*3.1. Community Stability*

Compared to the models at the low X2 position, the modeled communities at the mid- and high-X2 positions included a higher number of introduced species and more non-trophic interactions (Figure 3, Appendix A). Although all qualitative community models were stable, the percent of stable simulations decreased greatly from downstream (low X2) to upstream (high X2) positions in the LSZ, and such decrease in stability seemed primarily due to the increasing percent of models with stronger high-level feedbacks than low-level feedbacks at the mid- and high-X2 positions (Table 2).

**Figure 3.** Alternative fall community models for the Delta smelt subsystem under three scenarios of the salinity field in upper San Francisco Estuary. Dashed arrows show where the low salinity zone overlaps the position of the 2 psu isohaline (X2) at (**A**) high X2 (85 km), (**B**) mid X2 (81 km), and (**C**) low X2 (74 km) at low-, mid- and high-outflow, respectively. Community variables included in signed digraphs: CF = *Corbicula fluminea*; DS = Delta smelt; ED = *Egeria densa*; MA = *Microcystis aeruginosa*; PA = *Potamocorbula amurensis*; PH = phytoplankton; PR = predators of delta smelt; ZO = zooplankton. Salinity field after [75].


**Table 2.** Percent of quantitative community models meeting zero, one and both Routh–Hurwitz (R–H) stability criteria at three X2 positions in the low salinity zone of the upper San Francisco Estuary (based on 10,000 simulations at each X2 position).

### *3.2. Community Response to Outflow*

The predicted change in abundance for delta smelt and other community variables to outflow input varied greatly among the three X2 positions (Figure 4), both in the case of qualitative models (Figure 5) and simulations (Figure 6). In response to outflow input for the delta smelt subsystem at the low X2 position (Figure 4), the predicted direction of change in the abundance of all community variables was positive, except for the clam *P. amurensis*, with predicted responses of species and trophic levels generally showing high sign determinacy, particularly for delta smelt, its predators, and zooplankton across most outflow input scenarios (Figures 5 and 6). Outflow input at the mid X2 position (Figure 4), revealed the cyanobacterium *M. aeruginosa* was the only community variable with a consistently negative response and high sign determinacy in both qualitative models and simulations. Yet, the clam *C. fluminea* and predators of delta smelt showed high sign determinacy under most quantitative simulation scenarios at the mid X2 position (Figures 5 and 6).

The cyanobacterium *M. aeruginosa* suggested a negative response to outflow at the high X2 position (Figure 4), but to a lower extent compared to the mid X2 position (Figures 5 and 6). The Brazilian waterweed, *E. densa* was the only other variable at the high X2 position indicating high degree of qualitative sign determinacy but only at one outflow scenario (Figure 5). In contrast, simulations at the high X2 position indicated all the predicted responses of community variables had low sign determinacy (Figure 6).

The relation between Δ*p*<sup>ˆ</sup> and *Adj* − *A* indicated the predicted direction of change for species and trophic groups in response to outflow input was generally consistent between qualitatively and quantitatively specified subsystems at each X2 position; this despite a plateau in Δ*p*<sup>ˆ</sup> was towards its highest values (Figure 7A). As inferred from Δ*p*<sup>ˆ</sup> and *Ws*, the direction of change and degree of certainty in the direction of change in quantitatively specified simulations were associated with the corresponding qualitative model, with such relations appearing progressively more sigmoidal toward higher-X2 positions (Figure 7B).

Direction of change in parentheses

asterisk), and ? denotes complete ambiguity.

 denote

**Figure 4.** Signed digraphs of the modeled delta smelt subsystems at three positions of the 2 psu isohaline (X2) in the upper San Francisco Estuary. Dashed lines indicate the four alternative outflow (FL) input scenarios for community variables. Dashed lines in scenario 1 represent outflow perturbations to *Corbicula fluminea* (CF), *Egeria densa* (ED), *Microcystis aeruginosa* (MA), and *Potamocorbula amurensis* (PA). Dashed lines in outflow scenarios 2, 3, and 4 cumulatively add outflow perturbations to phytoplankton (PH, scenario 2), zooplankton (ZO, scenario 3), and delta smelt (DS, scenario 4). PR denotes predators of delta smelt. Community variables show the predicted direction of change in abundance (<sup>+</sup>, −) inresponsetosustainedoutflowinput.Directionofchangewithoutparenthesesisunconditional.

high-certainty

 (asterisk) and

low-conditional

 certainly (no

**Figure 5.** Predicted direction of change and its uncertainty for community variables based on signed weighted predictions (*Ws*) at low-, mid-, and high-X2 positions under outflow–input scenarios (1–4, Figure 4). Values of |*Ws*| for each community variable range between unconditional sign determinacy (1) and complete uncertainty (0), with |*Ws*| between 0.50 (dotted line) and ≤1 indicating high sign determinacy.

**Figure 6.** Predicted direction of change of community variables for low-, mid-, and high-X2 positions based on the difference between the proportions of quantitative simulations with positive and negative *Adj* − *A* (Δ*p*ˆ). Acronyms represent species or trophic groups (Table 1, Figure 3) and legend denotes the four outflow input scenarios (Figure 4). Values of |Δ*p*<sup>ˆ</sup>| can range between 1 (unconditional sign determinacy) and 0 (complete uncertainty), with |Δ*p*<sup>ˆ</sup>| between 0.5 (dotted lines) and <1 implying low uncertainty in the predicted direction of change.

**Figure 7.** Relations between the net proportion of positive and negative *Adj* − *A* in stable quantitative models (Δ*p*ˆ) at low-, mid-, and high-X2 positions and: (**A**) the estimated direction of change of corresponding variables in qualitative models (*Adj* − *A*); (**B**) the signed weighted feedback in qualitative models (*Ws*), as indicated for modeled subsystems in the low salinity zone at low-, mid-, and high-X2 positions.

### *3.3. Delta Smelt Abundance and X2*

When only considering years in which the average position of X2 in September–October was located at 81 km and further upstream, the relative abundance of subadult delta smelt was not associated to the position of X2 (Figure 8). However, when all years in which X2 was located at 74 km or further upstream were included, the relative abundance of subadult delta smelt was inversely associated to the average position of X2 in September and October (Figure 8). Moreover, when considering all the years with available relative abundance for subadult delta smelt over the period 1967–2017, an inverse association between the relative abundance of subadult delta smelt and the average position of X2 during September–October was also detected, and such relation included X2 positions as low as 65 km (Figure 8).

**Figure 8.** Relative abundance for subadult delta smelt based on the fall midwater trawl (FMWT) index (Y) versus the average position of the 2 psu isohaline (X2) during September and October (X) under four ranges of X2 over the period 1967–2017. Dark and light shaded areas denote 95% confidence intervals for regression lines and predicted values, respectively. Regression coefficients in bold type are significant (P < 0.05).
