FISHERY BULLETIN: VOL. 75, NO. 3 



estimates, assigning other mean daily growth in- 

 crements and other durations for nonfully vulner- 

 able larvae, were generated. Duration-corrected 

 abundances (Table 7) were then regressed on es- 

 timated mean ages, the resulting regression 

 coefficients from the fitted exponential functions 

 being estimates of the instantaneous mortality 

 coefficients (Z ) for age in days. 



Examples of probable thread herring larval 

 mortality estimates in 1971 and 1973 for a range 

 of possible mean daily growth increments and for 

 two probable stage durations of nonfully vulnera- 

 ble larvae are given in Table 8. The ranges of 

 probable larval mortality rates were similar in the 

 two years. The probable instantaneous mortality 

 coefficients ranged from 0.1371 to 0.2575 in 1971, 

 corresponding to daily mortality rates of 12.8 to 

 22.7%. In 1973 the estimates of instantaneous 

 mortality coefficients ranged from 0.1691 to 

 0.3050, which correspond to daily rates of 15.6 to 

 26.3% . The effect of varying the assumed duration 

 of nonfully vulnerable stages had a relatively 

 minor effect on mortality rate estimation com- 

 pared with varying growth rates (Table 8). 



The y-axis intercepts (N ) of the exponential 

 regressions used to obtain mortality estimates 

 (Table 8) also estimate annual spawning by thread 

 herring. The range of estimates in Table 8 encom- 

 passes the estimate obtained for 1971 and 1973 by 



the Sette and Ahlstrom (1948) or Simpson (1959) 

 techniques (Tables 3, 4). At a mean daily growth 

 increment of 0.8 mm, a probable value based on 

 laboratory growth data, the annual spawning es- 

 timates from the y-axis intercepts (Table 8) are 

 similar to those obtained by the other methods 

 (Tables 3, 4). 



I believe that the best estimates of larval mor- 

 tality were generated from abundance and age 

 data in Table 7. These data indicated that daily 

 mortality of thread herring larvae was approxi- 

 mately 20% in both 1971 and 1973. Instantaneous 

 mortality coefficients for conditions in Table 7 

 wereZ = 0.2124 in 1971 andZ = 0.2564 in 1973, 

 which correspond to daily mortality rates of 19.1 

 and 22.6% (Table 8). Regressions from which those 

 instantaneous mortality coefficients were derived 

 are given in Figure 11. Confidence intervals onZ 

 at the 0.95 probability level ranged from 0.0990 to 

 0.3258 in 1971 and from 0.1993 to 0.3224 in 1973. 

 The instantaneous coefficients were not tested to 

 determine if they differed significantly between 

 1971 and 1973 because variances of the estimates 

 were not homogeneous (Sg = 0.0028 in 1971, Sf = 

 0.0007 in 1973), but the overlapping confidence in- 

 tervals indicated that they did not differ sig- 

 nificantly. 



Regressions of duration-corrected abundance on 

 estimated mean age (Figure 11) suggested that 



TABLE 8. — Summary of mortality estimates for thread herring larvae from the eastern Gulf of Mexico, 1971 and 1973. Estimates were 

 obtained from the exponential regression of egg and larvae abundances on mean age. Instantaneous growth and mortality coefficients 

 were calculated for various possible combinations of mean daily growth increment and duration of the nonfully vulnerable larval stages. 

 Egg stage duration was assumed to be 0.84 days. Nonfully vulnerable larval stages were 1.1 to 4.0 mm SL in 1971 and 1.1 to 5.0 mm SL 

 in 1973. Explanation of the estimating method is given in Equations (12) to (16) of Houde (1977a). 



Year 



Mean daily 



growth increment, 



b (mm) 



Instantaneous 



growth coefficient, 



9 



Nonfully vulnerable 



larvae duration 



(days) 



Instantaneous 

 mortality coefficient, 



Z 



/-axis intercept, 

 (no. x 10 11 ) 



Daily mortality 



rate, 

 1 - exp(-Z) 



1971 



1973 



508 



