HOUDE: ABUNDANCE AND POTENTIAL YIELD OF ROUND HERRING 



stage to 20.0 mm SL, then the instantaneous mor- 

 tality coefficients, based on mean estimated ages 

 of larvae, can be calculated using Equations (12)- 

 (16). No information on growth rates of round her- 

 ring larvae was available, but mean daily 

 growth increments of other Gulf of Mexico clupeid 

 species have been determined in laboratory rear- 

 ing experiments and they range from 0.3 to 1.0 

 mm (Richards and Palko 1969; Saksena et al. 

 1972; Houde 1973b; Houde and Swanson 1975). 

 Growth rates in those experiments exceeded 0.7 

 mm/day only when temperature was above 26°C. 

 Mean daily growth of round herring larvae proba- 

 bly is between 0.3 and 0.7 mm. Duration of the egg 

 stage from spawning until hatching is about 2.0 

 days. The duration of nonfully vulnerable length 

 classes was estimated from a knowledge of growth 

 rate and development times of other clupeid 

 species that have been reared in the laboratory. 

 Larvae of yellowfin menhaden, Brevoortia smithi, 

 did not begin to grow in length until nearly 4 days 

 after hatching at 26°C (Houde and Swanson 1975) 

 when they were about 4.5 mm SL; larvae of 

 Harengula jaguana did not grow significantly 

 until they were nearly 3 days old and 4.5 mm SL at 

 26°-28°C (Houde et al. 1974). The exponential 

 growth phase was assumed to begin in the 4.1- to 

 5.0-mm length class for round herring. The non- 

 fully vulnerable length classes of 2.1-5.0 mm in 

 1971-72 were assigned durations that varied from 

 4.0 to 7.0 days; the nonfully vulnerable 2.1- to 

 4.0-mm length classes in 1972-73 were assigned 

 durations of 1.5-3.0 days. Various combinations of 

 mean daily growth increments and durations of 

 nonfully vulnerable length classes were entered 



into the program to estimate mortality in relation 

 to age of larvae (Equations (12)-(16)) for 1971-72 

 and 1972-73. Examples, for one combination of 

 values of the variables in 1971-72 and one combi- 

 nation in 1972-73, are provided in Table 10 and 

 Figure 12. 



Given mean daily growth increments of 0.3-0.7 

 mm (corresponding to instantaneous growth 

 coefficients of 0.0299-0.0698) and the most proba- 

 ble durations of nonfully vulnerable length clas- 

 ses, the probable range of instantaneous mortality 

 coefficients was 0.0866-0.1739 in 1971-72 and 

 0.0835-0.1719 in 1972-73 (Table 11). In terms of 

 daily mortality the 1971-72 probable estimates 

 ranged from 8.3 to 16.0%; in 1972-73 they ranged 

 from 8.0 to 15.8% . Although the estimated range is 

 great, it is nearly the same for the two seasons. 

 Varying duration of the nonfully vulnerable 

 length classes had only minor effects on mortality 

 rate estimation (Table 11), but varying the growth 

 rate had important effects. 



The values ofiV , they-axis intercepts, provide 

 yet another series of estimates of annual spawn- 

 ing, because they estimate the numbers of eggs 

 present at time zero. The intercept values are gen- 

 erally lower than spawning estimates by the other 

 methods and are not considered to be good esti- 

 mates of spawning. It seems that the exponential 

 model of loss fits the decrease in larval abundances 

 reasonable well, but that a greater than expected 

 mortality occurs between egg and fully vulnerable 

 larval length classes. Figure 12 illustrates this 

 possibility. If only larval mortality had been con- 

 sidered, rather than total mortality from egg to 

 16.0-mm larvae, the instantaneous coefficients 



TABLE 10. — Two examples of data treated to obtain class durations and mean ages of round herring larvae from the eastern Gulf of 

 Mexico. Abundance estimates are then corrected for duration, and the duration-corrected abundances were subsequently regressed on 

 mean ages to obtain mortality rates (Table 11). Data are from 1971-72 and 1972-73 egg and larvae abundance estimates that were pre- 

 viously corrected for daytime avoidance. In these examples the mean daily growth increment (b) was set at 0.50. The nonfully vulner- 

 able length classes were 2.1-5.0 mm in 1971-72 with duration of 6 days, and 2.1-4.0 mm in 1972-73 with duration of 2.5 days. Calculat- 

 ing procedures are given in Equations (12)-(16). The regressions for these data are given in Figure 12. 



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