Fishery Bulletin 90(1). 1992 



be treated as indices of relative abundance, rather than 

 estimates of absolute abundance of the stocks. The 

 definition of a stock, and its boundaries, is problematic, 

 but we follow the recommendations of Au et al. (1979), 

 for reasons stated by Anganuzzi and Buckland (1989), 

 except in two cases. A more southerly southern bound- 

 ary was found to be necessary for the southern offshore 

 stock of spotted dolphins (Anganuzzi et al. 1991), and 

 we adopt the recommendation of Perrin et al. (1991) 

 to combine the northern and southern whitebelly stocks 

 of spinner dolphins. We also derive estimates for pooled 

 offshore stocks of spotted dolphins and pooled stocks 

 of common dolphins, since they are not differentiable 

 in the field. 



Buckland and Anganuzzi (1988a) provided three 

 types of test for assessing whether abundance of a 

 stock had changed over time. For several stocks, the 

 tests failed to provide a clear indication of recent 

 changes, since the occasional large fluctuation in an- 

 nual estimates indicated that there were significant 

 changes in abundance that were biologically implaus- 

 ible. We present here a method of smoothing the 

 sequence of estimates of relative abundance. Used in 

 conjunction with the bootstrap, it yields a simple 

 method of assessing change over time which does not 

 require that trends are assumed to be linear, and which 

 does not yield biologically implausible rates of change. 



Edwards and Kleiber (1989) have questioned the 

 validity of estimating trends in abundance from sight- 

 ings data collected on commercial tuna vessels. We 

 carry out a simple simulation study to assess their 

 assertions, and compare the relative abundance esti- 

 mates calculated from tuna vessel data with those 

 calculated from research vessel data for the years 

 1986-89, for which data from both sources are 

 available. 



Methods 



The number of dolphins A^ in an area for a given stock 

 and year is estimated by 



N = A ■ S ■ D 



where A is the size of the area, 



s is the estimated average school size for the 



stock in area A, and 

 D is the estimated density of schools in area A. 



The line-transect method provides the estimate D 

 (Burnham et al. 1980). Suppose schools farther than 

 a distance w from the trackline are discarded from the 

 analyses. Then 



D = 



2L 



(1) 



where n is the number of schools detected in the area 

 that are within the truncation distance w, 

 /(O) is the estimated probability density function 

 of the n perpendicular distances, evaluated 

 at perpendicular distance zero, and 

 L is the total length of transect in nautical 

 miles within the area. 



If we define the encounter rate E to be the expected 

 number of sightings detected within m' of the trackline 

 per nautical mile of search, then its estimate is given by 



E = nIL. 



Hence, 



and 



D 



N 



E-m 



Ef{0)-s-A 



(2) 



(3) 



UD and N were estimates of absolute abundance, then 

 the following assumptions would be required: 



(i) Within each area or stratum, either the search effort 

 of the tuna vessels is random or the dolphin schools 

 are randomly distributed; 



(ii) any movement of schools is slow relative to the 

 speed of the vessel, at least before detection; 



(iii) all schools on or close to the trackline are detected 

 and identified; 



(iv) sighting distances and angles are measured with- 

 out error; 



(v) sightings of schools are independent events; 



(vi) school size is recorded without error, and for mixed 

 schools percent of each species is recorded without 

 error; 



(vii) probability of detection of a school is independent 

 of its size, at least out to perpendicular distance w. 



If the estimates are used solely as indices of relative 

 abundance, as here, then any or all of the above 

 assumptions may fail without invalidating the esti- 

 mates, provided that bias arising from the failure of 

 an assumption is consistent across time. Even this pro- 

 viso may be relaxed when trends in abundance over 

 a long sequence of years are estimated; in this case it 

 is merely necessary to assume that bias shows no trend 

 with time. Catch-per-unit-effort methods for estimating 

 relative abundance are known to show trends in bias 

 over time in some instances, due to increased efficiency 

 of vessels (Cooke 1985). We attempt to avoid such prob- 

 lems by incorporating a parameter that measures the 



