**1. Introduction**

The complexity of estuarine ecosystems is influenced by the broad range and extent of anthropogenic effects in these transitional waters [1,2], including morphological and hydrological alteration [3,4], entrainment of plankton and nekton to water pumps [5,6], contaminants [3,7], introduced species [8,9], and climate change [10,11]. Changes in freshwater flow, natural or otherwise, can perturb the estuarine salinity gradient [12,13], and influence the abundance and distribution of estuarine organisms through a variety of flow-mediated processes (e.g., [9,14,15]). Moreover, estuarine food webs can be sensitive to small variations in the freshwater input [16,17]. Thus, understanding how freshwater flow controls species abundance, their distribution and interactions requires explicit consideration of spatial and temporal scales and abiotic and biotic habitat components. Impaired freshwater flows can diminish the amount of habitat and the habitat quality for estuarine-dependent species [18,19]. Effects of impaired flows on fish populations include reductions in growth [20,21], survival [21], abundance [10,21], and biomass [22]. This highlights the variety of ecological roles freshwater flows may have on the population dynamics and sustainability of estuarine-dependent species.

The identification of specific ecological mechanisms linking species responses to freshwater flow in estuaries remains challenging due to the highly complex nature of such ecosystems [17,23]. In particular, there is a pressing need for analytical tools to evaluate ecological hypotheses in such ecosystems, and to inform adaptive managemen<sup>t</sup> of freshwater flows to conserve fish species at risk of extinction (e.g., [9,24]). Because species interactions are notoriously di fficult to quantify [25], qualitative analysis of the community matrix is particularly suited to model ecological interactions since essential community properties can be determined by ecosystem topology and sign structure of the interactions, rather than by the values of variables and parameters themselves [26–28]. Analysis of qualitative interactions provides a mathematically rigorous foundation for understanding ecosystem behavior [29–31] and has been used in a wide range of aquatic ecosystems to evaluate how community stability and community variables respond to abiotic and biotic perturbations, including, nutrient input in freshwater food webs (e.g., [26,32]); introduced species in freshwater communities (e.g., [30,33]) and environmental disturbance in kelp–urchin communities [34]. Qualitatively models in transitional waters have included evaluations of community responses to dumping of mine wastes in shallow-coastal communities (e.g., [35,36]); and increased ocean acidification in an estuarine community [37]. However, there is a need for further metrics to interpret community responses and to determine whether the predicted influence of a perturbation on a given community variable or species of interest is consistent with field observations.

The upper San Francisco Estuary (hereafter upper SF Estuary; California; Figure 1) is an imperiled ecosystem and the central hub of California's water supply infrastructure [38]. Outflow is the most ecologically important source of freshwater to the SF Estuary and represents the net flow at Chipps Island in the Suisun Region (river km 74; Figure 1) after subtracting water diversions and depletions in the upper SF Estuary and its watershed [6,9]. An ecologically meaningful metric of outflow forcing on the upstream distribution of the salinity field in the SF Estuary is X2, which is defined as the distance (km) from the mouth of the estuary (Golden Gate Bridge), to upstream locations where the near-bottom tidally averaged salinity is 2 psu [39]. The upper SF Estuary is home to several threatened and endangered species including the endemic delta smelt *Hypomesus transpacificus*, an osmerid particularly sensitive to human impacts due to its low fecundity, predominant annual life cycle, and limited spatial distribution [38,40]. Spawning of delta smelt occurs mostly in freshwater during spring and their planktonic larvae tend to gradually move downstream into the low salinity zone (hereafter LSZ, 1–6 psu), [24], where juveniles and subadults generally rear during summer and fall. Despite major long-term changes in pelagic food webs in the upper SF Estuary, calanoid copepods remain one of their most important prey [41]. Delta smelt was listed as threatened (federal and state) in 1993 and up-listed to endangered (state) in 2010 [42].

Understanding the ecological processes underlying the response of delta smelt to fall outflows is relevant to adaptive managemen<sup>t</sup> in the upper SF Estuary [24,43], and such managemen<sup>t</sup> actions are intended to improve fall habitat of delta smelt when preceding precipitation and runo ff conditions result in high outflows [43]. Outflow controls the location and range of the LSZ (Figure 1), the extent of the abiotic habitat available for subadult delta smelt [10,44], and the position of X2 which controls the upstream distribution of subadult delta smelt during the fall [45]. Nevertheless, because X2 has not been found to be a simple predictor of delta smelt abundance, the need to investigate more complex mechanisms or additional variables has been suggested [39,44]. The high outflows observed in the upper SF Estuary during 2011 prompted monitoring of abiotic and biotic factors, which along with long-term monitoring in the SF Estuary, enabled the performance of interannual comparisons of abiotic and community responses to changes in the position of fall X2 [24]. Although several of the predicted abiotic and biotic responses in that study could not be confirmed from available field data, the abundance of delta smelt in 2011 and early 2012 was one the highest reported since the early 2000s. Yet, delta smelt became very rare during the 2012–2016 drought and failed to increase its abundance during the wet year 2017, indicating the need to evaluate new managemen<sup>t</sup> options (e.g., [7,9,46]).

Given the complex abiotic and biotic responses to fall outflow in the upper SF estuary [24,38], there is a pressing need for further analytical approaches to evaluate how outflow controls the essential community structure and functional group interactions influencing delta smelt in the LSZ

under particular outflow scenarios (hereafter delta smelt subsystems), and to investigate the likely mechanisms controlling the population response of delta smelt in different subsystems (Figure 1).

**Figure 1.** The San Francisco Estuary showing the Suisun Bay and Delta regions in the upper estuary. Dashed lines denote the positions of the 2 psu isohalines (X2) considered in community models (74, 81, and 85 km) and the range of the average X2 position in September–October (64–94 km) from 1967 to 2017. Map adapted from [24].

The objectives of this study were to evaluate: (1) the stability of the delta smelt subsystems in the LSZ when fall outflows are alternatively maintained at low-, mid-, and high-X2 positions corresponding to 74, 81, and 85 km, (2) the predicted direction of change and its uncertainty for the abundance of delta smelt and other species and trophic levels in each subsystem under four outflow input scenarios, and (3) whether field patterns of relative abundance for delta smelt and X2 are consistent with the predictions of community models. Three community metrics were adapted to model the response of delta smelt and other community variables to outflows, first, the weighted prediction matrix [47] was modified to denote both the direction of change and its uncertainty in a signed weighted prediction matrix (*Ws*), second, a modified community matrix specifying press inputs (*A<sup>P</sup>*) was used to estimate the combined effect of outflow press perturbations on two or more community variables, and third, the proportional net change of adjoints in the negative community matrix (Δ*p*ˆ) was used as a measure of the determinacy in the direction of change of variables in quantitative simulations. Finally, statistical relations between the field relative abundance of subadult delta smelt and X2 enabled to evaluate the predicted population response of delta smelt in each of the modeled subsystems.

### **2. Material and Methods**
