Lindley et al.: Application of statistical power analysis to recovery of an endangered species 



765 



the river for spawning at age 3 or age 4, and although 

 approximately 90% of a brood's spawning adults do so at 

 age 3 (Fisher, 1994), this means that there is imperfect 

 temporal isolation between runs in adjacent years. It is 

 plausible that an environmental factor occurring in a par- 

 ticular spawning year could affect the returns in several 

 future years, creating a lack of independence among obser- 

 vations. Such autocorrelation would decrease the effective 

 sample size. Under this scenario, any test based on the 

 nominal sample size (number of years of data) would have 

 increased levels of both type-I and type-II errors (Lehm- 

 ann, 1986). Given the relatively low level of information 

 available on this population, this consideration is second- 

 ary and can be evaluated more thoroughly as the data base 

 increases. The current time series of IrJ values shows no 

 significant autocorrelation (P>0.05), which suggests that a 

 lack of independence is most likely not a serious issue. 



Choice of S and a 



In any hypothesis test, one must specify the type-I and 

 type-II error rates. The choice of these rates should reflect 

 the relative costs, as perceived by the investigator, of 

 making these errors (Toft and Shea, 1983). When these 

 costs can be specified in advance, and in comparable terms, 

 one can balance them explicitly through specification of 

 a and n (Mapstone, 1995). However, in the case of our 

 proposed winter chinook salmon monitoring protocol, the 

 cost of making a type-I error is unknown (no specific 

 actions have yet been associated with a rejection of the 

 null hypothesis), whereas type-II errors may be associated 

 with extinction. We believe the appropriate course in this 

 situation is to first identify growth rates that lead to unac- 

 ceptably high probabilities of extinction, fix the power ;rof 

 detecting these growth rate levels at a suitably high level, 

 and accept, within reasonable limits, the resulting type-I 

 error rate a Specifically, for the winter chinook salmon 

 monitoring protocol, we have specified an 80'/( chance of 

 detecting growth rates that would lead to a >5% chance of 

 quasi-extinction in 50 years, and accept the corresponding 

 type-I error rate. We have selected these values because 

 they are consistent with suggestions in the literature 

 (reviewed briefly below); resource managers should care- 

 fully consider whether they are appropriate. 



Setting 5 by way of p that leads to an unacceptable pre- 

 dicted extinction risk, as we have done, is natural in the 

 current setting, but just what level of extinction risk should 

 be of concern is debatable. Population viability models have 

 been widely used in consei-vation biology to quantify extinc- 

 tion risk as a function of population size and the magni- 

 tude and variability of population gi-owth rate (Beissinger 

 and Westphal 11998] have provided a recent review). Shaf- 

 fer (1981), in pioneering work on minimum viable popu- 

 lations, has tentatively suggested that viable populations 

 should have at least a 99*7^ chance of remaining extant 

 for 1000 years, but stated that specific probabilities and 

 time horizons are arbitrary, and other values might be 

 more appropriate. Indeed, other studies have used a vari- 

 ety of criteria: Botsford and Brittnacher (1998) used a 

 0.10 extinction probability in 50 years to develop criteria 



for removing winter chinook salmon from the Endangered 

 Species List; Shaffer and Samson (1985) used the criteria 

 of a 0.05 extinction probability over 100 years to identify a 

 minimum viable population size for grizzly bears. We have 

 adopted the 0.05 probability of extinction over 50 years as 

 a moderately conservative criterion. 



Specifying the value of n is also somewhat arbitrary. 

 Peterman and M'Gonigal (1992) contend that monitoring 

 programs must have high power (;r>0.8) to detect biologi- 

 cally important effects in order to be reliable. A reliable test 

 should also have a reasonable a value as well as sufficient 

 power In the proposed winter chinook salmon protocol, the 

 a-level stabilizes at 0.11 after 5 years of data have been col- 

 lected, and we feel that this behavior represents a reason- 

 able balance between the type-I and type-II error rates. 



Power analysis and the precautionary approach 



With the decline, collapse, or endangerment of numerous 

 fish populations around the world, the paradigm of precau- 

 tionary fishery management is receiving increasing atten- 

 tion. The "precautionary approach" to fishery management, 

 as developed by the Food and Agriculture Organization of 

 the United Nations (FAO, 1996), strives to avoid irrevers- 

 ible or slowly reversible damage to fisheries, places prior- 

 ity on conservation of productive capacity, and requires that 

 fishing activities be considered harmful unless proven oth- 

 erwise. The reauthorization of the U. S. Magnuson-Stevens 

 Fishery Consei-vation and Management Act (as amended 

 through October 11, 1996) is meant to ensure that "irrevers- 

 ible or long-term adverse effects on fishery resources and 

 the marine environment are avoided." 



Peterman and M'Gonigal ( 1992) have argued that power 

 analysis is a fundamental part of precautionary manage- 

 ment, because it provides an estimate of the reliability of 

 the monitoring program. There are four types of power 

 analysis, which correspond to determining one of either n, 

 K. a, or the effect size from the other three (Cohen, 1977). 

 In environmental studies, the determination of n and n 

 are fairly common (e.g. Gerrodette, 1987; Gryska et al., 

 1997; Urquhart et al., 1998). The determination of a, as 

 we have done here, is least common, in part owing to the 

 "strength of the significance criterion convention, which 

 makes investigators loath to consider "large" values of a" 

 (Cohen, 1977). 



Type-II errors in fisheries management are costly be- 

 cause populations and ecosystems can be slow to recover 

 (Dayton, 1998). In endangered species management, the 

 biggest risk is extinction of a species, rather than failure 

 to meet some fiscal or harvest goal, and is truly irrevers- 

 ible. Fixing the type-I error rate at a typical value such as 

 0.01 or 0.05 would make timely detection of dangerously 

 low growth rates unlikely (Table 1; Peterman, 1990). Thus, 

 we believe that using standard statistical protocols, which 

 control for the type-I error rate and accept the resulting 

 type-II error rate, is not an appropriate method when 

 monitoring endangered species. In such situations, it is 

 more logical, and certainly more precautionary, to set the 

 type-II error rate at an acceptably small value that yields 

 a reasonable type-I error rate. 



