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Improving the Statistical Power of Length Estimates of Reef Fish: A

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Improving the Statistical Power of Length Estimates of Reef Fish: A 72 Abstract–We calculated the power of Improving the statistical power of length estimates visual length estimates by novice and experienced scientifi c SCUBA divers of reef fi sh: a comparison of estimates determined and estimates generated by a stereo- video system to detect changes in the visually by divers with estimates produced by a mean length of three common species stereo-video system of reef fi sh from New Zealand. Length estimates from a stereo-video system had much greater power for blue cod Euan Harvey (mean length=33.1 cm., range 19.5–50.1 Department of Marine Science cm.) and snapper (mean length=31.7 University of Otago cm., range 23–71 cm.). For a third spe- 304 Castle Street cies, red cod (mean length=42.5 cm., Dunedin, New Zealand range 13–74 cm.), the statistical power Present address: Department of Botany of diver and stereo-video estimates was University of Western Australia much less for an equivalent number Western Australia 6907, Australia of samples owing to the greater vari- E-mail address: [email protected] ation in the true mean length of red cod recorded at different sites. At 90% power, a stereo-video system detected a David Fletcher 15% (~5-cm) change in the mean length Department of Mathematics and Statistics of blue cod with 63% less samples (10) University of Otago than those required by the experienced 539 Castle Street scientifi c divers (27). Novice scientifi c Dunedin, New Zealand divers required 28 samples. Mark Shortis Department of Geomatics University of Melbourne Parkville, Melbourne Victoria 3052, Australia Visual censuses of reef fi sh have been niques: they are quantitative, quick, used to monitor fi sh communities as nondestructive and repeatable (Eng- indicators of environmental degrada- lish et al., 1994). Visual census tech- tion (Hourigan et al., 1988; Fausch et niques have been widely adopted and al., 1990) and as a fi sheries manage- are used to monitor changes in the ment tool for assessing the condition relative abundance or mean length of of reef fi sh stocks (Ault et al., 1998). reef fi sh within marine protected ar- Ault et al. (1998) used data on the aver- eas (Bell, 1983; McCormick and Choat, age length of a fi sh stock as an index 1987; Alcala, 1988; Cole et al., 1990; of fi shing effects. Information on the Francour, 1991, 1994; Russ and Acala, length frequency or mean length of a 1996) and as a tool for assessing the fi sh population when linked with even standing stock or biomass of individual a rudimentary knowledge of the biol- species of reef fi sh (Craik, 1981; Russ, ogy of the species may allow estimates 1985; Medley et al., 1993; Polunin and of recruitment to the adult population, Roberts, 1993; Hart et al., 1996). Bio- fi shing intensity, and rates of recovery mass is estimated from the relationship from fi shing (McCormick and Choat, between length and the weight of an in- 1987). dividual fi sh of a certain species (Kul- Environmental surveys commonly bicki, 1989; Kulbicki et al.,1993). How- use SCUBA divers to count and visual- ever, the question not yet addressed is ly estimate the length of individual reef how useful are data from visual length fi sh (Jones and Chase, 1975; Harmel- estimates for detecting changes in the in-Vivien and Bouchon-Navaro, 1981; mean length or length frequency of a Bellwood and Alcala, 1988; Samoilys, population of reef fi sh? 1989; English et al., 1994). These visu- The advantages of assessing the sta- Manuscript accepted 14 July 2000. al censuses have many advantages in tistical power of environmental moni- Fish. Bull. 99:72–80 (2001). comparison with other sampling tech- toring programs has been discussed by Harvey et al.: Improving the statistical power of length estimates of reef fi sh 73 a number of authors (Green, 1979; Andrew and Mapstone, lowing simple scenario. Suppose we are interested in com- 1987; Gerrodette, 1987; Hayes, 1987; Peterman, 1990a, paring the mean lengths of two fi sh populations and we 1990b; Fairweather, 1991). Statistical power is defi ned as collect length estimates by randomly selecting dive loca- the probability of correctly rejecting a null hypothesis and tions within each site. At each location, the dive involves is 1–β, where β is the probability of a type-II error (An- the visual collection of data from a strip-transect or point- drew and Mapstone, 1987; Gerrodette, 1987; Fairweather, count method to measure the length of each of a number 1991). An example of a type-II error in environmental of fi sh of the species concerned. Later, we will assume that monitoring would be to conclude that no impact has oc- the same numbers of fi sh are encountered on each dive. curred when one has. Therefore, low statistical power can This is clearly unrealistic because the numbers encoun- be disastrous for environmental monitoring because ad- tered will obviously differ: it merely helps to simplify the verse environmental impacts go undetected (Fairweather, discussion of power analysis. The analysis we consider 1991). Despite this problem, few marine ecologists and bi- here involves fi rst transforming the estimated lengths by ologists make use of power analysis (Fairweather, 1991). using natural logarithms, calculating the mean log-length Power analysis has been used to determine the optimum at each location in each site, and then comparing sites by size of sample units and levels of replication needed to a standard t-test, with the locations acting as replicates. detect an effect of a particular size with a desired level The reason for considering log-length rather than length of probability (Andrew and Mapstone, 1987; Gerrodette, is twofold. First, it may be more prudent to perform such 1987; Fairweather, 1991). Power is a function of sample an analysis on the log-scale, for the usual reason of want- size, the probability of a type-I error (α) and the effect size ing to satisfy the assumptions of the t-test. Second, the (Gerrodette, 1987). Fairweather (1991) discussed the is- power analysis can then be framed in terms of our ability sues associated with deciding upon an appropriate level of to detect a percentage change in mean length. As a conse- power. Low power can be attributed not only to the sample quence, the standard allometric relationship between log- design, but also to biases and errors inherent in the sam- length and log-weight (Kulbicki, 1989) implies that the pling method (Andrew and Mapstone, 1987) and power results given here for the power to detect a percentage analysis must account for the uncertainty of measurement change in mean length will also apply to an equivalent error (Gerrodette, 1987). proportional change in mean weight. Historically, reef-fi sh ecologists have failed to calculate The estimated length of fi sh j at dive location i can be and publish the power of their sampling programs. Fur- written as thermore, it is frequently assumed by many researchers that their visual estimates of reef-fi sh length are both yij = xij eij , accurate and precise. In the published literature on reef fi sh studies containing data on visual length estimates, where xij = the true length of the fi sh; and we found only three examples out of forty-three papers in eij = the relative accuracy of the estimate (see St which the authors stated the accuracy of their in situ vi- John et al., 1990). sual length estimates (Sweatman, 1985; Polunin and Rob- erts, 1993; Green, 1996). This equation shows that variation in estimated length The aims of our study were 1) to examine the accuracy will arise from two sources: fi rst, from the natural varia- and precision of length estimates made by a number of ex- tion, both between and within dive locations, of the true perienced and novice scientifi c SCUBA divers, and so de- lengths of the fi sh; second, from the variation, between termine their power to detect changes in the mean length and within dives, in the relative accuracy of the estimate. of populations of three common species of reef fi sh from It is this second component of variation that will be infl u- around New Zealand coastal waters and 2) to demonstrate enced by using stereo-video system as opposed to experi- that the power to detect changes in mean length can be enced or novice scientifi c divers. The relative magnitudes greatly improved for two of the three species by using an of the two sources of variation will determine the benefi ts underwater stereo-video system instead of divers’ visual to be expected from improving the measurement of length. estimates. Thus, if the natural variation in true length is large in The three fi sh species that we consider are blue cod (Pa- relation to the measurement error, there will be little sta- rapercis colias), red cod (Pseudophycis bachus), and snap- tistical benefi t in reducing the latter. per (Pagrus auratus). All three species support commer- On a log-scale this equation can be written as cial trawl (red cod and snapper), long line (snapper), and trap (blue cod) fi sheries. Blue cod and snapper are also the log yij = log xij + logeij. focus of popular recreational fi sheries and thus are impor- tant species in New Zealand. The variation in logxij between and within dive locations can be expressed in a one-way random effects model as Methods and materials log xij = ai + bij , σ2 σ2 To assess the extent to which measurement error will with Var(ai) = a and Var(bij) = b (Sokal and Rolf, 1995).
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