*2.6. Statistical Analyses*

To determine the extent to which the predicted response to outflow input by each variable in qualitative models represented the overall direction of change in quantitative simulations, Δ*p*<sup>ˆ</sup> was plotted vs. *Adj* − *A* for all scenarios at each X2 position. Values of Δ*p*<sup>ˆ</sup> were also plotted vs. *Ws* to compare the direction of change and uncertainty between qualitative and quantitative predictions. These variables were fitted at each X2 position using Lowess smoothing. The predicted population response for subadult delta smelt by community models at each X2 position was compared with the relative abundance for subadult delta smelt as a function of X2 to evaluate model predictions. Relative abundance data for subadult delta smelt, monitored since 1967, was obtained from the California Department of Fish and Wildlife's Fall midwater trawl index for the period 1967–2017 [97]. The average position of X2 during September–October was derived from the California Department of Water Resources Dayflow program [51]. Linear regression analysis was used to evaluate the slope of the relative abundance for delta smelt during fall (Y) versus the average X2 position in September–October (X). Regressions were conducted for three ranges of X2, which included the three X2 positions in community models (X2 ≥ 74, ≥81, and ≥85 km). The entire historical record of subadult delta smelt abundance as a function of the average September–October X2, was further considered as a baseline relative to the three X2 positions evaluated in the present community models and a previous fall

outflow evaluation [24]. Data were analyzed and plotted using Curve Expert Professional (version 2.6; D.G. Hyams).
