NOTE Edwards and Perkins Detecting linear trends in dolphin abundance 



631 



spread and subsequent overlap between null and alter- 

 native distributions is so great that differences between 

 the cut-off point in the null and the mean of the alter- 

 native is effectively inconsequential). 



Discussion 



Given the observed variability in TVOD, it does not ap- 

 pear that linear trends in dolphin abundance estimated 

 from these data with these techniques will be detect- 

 able at any levels practical for management purposes, 

 except possibly for the stock of northern spotted dol- 

 phin. Even for this stock, survey series at least a decade 

 in length are required. 



Our estimates of 5-year trends agree with previous- 

 ly published estimates derived by the same methods, 

 where 1983 has been omitted from the analyses (An- 

 ganuzzi and Buckland 1989). Our results imply that for 

 time-periods as short as 5 years, considerably larger 

 trends than those observed would be necessary to pro- 

 duce estimates of significant change with any reason- 

 able power. Except for northern offshore spotted 

 dolphin, this applies also to all other stocks, even for 

 the maximum time-series tested (10 years in this study). 

 It appears that other methods must be found to deter- 

 mine whether trends truly exist in dolphin abundance 

 in the ETP. For management purposes, longer time- 

 series must be monitored, for which linearity cannot 

 be assumed. Other regression procedures making 

 greater use of the precision estimates (standard errors) 

 of the indices could have more power, but for linear 

 analyses, at least, it is uncertain whether the increase 

 in power could overcome the inherent variabiity and 

 probable nonlinearities in the data. 



A more effective approach to estimating trends in 

 dolphin abundance is probably represented by the 

 sophisticated smoothing method applied recently to 

 these data by Buckland et al. (1992). The method 

 reduces the relatively-scattered abundance estimates 

 to smoothly-changing estimates of abundance, but with 

 the advantage of producing confidence limits about the 

 smoothed trend and generating a more biologically- 

 reasonable result (abundance of natural populations 

 rarely changes linearly). However, simulation experi- 

 ments will be required to determine the circumstances 

 under which the smoothed trends do, or do not, reflect 

 accurately the true underlying dynamics of the stocks. 

 Such simulations are currently underway, but results 

 are as yet unavailable (Alejandro Anganuzzi, Inter-Am. 

 Trop. Tuna Comm., La Jolla, pers. commun., July 

 1991). 



Regardless of the results of the tests of various 

 smoothing methods, it appears fruitless, based on the 

 results presented here, to use linear-regression tech- 



niques to estimate trends in abundance of dolphin 

 stocks in the ETP, even for periods as long as a decade. 

 The power to detect ecologically (or managerially) rele- 

 vant trends, given the observed variability in the data, 

 is simply not sufficient. 



Future efforts should, as suggested by Buckland et 

 al. (1992), focus on developing or applying robust, 

 curvilinear smoothing techniques that are reasonably 

 responsive to the underlying processes or mechanisms 

 controlling actual changes in dolphin abundance. 



Acknowledgments 



This study has benefited greatly from technical assis- 

 tance by Cheryl Glick and extensive helpful discussions 

 with Tim Gerrodette and Doug DeMaster. 



Citations 



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