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Fishery Bulletin 97(3), 1999 



An observer size estimation bias would scale or 

 otherwise deform those estimates of if'' is) or pis) (or 

 both), depending on whether the bias was propor- 

 tional to size or was more complex. Even if the ob- 

 servers were unbiased in their individual estimates, 

 estimation variance would still increase both tails 

 in the density estimates. Thus, if research vessel 

 observers and tuna vessel observers consistently 

 made different errors in estimating school sizes, then 

 S the trend in our estimates of capture frequency, e.g. 

 Figure 4, could have been in part or entirely due to 

 those errors. 



Gerrodette and Perrin^ studied dolphin school size- 

 estimation errors for research vessel observers by 

 ground-truthing observer estimates against aerial 

 photo counts of the same school. They found that the 

 counts from a single observer could be modeled as 

 lognormally distributed given the true school size. 

 They also found that a given observer in the study 

 might have a substantial positive or negative bias. 



Using their photo and observer dataset, we fitted 

 a lognormal model for the geometric means of the 

 observer estimates from each sighting.'' The fit indi- 

 cated that the observers had essentially no bias at a 

 true school size near 100, but that there was a nega- 

 tive bias of 21% at a school size of 1000. Because the 

 lognormal is a skewed distribution, this mean bias cor- 

 responds to essentially no median bias. The estimated 

 CV for the estimates, given the true size, was 48%. 



Given this information, it would have been pos- 

 sible in theory to correct the research vessel observer 

 estimates for bias. However, we did not make that 

 correction because the corresponding correction for 

 the tuna vessel set data was not possible in the ab- 

 sence of a suitable ground-truth study. Significant 

 differences between observers and observing condi- 

 tions on research vessels and tuna vessels precluded 

 the assumption that any size-estimation biases are 

 similar in the two types of data. 



Spatial distribution of schools and school sizes 



Our analysis can be taken to imply full spatial mix- 

 ing, that is, all schools of a given size within the stock 

 boundaries (or within each stratum for the strati- 

 fied case) have the same probability of being set upon. 

 A more realistic model is that some schools have a 

 higher or lower probability depending not only on 

 their size but also on their geographic location in 



relation to areas of high school density or high fish- 

 ing effort. Other factors, such as seasonal effects and 

 the amount of associated tuna, are also interrelated 

 with location in determining the rate of capture for 

 a given school. Because we included only limited spa- 

 tial information in our model, the appropriate inter- 

 pretation of our results is that we estimated an av- 

 erage probability of being set upon, as a function of 

 school size, for schools within the stock boundaries 

 (or each stratum). 



Observer experience suggests that pressure from 

 fishing on dolphin can reduce average dolphin school 

 size, i.e. areas of high fishing effort tend to have 

 smaller schools. ' This decrease in school size may be 

 a result of chase and capture operations during sets 

 intentionally or unintentionally splitting schools into 

 smaller subgroups.*^ However, we did not find any 

 indication of such a trend in our NE offshore spotted 

 dolphin school-size data. We concluded that if fish- 

 ing pressure did affect spotted dolphin school size, 

 its effects may have been masked by size selection 

 in the tuna vessel set data and by the relatively lim- 

 ited number of observations in the research vessel 

 sighting data. 



Dolphin schools 



Variation in school size over time The simplest in- '' 

 terpretation of this analysis would assume that a 

 dolphin school is a fixed entity that does not change 

 in size. If, on the other hand, a school is not a well- 

 defined entity over any length of time, i.e. schools 

 often fragment and reaggregate (e.g., Scott and 

 Cattanach, 1998), then defining capture frequency 

 for anything other than an individual dolphin be- 

 comes problematic. The superpopulation model that 

 we used is one way to account for this fiuid nature of 

 dolphin schools. In particular, the research and tuna 

 vessel school-size data represent time-averaged 

 samples, i.e., averages over repeated realizations fi-om 

 the superpopulation. Estimated capture frequencies 

 can be interpreted in terms of short-term rates. 



Species composition Most schools in both the re- 

 search vessel and tuna vessel data included not only 

 NE offshore spotted dolphins, but other species as 

 well, primarily spinner dolphins iStenella longir- 

 ostris). We did not differentiate between pure and 



5 Gerrodette, T. and C.Pcrrin. 1991, SWFSC Admin. Rep. LJ- 

 91-36, Southwest Fisheries Science Center, La Jolla CA, 74 p. 



* Details of this exploratory analysis can be found in Perkins, P. 

 C. and E. F. Edwards, 1997, SWFSC Admin. Rep. LJ-97-03, 

 Southwest Fisheries Science Center, La Jolla CA, 36 p 



' Rasmussen, R. 1997. Southwest Fisheries Science Center, La 



Jolla, CA. Personal commun. 

 ** Hall, M. 1997. Inter-Amencan Tropical Tuna Commission, 



La Jolla, CA. Some limited data have been collected to study 



.school fragmentation and reaggregation (Perrin et al., 1979; 



Scott, M. 1997. Inter-American Tropical Tuna Commission, La 



Jolla, CA. Personal commun. 



