HOLT ET AL : MONITORING DOLPHIN ABUNDANCE 



120 days each by plotting hypothetical tracklines. 

 Approximately 370 km (200 nautical miles) of 

 trackline could be covered in each survey day; 

 with searching restricted to daylight hours, only 

 about one-half of this distance would be searched. 

 Approximately 40,700 km of trackline could be 

 covered by each ship with less than 50^^ of this 

 distance searched during daylight hours. Each 

 ship's searching distance was allocated to each 

 stratum by the square root of school density in the 

 stratum. Effort of each ship was partitioned into 

 30-d segments between ports to meet logistical 

 constraints of the vessels. We found that thor- 

 ough coverage of the entire area was provided 

 when three ships were used, two ships provided 

 adequate coverage, and one ship provided very 

 poor coverage with tracklines separated by large 

 distances (Fig. 2). 



DETECTION OF CHANGES 

 IN POPULATION SIZE 



Survey Design 



The relationship among the number of samples, 

 the rate of change, the precision of the population 

 estimate, and the levels of alpha (type I) and beta 

 (type II) statistical errors for several models of 

 change and sample variability was investigated 

 by Gerrodette (in press). We assumed that popu- 

 lation size would change exponentially (constant 

 rate per year). From Gerrodette's equation 15, 

 using slightly different notation, 



a(a + l)2(a + 2)[ln(l - r)]2 



12(Z„ + Zp)2 ^\n 



(=0 



_cv_ 



(1 -rY 



+ 1 



(1) 



where 



a - number of years in the survey 



period, 

 r = annual rate of decrease, 

 Za = percentile of standardized normal 



curve for one-tailed Type I error, 

 Zp = percentile of standardized normal 

 curve for Type II error, and 

 CVq = coefficient of variation of the 

 population estimate at the present 

 population size. 



In this formulation, r is a positive number, and, 



since the first survey occurs at time 0, the total 

 number of samples (i.e., number of annual sur- 

 veys) is a + 1. Note that the null hypothesis is 

 one-sided, namely, that spotted dolphin abun- 

 dance is decreasing. In addition to the annual 

 rate of decrease (r), the total population decrease 

 which would occur over the entire survey period 

 was calculated as 



Total decrease = [1 - (1 - r)°]. 



The survey design to detect changes in dolphin 

 abundance was investigated in three ways. Using 

 Equation (1), we computed 1) the minimum num- 

 ber of years (a), given one to three ships per year 

 and 120 searching days per ship per year, re- 

 quired to detect various annual decreases in spot- 

 ted dolphin abundance; 2) the minimum propor- 

 tional annual change (r) that could be detected in 

 5 years given one to three ships per year at vari- 

 ous levels of alpha and beta; and 3) power (1 - p) 

 or the probability of detecting various decreases 

 in population size in 5 years, given one to three 

 ships per year. 



To use Equation (1), the relationship of CV (N), 

 the coefficient of variation of the population esti- 

 mate, and n , the number of schools detected must 

 be determined. In addition, the rate per day at 

 which dolphin schools are expected to be encoun- 

 tered must be known. We used the 1977-83 re- 

 search vessel data to investigate these factors as- 

 suming these data would be representative of 

 data that we will obtain during the proposed sam- 

 pling period of 1986-91. 



Abundance Estimation 



Relative estimates of population abundance of 

 spotted dolphins in the north and total areas were 

 calculated using two methods, methods A and B. 

 In method A, density and mean school size esti- 

 mates were calculated in each stratum and abun- 

 dance was determined (Holt and Powers 1982) as 



A^ 



Pt^D 



kStkPk-^k 



(2) 



k=i 



In method B, density and mean school size esti- 

 mates were calculated for data pooled for the en- 

 tire area (north area or total area) and abundance 

 was determined as 



437 



