Species Habitat Suitability Criteria 



Previous investigators'^'^,!', is treatment of fish habitat criteria have assumed 

 statistical independence among variables used in describing the preferred instream 

 station (focal point) and spawning requirements comprising microhabitat condi- 

 tions. Although this assumption has permeated instream flow literature for 10 years 

 without challenge, the IFG«has focused attention upon the mathematical theory 

 responding to an expressed need for critical examination of this general assumption. ^^ 



Bovee and Cochnauer^^ and Bovee'" assembled information relating the observa- 

 tions offish types (including life stages as well as species) to the stream attributes of 

 velocity, depth, and substrate. Water quality was observed (and in some cases 

 inferred from other information) to be within suitable ranges so as not to affect the 

 distribution of the fish. The field data included values of the attributes for each 

 observed fish. However, no data were collected for^attributes where fish were not 

 observed, i.e., avoidance. 



Univariate functions were obtained by fitting histograms of the data with piecewise 

 linear curves. Due to the nature of the data available, the assumption of 

 independence among variables was unavoidable. Joint suitability, (p(\), of a 

 particular combination of variables was approximated by the product of the 

 marginal distribution functions: 



i0(x) = f(v)«f(d)«f(s) 



where: 



f(v) = the marginal suitability function for velocity, integrated over all depths and 



substrates, 

 f(d) = the marginal suitability function for depth, integrated over all velocities and 



substrates, and 

 f(s) = the marginal suitability function for substrate, integrated over all velocities 



and depths. 



The assumption of variable independence was tested by Voos,^^ Prewitt,^^ and 

 Gore and Judy.^^ Prewitt concluded: 



". . .in the more complex environments, WUA [weighted usable area] 

 appeared to be quite stable across a broad range of discharges, p^ values 

 [depth, velocity, substrate interactions], and preference curves supporting 

 the hypothesis that with these complex stream physical habitats, the uni- 

 variate approach effectively duplicated results of the multivariate ap- 

 proach." 



Although the correlation coefficients from these studies were small, some statistically 

 significant correlations were found. Therefore, future field studies should be 

 conducted so as to describe these correlations (cross products) where practicable. 



In addition to the lack of evidence indicating strong dependencies, there are 

 advantages for estimating (//(JU) from the product of the marginals. Because of the 

 irregular shape of the function, none of the standard multivariate statistical 

 distributions appear to model all of the shapes observed from the data. Defining the 

 joint distribution in terms of the marginals allows the use of completely general, 

 piecewise linear functions. Also, fishery scientists have a wealth of experience 

 regarding the behavioral and physiological characteristics of fish in response to 

 depth, velocity, substrate temperature, and other factors. This subjective information 

 can be directly included in the joint function 0(^) by controlling the form of the 

 marginals. Consequently, habitat evaluations can incorporate the best judgment of 

 fishery scientists. 



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