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RANGE AND OPTIMUM ANALYSIS Where frequency of occurrence data was not available, the litera- ture sometimes contained information on both the range and optimum conditions occupied by a species based on conditions measured in the field. In other cases, some of the parameters (particularly velocity) were calculated indirectly from measurements and descriptions of the stream reach. Using this method, the portion of the total range of a given param- eter representing optimum conditions was assigned a probabilty of 1.0, and the end points of the total range a probability of O. Abell-shaped curve was then drawn to these four points. Occasionally, information was available which allowed modification of the-curve to indicate skew. In the absence of this type of information, it was assumed that the frequency distribution would be essentially normal between the total range and the optimum (Figure 3). PARAMETER OVERLAP Much of the literature, in particular those studies dealing with ecological succession in streams, describes the fish fauna in terms of the type of habitat most commonly associated with each species. More- over, these studies often describe the degree of use by a species and indicate the type of habitat which is seldom, if ever, used. Given a description (including field-measured and calculated hydraulic parameters) of the types of habitat frequently and seldom used by a species, it is possible to roughly determine the total range and the optimum conditions of a certain parameter for a species. Figure 4 shows the concept involved under the parameter overlap approach. For example, assume a particular species is most commonly associ- ated with habitat type A, but is also found occasionally in habitat types Band C. It is almost never found in habitat type D. The depth range for A is from 3 to 6 feet, for B from 2 to 4 feet, and for C from 1 to 3 feet. The depth range for habitat type D is from 0.5 to 1.5 feet The end point of the range is defined, in this case, as 1.5 feet in depth, while the smallest value for the optimum depth is defined as 3 feet. Thus, parameter overlap simply uses presence-absence informa- tion for habitat types as a tool to define total range and optimum conditions. Curve construction follows the same general procedure as the range-and-optimum technique. 11