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? 0 O.e n.g ; o tt ? ORTH- ; U t , i 0.6 BOVEE 06 t / ? I C7 ' , Z 0.4- +--ORTH OA ' r C7 i / t W 0.2- 02 I BOVEE 0 30 `60 90 120 150 O 30 60 90 120 50 VELOCITY (cm/s) DEPTH (cm) Fir,. 1. Comparison of velocity and depth preference curves for the adult snralltnouth bass from Bowe (1978) (solid lines) and Orth ( 1980) (broken lines). Orth used the term weighting factor. and Bovee used probability. day to day, day versus night. and in response to prey-predators. etc. (Emery 1973; Helfman 1981; Fraser and Emmons 1984). Yet the total number of fish in a stream usually does not change over the period of observations on these normal behavioral responses. It is important for investigators, therefore, to dis- tinguish between distribution (occurrence of a life stage at a location) and abundance (absolute or relative size) of a fish population at a stream reach. A careful evaluation of,the usability of a "preference" or "suitability" curve is necessary. The shape of the curve can he highl% dependent on the site, stream, and time of collection. Consider the velocity and depth suitability curves developed using a similar method for the adult srnallrnouth bass from two different sources in Fig. I . No resemblance is evident, and the optimum "preferred" or "suitable" depth and velocity differ by an order of ma nitude between curves for each variable. rte tanv aceace.1I n ie"{lev lop eat f' re e cecurve rs-tha t e - _ btained. 6onitV eWIalte ;stream a 1 ? cis ee f Z . , uc icon i(ions are rare, at best, especially for high-quality habitats. It is also rare that before initiating a study that the investigators know the carrying capacity of streams or that of a given stretch within a stream. Note Drat only when a suhstantial positive correlation is oh- tained between WUA and fish biomass a posteriori is the fish population considered to be at carrying capacity (Orth and Maughan 1982). Assungptum q independc•nee The derivation of «'UA is based on the assumption that organisms select each habitat variable independently of the other variable(s), Examination of the published analysis shows violation of this assumption. Ill table 1 of Orth and Maughan (1982) Ilse inteviclion lean fur depth r velocity was highly significant (P < 0.01) in three of file four analyses presented. Interaction exists where two factors combine to produce an added effect not due to one of them alone; neither factor individually can show the "best" predictor to optimize the habitat. That is, the suitability of a given depth may depend upon velocity. For example, in the case of central stoneroller, Campostonta anotnalmn. the interaction of depth and velocity explained about 30% of the known variation in abundance of' fish during spring. None of the other variables were significant. Because the two variables (depth and veloci(y) are highly interactive they may not be used to calculate unbiased estimates of WUA under the assumption of independence. Orth and Maughan (1982) belie-,ed this interaction would be of limited significance on their minimum flow reconunenda- tions; a preference for greater depths at greater velocities would be observed. Using the exponential multiple regression models given by Orth and Maughan 0 982) in their table 4, we estimated the response surface for densities of adult central stnneroller at various depths and velocities (Fig. 2). The effe, rs of sir, depth-velocity interaction are obvious; fish densities in,:r.a,: radically with a slight increase in either depth or velocity .Ili h densities of central stoneroller will occur (according to the model) at very low- velocities and ;halloo, depths. In fact. this model suggests that highest densities will occur at no flow. an illogical conclusion that can result when assumption of indepen- dent selection of variables is not met. The violation of the assumption of independen,.e may be more universal than might have been previously believed. Studies by Gore and.ltdfy (1981, and Orth and Maughan 0 983) on benthic organisms also shoe the violation of assumption of independence- =Ai any rate, because depth and velocity are correlated in a.s(re's n (Fraser 1972), it is diffrcull to nwaningfull) ascertain in the field that the' ,?elcction of one habitat variable by fish is independent of the other variable- The basic foundation of 11-IM is the calculation of-WUA at iltcrementa flows and assume. a positive linear reletinn4011 Cm,. J. Fish. Aquat. 5cl.. Vol. 42. 14.rt 82' As%umption of Po.0ive Linear Rolationship of IVU.t and Standing Crop