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INSTREAM FLOWS TO ASSIST THE RECOVERY OF ENDANGERED FISHES 27 but also see Morhardt 1986), of the regulated flows to the historical flow regime that occurred on the average. This approach to habitat optimization, though still widely used (Reiser et al. 1989a), does not consider the importance of flow variation and its complex relation to channel geomorphology. Statistical Approaches Many studies have attempted, with varied suc- cess, to statistically relate some measures of the biophysical attributes of rivers and streams to the disturbance effect of flow variation. Most of these studies are basic science, where the intent was to document aspects of the structure and function of stream ecosystems with respect to flow changes. Much of the work was focused on demonstration of relationships between the distribution, abun- dance, and behavior of aquatic biota and important physical variables using various regression and multivariate analyses in natural (regulated situ- ations compared with unregulated controls) and experimental designs (experimental manipula- tions designed to simulate flow effects; cf., Kroger 1973; Reice 1985; Perry et al. 1986, among many others). However, very few studies actually dem- onstrate a statistically valid relationship between biomass or some other abundance measure and flow variables that apply to different streams or even different stream segments. Morhardt (1986) reviewed and annotated 72 studies that attempted to derive a general instream flow model that would accurately predict productivity related to flow vari- ables in different streams. Only one (Binns and Eiserman 1979) produced a statistically valid re- sult, and Morhardt (1986) concluded that was be- cause the streams were in the same region and were biophysically very similar. Armitage (1989) was able to predict the occurrence and biomass of macroinvertebrates from a suite of environmental variables using gradient analysis (TWINSPAN) in regulated streams in England. But, again, these streams are homogeneous compared with the large rivers of the Upper Colorado River Basin, and the distribution of zoobenthos in English rivers, which have been regulated for centuries, is well known. In small streams where flow processes are rela- tively uniform (nonstochastic) and distribution and abundance of biota are well known, relation- ships can be demonstrated with statistical accu- racy and precision. Detailed presentations of the science of stream ecology with respect to the effects of flow and hydraulics were given by Resh et al. (1988) and Statzner et al. (1988). In rivers that are large and complex most studies are site specific by design because unbiased repli- cation of sites across streams is difficult, if not impossible, owing to the stochastic nature of large rivers. In fact, replication within a stream segment is difficult because flow mechanics produce so many different microhabitats that it is almost impossible to take enough samples to describe biotic distribu- tions. Pseudoreplication is a problem in many stud- ies. All streams are ecologically different, and therefore mechanistic models must compromise re- ality to gain generality. The alternative is essen- tially a trial and error approach. In other words, multivariate analyses may show that certain flow variables influence biotic productivity in a regu- lated stream; therefore, a particular flow pattern should optimize productivity. The only way to verify that prediction is to implement the flow regime and monitor productivity. Incremental Flow Modeling Despite the inherently variable nature of lotic ecosystems, the need to describe continuous func- tions between flow and habitat is widely perceived, along with the assumption that aquatic biota in rivers are primarily limited by availability of physi- cal habitat. Physical variables, such as tempera- ture, velocity, size of gravel, cover, and so forth, obviously vary with flow. So models were developed in an attempt to describe change in these habitat variables in increments of flow. This vastly more complicated approach still implies, incorrectly per- haps, that as habitat increases so will fish carrying capacity and hence fish populations. By far the most used (Reiser et al. 1989a) and most sophisticated incremental method is that de- veloped by the U.S. Fish and Wildlife Service (Bovee 1982). This method is called the Instream Flow Incremental Methodology (IFIM) and is a collection of computer programs and analytical pro- cedures designed to predict changes in fish or in- vertebrate habitats in a "representative" stream reach due to flow changes. The IFIM has three major components: (1) transects across a "repre- sentative" reach are divided into cells (intervals) in which depth, velocity, cover value, and often sub- stratum roughness or quality are measured or simulated. These variables are assumed to be inde- pendent of one another; (2) the ranges of velocities, depths, and cover or substratum used by the biota are determined by relating occurrence of various life history stages (e.g., YOY, juveniles, adults, spawners) of target species to "hydraulic" variables.