Hunter et al.: Fecundity, spawning, and maturity of Microstomus paaficus 



123 



teria set. The second equation assumed that qn,|i 

 changed hnearly with criteria set number i: 



Cbiili 



b, + boi. 



(Eq. 13) 



Combining equations (12) and (13) results in the final 

 equation 



Yij = bixij + b2X2j (Eq. 14) 



where yij =qj|i - qj|™, 



xij =qj|m - qjiim, and 



X2j =i(qj|m - qjlim)- 



For each criteria set i, we obtained the estimate of the 

 fraction of mature fish (qm|j|i) in each length-class j as 



ImlJli 



qm.jii/qjii = [qmiiqjim]/qj 



ii- 



We then obtained the estimated number of mature fish 

 of length-class j in the criteria set i (iVmijii) as the pro- 

 duct of the total number of fish at length-class j (A^j | i ) 

 and the estimated fraction of mature fish at length- 

 class j (q^ijii): 



■^mljli = -^jli qniljli- 



The summation of iVm|j|i over all criteria (i) is the total 

 number of mature fish at length-class j (7^m|j = Zi 

 iV^ijii). The total number offish in length-class j (ATj = 

 Zi iVjii) and the number of mature fish (iV^ij) were 

 used to estimate ML50 for all females taken before the 

 onset of spawning (California and Oregon data com- 

 bined) using BMDPLR (Dixon et al. 1988). 



We compared the above estimate with the ML50 for 

 each of the five maturity definitions created by in- 

 cluding progressively more criteria sets (Table 16). 

 When the definition of sexual maturity is expanded by 

 progressively adding criteria sets 2 to 5 to the defini- 

 tion, the ML50 decreased for each additional set of 

 criteria added. Our estimate of ML50 from the model 

 was 332 mm and is most similar to maturity definition 

 IV in Table 16. Thus, definition IV is the preferred 

 histological definition of maturity because it is probably 

 the least biased. 



Inspection of Table 16 also indicated that the ML50 

 is always greater when measurements are made dur- 

 ing the reproductive season than before it begins, 

 regardless of the number of criteria sets used to define 

 sexual maturity. This implied that during the spawn- 

 ing season the ovaries of some postspawning females 

 are reabsorbed to the extent that they become indis- 

 tinguishable from females defined as immature. Thus 

 maturity should be estimated prior to the onset of 

 spawning, and the definition of maturity should be 

 broader than definition I. 



We believe the preferable estimate of ML50 is one 

 based on the maturity algorithm because it uses all the 

 histological data, while those based on definitions use 

 only a portion of it. The maturity algorithm should be 

 applied only to data taken before the spawning season, 

 since data collected later in the season will be biased. 

 This method demands detailed histological classifica- 

 tion which may be too costly for many purposes. Defini- 

 tion III could be used if tissue were examined micro- 

 scopically or with a powerful hand lens, and it gives 

 an ML50 value close to that provided by the model. 



