488 



Fishery Bulletin 88(3). 1990 



tr 



1980 



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



0- 



r 



234567" '3 45678 '3 45678 



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



. 2r 



CD 



456789 '5 6789 10 "6 789 10 11 



CJ) cohort 8 vs 7 cohort 9 vs 8 cohort 10 vs 9 



O If . Ir ' 



"''7 8 9 10 11 12 "8 § 10 11 12 13 ~ '9 10 11 12 13 14 

 cohort 1 1 vs 10 cohort 12 vs 11 cohort 1 3 vs 1 2 



1r lr ir 







9o 11 12 13 14 15 ^1 12 13 14 15 16 '^2 13 14 15 16 17 



sampling period 



Figure 1 



Plots of the logarithm of the ratio of abundance (cohort 

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

 5-day intervals) in 1980. Slopes of the linear regression 

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

 nate varies among plots.) In all 12 comparisons of cohorts, 

 the slope is positive (later cohort has the better survival). 



where %- and ni are the total number of animals ob- 

 served in groups E and L, respectively, t, is the time 

 when the tth individual from group 1 was caught, and 

 similarly for tj. The major statistical packages have 

 routines for maximizing this function. 



Generalizations 



The logistic model is easily extended to enable one to 

 incorporate the effects of covariates. For example, sup- 

 pose one has information on the time elapsed since the 

 sampling program began (/ ) and also on the number 

 of days (t *) a power plant, which can be an additional 

 source of mortality, has been operating for each of the 

 sampling dates. Then instead of having t as the only 

 explanatory variable, we can have a linear combination 

 of explanatory variables in the exponent 



AZt, + 6] t* 



where 6i is the differential mortality rate (per time) of 

 the two groups attributable to power plant operation. 



Example 



We consider data on American shad Alosa sapidissima 

 in the Connecticut River, Connecticut, USA, kindly 

 supplied by Victor Crecco and Thomas Savoy (Dep. 

 Environ. Prot., Mar. Fish Office, Waterford, CT). A 

 description of the study area and sampling methods, 

 and a careful analysis of the data, are given in Crecco 

 et al. (1983). Our purpose in considering these data 

 is to illustrate the use of our method and to explore 

 the kinds of questions that can be asked by study- 



