Holt and Sexton Dolphin abundance in eastern tropical Pacific 



107 



conditions were consistent) of searching effort was 

 tabulated, and then effort legs equal to that number 

 were randomly selected with replacement. This effort 

 and the associated sightings were used to calculate 

 school density, school size, species proportions, and 

 finally estimates of Nij. This process was repeated 

 100 times. The bootstrapped variance oi N,i for each 

 stock was calculated using these 100 estimates. 



Formulae used to estimate school density are from 

 Burnham et al.'(1980). Holt (1985, 1987), and Hayes 

 and Buckland (1983). The Fourier series (Grain et al. 

 1979) and hazard rate (Hayes and Buckland 1983, 

 Buckland 1985) models both provided adequate fits to 

 the perpendicular (sighting) distance data; however, the 

 hazard rate model was used because, unlike the Fourier 

 series model, it does not require subjective selection 

 of the number of terms in the model and, therefore, 

 could be used in the bootstrapped procedures. Of 

 schools containing both target and non-target species, 

 only the proportion of individuals of the target species 

 was used in the school size estimates. Estimates of the 

 proportion of all dolphin schools that were target 

 schools (Pi I;) were calculated using formulae from 

 Holt and Powers (1982). Formulae to estimate the pro- 

 portions (Pa) of the number of individuals for each 

 species of all target individuals are given by Barlow 

 and Holt (1986). 



All species of dolphins encountered in the study area 

 were included in the density analyses. Estimates were 

 calculated using only schools containing 15 or more 

 animals. Smaller schools were not used because we 

 believe small schools both on and off the ships' track- 

 lines may be difficult to detect, especially during rough 

 weather and may have been missed at a variable rate 

 depending on prevailing weather conditions (Holt and 

 Powers 1982). 



Schools detected at increasing distances from the 

 trackline tend to include disproportionately more large 

 schools because there is a direct correlation between 

 the size of a school and the probability of it being 

 detected (Drummer 1985). This biases school size esti- 

 mates upward and species proportions toward species 

 which tend to occur in large schools. We attempted to 

 adjust for this bias by weighting school size and species- 

 proportion estimates by the inverse of the logarithm 

 of school size (Holt and Powers 1982). Schools for which 

 there were no "best" estimates of size were not used 

 in the school-size or species-proportions calculations. 



Because a 3.7 km (2.0 nm) truncation point provided 

 the best fit of the hazard model to the data, only schools 

 detected within 3.7 km perpendicular distance of the 

 trackline were used to estimate school density. Schools 

 detected greater than 3.7 km have little affect on the 

 density estimates, and the perpendicular distance 

 distributions of schools at greater distances were 



"spiked". These spikes are a result of the ob.servers' 

 tendency to round-off estimates of radial distances 

 and sighting angles of schools detected at large 

 distances from the vessel in multiples of 0.5 nm or 5°, 

 respectively. 



Some stocks of the same species have overlapping 

 ranges (A',i^.). These overlapping stocks include (1) 

 coastal and northern spotted, (2) eastern and whitebelly 

 spinner, and (3) Baja Neritic and northern common 

 dolphins (Perrin et al. 1984). The relative number of 

 dolphins of each overlapping stock (P,^) was calcu- 

 lated for data pooled over the range and, if applicable, 

 over strata. The relative proportions of coastal and 

 northern spotted, and of eastern and whitebelly spin- 

 ner stocks, within their respective areas of overlap, 

 were calculated as the average of their relative abun- 

 dances (percent occurrence). Few data were available 

 to determine relative proportions of the overlapping 

 Baja Neritic and northern common dolphins. Therefore, 

 population estimates for Baja Neritic were combined 

 with northern common dolphins. 



The area inhabited by each target species (/I,/,) and 

 each stock (/I,,/,) used to calculate the population 

 abundance estimates were those defined liy Au et al. 

 (1979) and Perrin et al. (1984). The size of each stratum 

 (Aj;) and the size of the area occupied by each stock in 

 each stratum were calculated liy counting the numlier 

 of 1° quadrilateral squares in the stratum at each 

 degree of latitude; partial squares were approximated. 

 Next, the number of 1° squares was multiplied l:)y the 

 area in a 1° square for that latitude as described by 

 Holt and Powers (1982). 



Detecting trends in abundance 



The variability associated with the population abun- 

 dance estimates of northern offshore spotted dolphins 

 during this first survey was examined to determine 

 changes which may be detected from subsequent 

 surveys using methods presented by Holt et al. (1987) 

 and Gerrodette (1987). For Type I "(a) and Type II ((i) 

 error levels of 0.10, we computed the number of years 

 required to detect a minimum annual decrease of 0.10 

 and the minimum annual decrease in northern offshore 

 spotted dolphins which could be detected at the end of 

 the planned 5-year (6-survey) period. In addition, we 

 calculated the total population decrease that would 

 occur over the 5-year period given that annual level of 

 decrease. 



Results 



During the entire survey, observers aboard both vessels 

 searched 30,339 km and detected 1150 marine mam- 

 mal schools. Dolphins were present in 749 of these 



