490 



Fishery Bulletin 88 (3|, 1990 



1980 



2 3 4 5 6 7 8 910111213 

 cohort number i+1 



1981 



0) 

 Q. 

 O 



23456789 1011 1213 

 cohort number i+1 



Figure 3 



Plot of estimated differential mortality (i.e.. Z for cohort i + 1 minus 

 Z for cohort ( ) versus cohort number, i + 1 . Differential mortalities 

 are estimated as the slopes of the regressions in Figure 1 (top) and 

 Figure 2 (bottom). Note that in all but three cases, the later-spawned 

 cohort is estimated to have lower mortality (higher survival) than 

 the earlier-spawned cohort. 



pair, then one would expect half the comparisons would 

 have a positive estimate of differential mortality and 

 half would have negative estimates. 



Discussion 



We have presented three methods for estimating rela- 

 tive survival rates of larval fishes. The first method is 



based on a logistic regression model. It provides a 

 graphic way to check the assumptions of constant 

 relative survival and constant ratio of catchabilities. A 

 special case of this method is the two-sample estimator 

 of Paulik and Robson (1969) (our eq. 4). Explicit spec- 

 ification of the likelihood function (eq. 6) is necessary 

 when many small samples are obtained, e.g., from a 

 daily sampling program where the catch per tow is very 

 small. 



An intuitive method for estimating relative survival 

 rate would be to estimate the absolute survival rate of 

 each group by the decline in catch-per-unit-effort be- 

 tween two sampling times, and then to take the ratio 

 of the two survival estimates. Thus, 



alternative estimate of S^ IS^ = 



Cl2 



Ce2 



Cfii C'j 



L2 



Cpo c. 



.(7) 



£2 '-'LI 



The assumption necessary for the estimation of each 

 survival rate is that the catchability has not changed 

 over time. If one were to obtain an estimate of survival 

 that is unfeasible (>1.0) one would be tempted to dis- 

 card the data without computing relative survival. 

 However, the expression to the extreme right in (7) is 

 exactly equivalent to the two-sample estimator in (4). 

 Thus, one can validly estimate relative survival rates 

 even when estimates of absolute survival are obtained 

 which are nonsensical. This is because the relative 

 survival estimators do not require the catchabilities 

 to remain constant over time, only the relative catch- 

 abilities. 



On the basis of existing information, it is not possi- 

 ble to state quantitatively in what proportion of fish 

 populations or in which situations late-spawning larvae 

 will survive better than early-spawning larvae. In our 

 example, sample sizes were quite small (~30-40 age 

 determinations per 5-day sampling period) so that esti- 

 mates of relative survival rate were imprecise. It is in- 

 teresting to note, however, that in 12 of 12 comparisons 

 in the 1980 data and in 8 of 11 comparisons in the 1981 

 data the later-spawned cohort (week / -i- 1) had a higher 

 survival rate than the earlier-spawned larvae (cohort 

 from week (Fig. 3). However, our results indicate 

 that late-hatching (smaller) larvae survive a given 

 calendar period better than early-hatching (larger) lar- 

 vae which is opposite to the general findings that lar- 

 val fish mortality rates decrease with increasing size 

 and/or age (Peterson and Wroblewski 1984, McGurk 

 1986). This suggests that whatever the cause of mor- 

 tality (e.g., predation, transport), the vulnerability of 

 larval shad in the Connecticut River to this factor in- 

 creases with age and/or size during the period studied. 



