# River-Wide Habitat Availability for Fish Habitat Guilds: Implications for In-Stream Flow Protection
## 2 Materials and Methods
### Guild Specific Habitat Suitability  
We used multiple logistic regression models to compute habitat selection for fish habitat guilds. The habitat characteristics collected at each HMU where a PAE was located were the independent variables and the presence and abundance of representatives of the fish habitat guilds were the dependent variables. Habitat characteristics used in the model were those measured during the habitat mapping survey (discussed above). We employed a stepwise forward logistic regression model to identify the habitat characteristics that were used for each fish guild. We used Akaike's information criteria (AIC) to determine which habitat characteristics were included in the regression formula:  
\[R=\ e^{-z}, \tag{1}\]  
\begin{table}
\begin{tabular}{c c c} \hline
**Guild Name** & **Guild Members** & **Guild Description** \\ \hline \multirow{6}{*}{Lobate Margin} & Bigmouth shiner, _Notropis dorsalis_ & \\  & Red shiner, _Cyprindul Intrensis_ & \\  & Plains topminnow, _Fundulus sciadicus_ & \\  & Fathead minnow, _Pinphales promelas_ & \\  & Brook Stickleback, _Culaen incostans_, Age 0 & \\  & Channel catfish, _Iclaturus punctatus_ & \\  & & \\  & Sand shiner, _Notropis stramineus_ & \\  & Emerald shiner, _Notropis atthernioides_, & \\  & Brassy minnow, _Hybgnathus hankinsoni_, & \\  & Central stoneroller, _Campostoma anomlum_ & \\  & Longnosse dace, _Ritinichthys cataractate_, River & \\  & shiner, _Notropis biemuis_ & \\  & & \\  & Largemouth bass, _Microterus suloides_, & \\  & Bluegill, _Leponis macroclirus_, Green surfish, _Leponis cyanellus_, Yellow perch, & \\  & _Perca flawescens_ & \\  & White sucker, _Catostomus commsornii_, Creek & \\  & chub, _Semotilus atromaculatus_, Shorthhead & \\  & redhorse, _Maxostoma macroplidatum_, Age 0 & \\  & River corpsucker, _Carpiodes carpio_ & \\ \hline \end{tabular}
\end{table}
Table 1: Description of fish guilds determined for the Niobrara River using empirical fish species data collected within hydromorphologic units using prepositioned area electrofishing. Detail of guild formation is available in [PERSON] et al. [23].  
where \(e\) is the natural-log base and \(z=b1\times 1+b2\times 2+\dots+bn\cdot xn+\) a (\(xn\) are the habitat characteristics, \(bn\) are the regression coefficients, and \(a\) is the constant). We included HMUs where fish were caught to distinguish suitable habitat from unsuitable. In a second model, we classified fish habitat guilds as either low or high abundance in each HMU. We calculated guild specific cut-off values for low or high abundance from observed abundances within HMUs. The logistic regression functions highlighted environmental attributes that significantly corresponded with fish habitat guild presence and abundance and the regression coefficients indicated the strength and direction (+ or -) of the association. We calculated the probability of guild presence or abundance for each HMU using the regression equations and the following formula:  
\[P=\ \frac{e^{z}}{1+e^{z}}, \tag{2}\]  
where \(P\) is the probability of presence or high abundance, \(e\) is the constant, and \(z=b1\times 1+b2\times 2+\dots+bn\cdot xn+\) a. We used receiver operating characteristic (ROC) curves to assess predictive ability for the presence and abundance models. The area under the ROC curve defines the discrimination capacity of the model based on Mann-Whitney statistics [24]. The inflection point on the ROC curve defines the probability (\(Pt\)) that has the highest true positive rate and lowest false positive rate and, thus, the best separation of occupied and not occupied areas. We determined separate \(Pt\) values for the presence and abundance models. We used the resulting \(Pt\) thresholds to determine suitable habitats as those that had presence \(>Pt\) and optimal habitats as those that predicted high abundance \(>Pt\). Each HMU was assigned to unsuitable, suitable, or optimal categories. We quantified the amount of suitable habitat at each target discharge as a proportion of the river channel area.