FISHERY BULLETIN: VOL. 87, NO. 4, 1989 



are unrealistic, but in fact these slopes extend 

 over at least two 1° squares (Fig. 2b). This is a 

 distance of at least 120 nmi. Conditions change 

 across ocean fronts in distances much shorter 

 than this, and ocean fronts are aggregating 

 mechanisms for many marine biota (Owen 1981). 

 Of course, such fronts are never static and the 

 smoothing algorithm worked quite well in the 

 complex, dynamic environment, apparently 

 owing to the smearing effect discussed pre- 

 viously. However, as in the previous case, we 

 have as yet insufficient data to identify the con- 

 ditions actually pertaining in the real ETP. 



The major point is that the simulations have 

 shown that clustering characteristics on rela- 

 tively small scales (10s to 100s of miles) can 

 seriously bias estimates of abundance derived 

 via the smoothing algorithm, which is a problem 

 because as yet we know almost nothing about 

 clustering on this scale in the real ETP. The 

 model results indicate strongly that future re- 

 search should be focused either on resolving this 

 lack of information or on developing alternative 

 analyses that are not as sensitive as this smooth- 

 ing algorithm to these small-scale spatial effects. 



Change Estimates 



These demonstrated problems with estimating 

 school abundance are serious but in real-world 

 analyses could perhaps be ignored; the next set 

 of dolphin quotas will be determined not on the 

 basis of estimated absolute abundance at some 

 point in time but rather on the basis oi estimated 

 changes in abundance (Holt et al. 1987). This is 

 an advantage in the estimation process because 

 as long as nothing other than dolphin abundance 

 changes from one sampling period to the next 

 (i.e., as long as biases remain consistent), then 

 accurate estimates of those changes in abun- 

 dance can be derived from TVOD. 



However, we know almost as little about 

 whether biases truly remain constant (consis- 

 tent) in the ETP, as we know about small-scale 

 spatial distributions of dolphin schools. It is ob- 

 vious from Figure 5 that even relatively small 

 changes in bias can lead to considerably inac- 

 curate estimates of change and, by impHcation, 

 estimates of trend. A change as simple as mov- 

 ing from a static to a slowly moving environment 

 produced an overestimate in the ratio estimate 

 of almost 20% (Fig. 5, Lo(2, l)S/Hi(2, 1)NS). Not 

 even the direction of bias remained consistent, 

 changing from positive in some cases to negative 

 in others. 



The ratio estimate based on a simple static 

 environment during one sampling and a complex 

 static environment during the other period (Fig. 

 5) is of particular interest, because an effect of 

 this type may be the basis for the anomalous and 

 biologically unlikely dip in Buckland and 

 Anganuzzi's (1988) estimates of abundance for 

 northern offshore spotted dolphin, Stenella at- 

 tenuata during 1983 (Fig. 8), the year of an ex- 

 ceptionally strong El Nino. Our simulation re- 

 sults in this case lead to a potentially testable 

 hypothesis about a factor that may have signifi- 

 cantly affected analyses of real TVOD. Prelimin- 

 ary analyses of apparent differences in distribu- 

 tions of dolphins during El Niiio versus non-El 

 Nino years support the hypothesis that changes 

 in spatial distributions led to inconsistent biases 

 and thus to inaccurate trend estimates during 

 these years. '^ 



SUMMARY 



The results from these simulations are useful 

 in a general sense; they show that significant 

 biases can develop within the simple model 

 structure used here. The quantitative results are 

 specific to the parameter values and movement 

 rules chosen for these particular simulations and 

 are neither intended nor assumed to mirror spe- 

 cific distributions of either vessels or dolphin 

 schools in the real environment of the ETP. Al- 

 though parameter values controlling rates and 

 abundances are "correct" to the best of our 

 knowledge, choosing different parameters for 

 the functions controlling dolphin responses to 

 the environment, or vessel responses to dol- 

 phins, would probably change both the rates and 

 spatial characteristics of pattern development 

 and thus estimates of abundance derived. 



Other clustering patterns could have been 

 used, and other results generated. However, our 

 purpose at this stage was not to generate a cata- 

 logue of patterns and responses. Our purpose 

 was to test the effects of varying a simple but 

 reasonably realistic (in terms of rates and spac- 

 ings) aggregating pattern for dolphin schools, 

 using the results to determine whether any in- 

 sight could be gained into the problem of esti- 

 mating abundance of dolphin schools in the real 

 worid, using real TVOD. 



Indeed, we found that our simplified simula- 



'-S. B. Reilly, Southwest Fisheries Center, National Mar- 

 ine Fisheries Service, NOAA, P.O. Box 271, La Jolla, CA 

 92038, pers. comniun. 



874 



