a given year (M) was divided by the average proportion of marked dolphins to yield a 

 population estimate (N). A 2000-replicate non-parametric bootstrap resampled the 

 m/n proportions from observed groups to produce variance estimates and percentile 

 confidence limits. 



Method 3 (mark-resight method) uses the Bailey modification of the Petersen 

 method to estimate abundance (Bailey 1951; Seber 1982; Hammond 1986). The Bailey 

 modification incorporates resampling with replacement in the model. Because both 

 marked and unmarked dolphins may be resighted multiple times, this modification 

 was deemed appropriate. The equation used was: 



N=M(n2+ l)/(m2+ 1) 



with a binomial variance of 



v = M 2 (n2 + 1) (n2 - m2) / (m2 + l) 2 (m2 + 2) 



where N is the population size, M is the total number of different marked dolphins 

 sighted during the year, n2 is the total number of dolphins sighted during all 

 complete surveys of the area, and m2 is the total number of marked dolphins sighted 

 during the same surveys. A complete survey consisted of a combination of daily 

 surveys that covered all of the regions ( Figure 1 ) once during good or excellent 

 sighting conditions. These combinations were developed a posteriori for the purpose 

 of testing this estimation technique. The "complete surveys" required six to nine 

 boat days over periods of 4 to 38 days for completion due to the large area to cover 

 and the incidences of poor weather conditions. Only "Grade- 1" sightings were used to 

 ensure that all marked dolphins present during these sightings were identified and 

 the group size was accurately counted. Because of the difficulties of covering such a 

 large area, only 1-3 complete surveys were conducted each year. CVs were calculated 

 from binomial variance estimates. 



Method 4 (resighting-rate method) attempts to first estimate the number of 

 unmarked dolphins (u) in the area and then add them to the number of marked 

 dolphins in the catalog sighted that year (M) to estimate N. By assuming that 

 unmarked dolphins are resighted at the same rate as marked dolphins, the following 

 equation would estimate the number of unmarked dolphins: 



u = (M/m2) (n2 - m2) 



where M is the number of different marked dolphins sighted during the annual 6- 

 week survey period, n2 is the total number of dolphins counted from "Grade- 1" 

 sightings during the annual survey period, m2 is the total number of marked 

 dolphins counted from "Grade- 1" sightings during these same sightings, n2-m2 is the 

 number of unmarked dolphins counted from these sightings, and N/m2 is the 

 proportion of the number of marked individuals to the number of sightings of these 

 marked individuals. The population size is then estimated by 



N = M + u 



and the CV is estimated by the regression analysis described in Method 1. 



