FISHERY BULLETIN: VOL. 75, NO. 1 



recently have discussed the problem of obtaining 

 crude mortality rates of larval fishes. A range of 

 possible mortality estimates for round herring egg 

 and larvae stages has been obtained which is use- 

 ful for year to year comparisons and for compari- 

 son with larval mortality estimates that have 

 been published on other species. Growth rates of 

 round herring larvae are unknown and could not 

 be determined from the data. But, from my experi- 

 ence in laboratory culture of clupeid larvae, an 

 exponential model describes growth reasonably 

 well during the larval stage. Ahlstrom (1954) and 

 Nakai and Hattori (1962) assumed that exponen- 

 tial growth was valid in determining survival 

 rates of California sardine, Sardinops caeruleus, 

 and Japanese sardine, S. melanosticta, larvae. 

 From laboratory rearing experiments it is evident 

 that mean daily growth increments (6) of clupeid 

 larvae range from 0.3 to 1.0 mm (Houde 1973b), 

 the increments depending on such factors as 

 temperature and food concentration. Using this 

 basic information, the probable mortality rates of 

 round herring larvae from hatching until 16.0 mm 

 SL (standard length) were estimated for the 

 1971-72 and 1972-73 spawning seasons. 



Using a computer program several variables 

 were considered and then the instantaneous mor- 

 tality coefficient was calculated for larvae based 

 on predetermined combinations of values of the 

 variables. The following procedure was used: 



1) For each designated mean daily growth incre- 

 ment (b), an instantaneous growth coefficient 

 (g) is calculated. 



a) 



t = 



L, L 



(12) 



where t = the time in days to grow fromL toL, at 

 a mean daily growth increment b 

 L t = the maximum length of larvae consi- 

 dered to adhere to the exponential 

 growth model (usually 20.0 mm SL) 

 L = the minimum length of larvae to be 

 considered in calculating the instan- 

 taneous growth coefficient (g). (This 

 value was 4.1 mm SL for round her- 

 ring.) 



lo&X, - log,L 



S = : 



b) 



(13) 



value of b that is submitted to the pro- 

 gram. 



2) The annual spawning estimate {P a ) for a given 

 spawning season and the larval abundance es- 

 timates by 1-mm length classes, corrected for 

 night-day variation (P a! ) are entered. 



3) The duration (in days) of each class from 2) 

 above is determined: 



a) The egg: Duration is arbitrarily assigned, 

 based on knowledge of developmental 

 stages in plankton collections or from 

 laboratory rearing experiments. For round 

 herring in the eastern Gulf of Mexico it is 

 2.0 days. 



b) Nonfully vulnerable length classes: Dura- 

 tion is arbitrarily assigned, usually by 

 submitting a range of possible values in the 

 program. Larvae in these length classes are 

 underrepresented in catches because of es- 

 capement through the meshes, and are not 

 considered in subsequent mortality estima- 

 tion. 



c) Fully vulnerable length classes. 



D, 



\og e L B - log,L; 

 g 



(14) 



where g = the instantaneous growth coefficient. 

 A different value ofg results from each 



where D t = duration of the class (in days) 



L B = upper boundary of length of a size 



class 

 L A = lower boundary of length of a size 



class 

 g is defined in Equation (13). 

 4) The mean age of each class is then estimated: 



a) The egg: Mean age is arbitrarily assigned. 

 (It is one-half the assigned duration.) 



b) Nonfully vulnerable length classes: Mean 

 age is assigned. It equals duration of the egg 

 stage plus one-half the duration of nonfully 

 vulnerable length classes. 



c) The mean age of fully vulnerable length 

 classes. 



T A = duration of the egg stage + duration 

 of nonfully vulnerable length classes 

 \og e L b - log.X a 



+ _B L _h 6^ (15) 



g 



where L b = the midpoint of the length class under 

 consideration 

 L a = the smallest length larva considered 



to be fully vulnerable to the gear 

 g is defined in Equation (13). 



68 



