Abstract. —An analysis of alter- 

 native methods for detecting trends 

 in a series of abundance indices is 

 carried out through simulation. The 

 alternative procedures explored have 

 been applied to analysis of relative 

 abundance indices of dolphins in the 

 eastern Pacific Ocean. They include 

 a linear test over a moving time- 

 period, and a nonparametric proce- 

 dure based on smoothing of the time- 

 series of abundance indices. Results 

 indicate that the nonparametric pro- 

 cedure outperforms the linear tests 

 in most of the situations tested. 



A comparison of tests for detecting 

 trends in abundance indices 

 of dolphins 



Alejandro A. Anganuzzi 



Inter-American Tropical Tuna Commission 



8604 La Jolla Shores Drive, La Jolla. California 92037- 



508 



Manuscript accepted 26 January 1993. 

 Fishery Bulletin, U.S. 91:183-194 ( 1993). 



An important part of the analysis of 

 any set of abundance indices is the 

 application of an objective procedure 

 or test to determine whether changes 

 in the estimates are due to random 

 fluctuations in conditions of the sam- 

 pling procedure or to actual changes 

 in the population size. Such a proce- 

 dure must exhibit certain properties 

 in order to be effective. Among these 

 properties, perhaps most important 

 is the power of the test for a given 

 significance level. 



In deriving conclusions about 

 changes in the size of a population, 

 we can fall into two types of error. 

 First, we can erroneously conclude 

 that population size has changed 

 when, in fact, differences in estimates 

 are due to random errors. This is 

 usually known as a Type-I error. A 

 Type-II error occurs when we con- 

 clude that the estimates reflect ran- 

 dom fluctuations when, in fact, there 

 has been a change in population size. 

 The probability of falling into a 

 Type-I error is usually referred to as 

 the significance level of the test. The 

 power of a test is defined as 1 minus 

 the probability of a Type-II error. An 

 ideal test will minimize the trade- 

 offs between both types of error. An- 

 other desirable property of a test is 

 robustness to underlying assump- 

 tions about the populations. For ex- 

 ample, tests commonly carried out to 

 detect changes in population size are 

 based on specific assumptions about 

 the error structure of the estimates 

 (e.g., normality) and the model that 

 would best describe the population 



size as a function of time (e.g., lin- 

 ear, exponential; see, for example, 

 Gerrodette 1987). 



In the case of dolphin stocks in- 

 volved in the tuna fishery in the east- 

 ern Pacific Ocean (EPO), it has been 

 recommended that their management 

 should include both estimates of ab- 

 solute abundance, derived from re- 

 search-vessel data (RVD), and analy- 

 sis of trends in relative abundance, 

 derived from tuna-vessel observer 

 data (TVOD) (IWC 1992:218). In the 

 case of EPO dolphin stocks, the use 

 of TVOD seems the natural choice 

 for analyzing trends, given the vast 

 amount of low-cost information avail- 

 able from the observer programs. 

 However, for this analysis to be ef- 

 fective, it is necessary to obtain abun- 

 dance estimates with a constant bias 

 over the years, or, at least, a bias 

 that shows no trend over the years. 

 Procedures developed by the Inter- 

 American Tropical Tuna Commission 

 (IATTC) to analyze the TVOD, de- 

 scribed in Buckland & Anganuzzi 

 (1988) and Anganuzzi & Buckland 

 (1989), were specifically aimed at re- 

 ducing the magnitude of year-to-year 

 fluctuations in the estimates due to 

 changing biases. These procedures 

 were complemented with more spe- 

 cific analyses when there were rea- 

 sons to suspect that biases might be 

 changing, for example, due to wide- 

 spread use of high-resolution radar 

 for the detection of birds (Anganuzzi 

 et al. 1991). However, in spite of the 

 robustness of the methods, randomly 

 fluctuating biases (an extra source of 



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