted truncated normal density curves, as in Figure 5. 



minimization algorithm. The two occurrences of the pa- 

 rameter, r, in the Richards formula L = L./ll + re''^" 'Ol"^, 

 as a factor in front of the negative exponential and as its 

 reciprocal exponent around the entire function apart from 

 L^ can act in contrary fashion. For /• > 1, increases in r im- 

 ply an increase in length-at-age because of the parameter 

 as a reciprocal exponent, and the opposite for the second 



role the parameter plays in describing mean length. We 

 speculate that the Richards growth formula was less nu- 

 merically robust because r can rise and fall at different 

 parameter ranges along the path to convergence, resulting 

 in a more complex likelihood surface. 



Modeling the full length distribution at each monthly 

 age is valuable for assessing populations of heavily ex- 



