FISHERY BULLETIN: VOL. 85, NO. 3 



Table 1 . — School density of all dolphin schools, proportion of all schools which were 

 target schools, mean school size of target schools, proportion of target animals which 

 were spotted dolphins, area of each stratum, abundance and K values for spotted 

 dolphins. SE and CV denote standard error and coefficient of variation, respectively. 

 Methods A and B refer to different ways of pooling data on school size and density (see 

 text). 



'Source Holt (in press). 

 2Source Barlow and Holt (1986). 



Relationship Between 



Var (N} and Number of 



Schools Detected 



In order to minimize the number of ^ears re- 

 quired to detect a specific trend, Var (N ) should 

 be as small as possible (Gerrodette in press). Var 

 (A^) depends on the variance of the estimates of 

 school size, school density, and proportions of the 

 various dolphin species, as shown in Equation (4). 

 Each of the variances of these estimates, in turn, 

 depends on n, the number of sighted schools. 

 Therefore, the dependence of Var (N) on n must 

 be known to calculate the number of sightings 

 needed to attain a given level of precision (Var 

 (A^)). We investigated the dependence of each of 

 the individual variance terms on n. 



size estimates, its variance is Var iStk ) — Var 

 {Stk )/n where Var iSfk ) is the variance of school 

 size. The Var (P^) = Pfil - Pt)ln where Pf is the 

 true proportion of target schools among all dol- 

 phins. Var (Sfk) and P^(l - Pf) are both constant 

 with respect to n, so Var (Sf) = Odin) and Var 

 {Pf) = Odin), where Odin) means "of the same 

 order as II n" and implies that as II n approaches 

 zero, the variance approaches zero at the same 

 rate. Similarly, Var (Pik), which is also a pro- 

 portion, is equal to Odin). 



Dependence of Var (D ) on w 



The Var (D), based on replicate tracklines 

 (Burnham et al. 1980), is 



Dependence of Var (5^^), Var (P,), 

 and Var (P^ ) on m 



Because Stk is the mean of n individual school 



440 



Var (D) = i)2 



Var(n) ^ Var[/'(0)] 

 n2 



(5) 



[/■(0)]2 

 where n is the number of sightings and/"(0) is the 



