FISHERY BULLETIN VOL 77. NO :i 



Table 2. — Basic terms and figures for population size and density estimates of bottlenose dolphin m the Texas bays resulting from 



replicate surveys 1-4. 



andnot the variances of'each replicate. Quinn has 

 suggested a more refined treatment that is appli- 

 cable if two conditions are met: the numbers of 

 sightings for each replicate follows a Poisson 

 distribution, and no real differences exist in the 

 replicate herd densities. If these assumptions 

 hold, a variance can then be legitimately com- 

 puted for each replicate survey and these numbers 

 pooled to produce a more precise estimate of mean 

 population size variance. Accordingly, we pro- 

 ceeded as follows. The estimation of the popula- 

 tion size for each replicate was calculated as: 



N, 



ADjhj 



(3) 



where N^ = estimated population size on repli- 

 cate^, 

 A = total area assumed to be 5.76 x of 



the searched area (a), 

 t)j = estimated herd density on replicate 



hj = mean herd size on replicate j. 



Results are shown as "number of dolphins" in 

 Table 2. 



The computed variance of the estimated popula- 

 tion size for each replicate was: 



VarATj = A'^Var(bjhj) 

 which simplifies to: 



VarjV, = 



■-(^r 



Var {rijhj) 



(4) 



(5) 



wherea is assumed to be l?"/; of the total area l/\ ). 

 The estimated variance of mean herd size 

 within replicates was then estimated from: 



'Terrance J. Quinn II, Center for Quantitative Science, Uni- 

 versity of Washington, Seattle, WA 98195, pers. commun. to S, 

 Leatherwood, March 1978. 



Var/i; 



y 



(6) 



Following Elliott (1971), a chi-square value 

 utilizing the index of dispersion was computed for 

 the number of herd sightings on replicate surveys 

 1-4 to test agreement with a Poisson series. The 

 index of dispersion was 0..'i.5 with a resulting x- 

 value of 1.05. These values support the Poisson 

 distribution assumption. This allows us to con- 

 sider the variance of replicate herd sightings as 

 equal to the numbers of herd sightings. Thus: 



Var (?, 



(7) 



Using the chi-square test again we also found 

 that there was no difference at the 5% significance 

 level in the herd densities of the replicate surveys. 

 The mean herd size [hj ) and the numbers of herds 

 sighted (/?,). however, were obtained from the 

 same set of observations, and as one reviewer has 

 rightly pointed out, it is not known if in fact these 

 estimates were independent. We therefore tested 

 for interrelationship using Spearman's Rank Cor- 

 relation Test (Zar 1974). Finding no demonstrable 

 correlation at the 5% significance level, we pro- 

 ceeded to treat the results of the replicate surveys 

 generated from Equation (5) in terms of Good- 

 man's ( 1960) equation for estimating the variance 

 of a product as suggested by Leatherwood et al. 

 (1978). Thus: 



Var N: 



5^{n/ Var hj + h-^ Var Oy - Var rij Var h,) , (8) 



and substitution of/?, for Var n. results in: 



590 



