Hoenig et at Estimating survival rate over time for larval fishes 



489 



cr. 



1981 



cohort 2 vs 1 cohort 3 vs 2 cohort 4 vs 3 



2 3 4 5 6 7 '345678 ^3 X 5 6 7 8 

 cohort 5 vs 4 cohort 6 vs 5 cohort 7 vs 6 



0) 



'456789 56 



"6 7 8 9 to ^ 7 8 9 10 



CTi cohort 8 vs 7 cohort 9 vs 8 cohort 10 vs 9 



O 2 



-1.7 



—1 ' ^ 



8 9 10 11 12 '8 9 10 11 12 13 '9 10 11 12 13 14 

 cohort 11 vs 10 cohort 12 vs 11 



1o 11 12 13 14 15 9l 12 13 14 15 16 



sampling period 



Figure 2 



Plots of the logarithm of the ratio of abundance (cohort 

 I + 1 -i- cohort i ) versus sampling period (measured as 

 5-day intervals) in 1981. Slopes of the linear regression 

 lines estimate Z^ - Z[^. (Note that the scale of the ordi- 

 nate varies among plots.) In 8 of the 11 comparisons of 

 cohorts, the slope is positive (later cohort has the better 

 survival). 



ing relative survival. For instance, Crecco and Savoy 

 suggest that cohorts spawned later in the season have 

 a higher relative survival based on comparison of lar- 

 val and juvenile numbers. Our method provides a tool 

 with which we can test this hypothesis for the larval 

 stage while overcoming problems which may be associ- 

 ated with sampling variability or limited sample sizes. 

 Ichthyoplankton were sampled throughout the spring 

 of 1980 and 1981. Approximately 30-40 larvae were 

 aged for each 5-day sampling period. We compared the 

 mortality of cohort i + 1 with that of cohort i for all 

 possible i where cohort i is defined to be animals born 

 in the ; th 5-day period of the season. This resulted in 

 12 comparisons for 1980 and 11 comparisons for 1981 

 (Figs. 1, 2). Because information on exact sizes of 

 the samples was not available to us, we computed un- 

 weighted regressions. This provides imbiased estimates 



of the regression parameters, but the estimates are not 

 of minimum variance and the standard errors are not 

 accurate (Weisberg 1980). 



The coefficients of determination were poor (r- 

 range 4-98%, mean 55%, for comparisons with three 

 or more observations) suggesting we cannot place much 

 confidence in the magnitude of the estimates of dif- 

 ferential mortality (Z^ - Zi). This is undoubtably due 

 to the very small sample sizes. However, it is worth 

 noting that in 12 of the 12 comparisons using the 1980 

 data, the differential mortality was positive (see Figure 

 3), i.e., the survival rate of cohort i + 1 (the later 

 spawned cohort) was higher than the survival rate of 

 cohort I (the earlier spawned cohort). Also, in 8 out of 

 11 comparisons using the 1981 data, the later-spawned 

 cohort had the higher survival rate. If there were no 

 differences in survival rates of the two cohorts in each 



