v = M 2 (n2 + 1) (n2 - m2) / ( m 2 + I) 2 (™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. Each 'complete survey" required 

 three to six boat days over periods of three to fifteen 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 2-3 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 

 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 M/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 a CV was estimated by the regression analysis described in Method 1. 



Estimation procedures: Interannual Tren ds and Power Analysis 



Linear regression analyses were conducted to determine whether a trend was 

 present in the indices or estimates of abundance (i.e., the slope of the regression line 

 of abundance vs. year was significantly different from zero). 



We used a power analysis to calculate the number of surveys or the CVs of 

 the estimates required to detect a trend (Gerrodette 1987). The power analysis relates 

 five parameters: alpha (the probability of making a Type-1 error, i.e. concluding that 



