# Modeling the Influence of Outflow and Community Structure on an Endangered Fish Population in the Upper San Francisco Estuary

## Abstract

**:**

## 1. Introduction

## 2. Material and Methods

#### 2.1. Study Area

^{2}when X2 is positioned at 74 km, 50 km

^{2}when X2 is positioned at 81 km, and 40 km

^{2}when X2 is positioned at 85 km [24]. Altered fresh water outflow in the upper SF Estuary has greatly changed the abiotic habitat for pelagic fishes [9,54], and facilitated the introduction of species [60,61]. A high proportion of pelagic and planktonic organisms in the upper SF Estuary are also lost due to prevailing upstream flows in the south Delta caused by massive water pumps [5,6]. As is the case of the lower SF Estuary, most communities in the upper SF Estuary are dominated by introduced species [61,62]. The introduced macrophyte Egeria densa was first reported in the Delta in 1946 [63] and became the most abundant submersed plant in the Delta, where it has greatly altered community structure and functions [58,64,65]. The introduction of the clam Potamocorbula amurensis in the late 1980s caused major trophic changes in the benthic and pelagic communities of the SF Estuary [60,66], greatly adding to the filter feeding activity of the clam Corbicula fluminea, an earlier introduction in the upper SF Estuary [67]. In addition, the cyanobacterium Microcystis aeruginosa was first observed in the Delta in 1999 [68] and produces toxic algal blooms that can be harmful to upper trophic levels [69,70].

#### 2.2. Community Matrix Models

_{i}), the change in the equilibrium level of species n

_{i}

^{*}is

_{i}represent species abundances or abiotic factors. The c

_{i}are parameters that govern biological rates (e.g., birth, mortality, growth), and depend on the species and environment [72,73]. Modeled subsystems were represented by a signed digraphs, where element a

_{ij}of a qualitatively defined community matrix (A

^{o}) of order n denotes the net effect to variable i from variable j (for i and j from 1 to n). For example, a subsystem composed of three trophic levels can be represented by three variables and their interactions (Figure 2). Three possible qualitative effects to variable i from variable j were assigned to each matrix element: a

_{i,j}= 1, a

_{i,j}= −1 and a

_{i,j}= 0, which in the neighborhood of any equilibrium point respectively denote positive, negative, and no effect on the instantaneous growth of variable i due to increase in the level of variable j. The stability of the community matrix was evaluated using the characteristic polynomial:

^{o}− λI| = a

_{0}λ

^{n}+ a

_{1}λ

^{n}

^{− 1}+ a

_{2}λ

^{n}

^{− 2}+ … a

_{n}= 0

^{o}is as defined earlier, I is the n-dimensional identity matrix, and λ are the roots or eigenvalues [71]. Following a perturbation, negative real roots means the community can return to equilibrium. Conversely, positive real roots indicate the ecosystem moves away from equilibrium, as in unstable ecosystems. Multiple zero roots can result in unstable equilibrium [73], and zero overall feedback indicates neutral stability [74].

#### 2.3. Community Structure and Outflow Scenarios

- (1)
- Compilation of long-term data and studies in the upper SF Estuary, including: monitoring data for delta smelt and other species [53], outflow and X2 data [51], interpretation of the spatio-temporal distribution of the salinity field in the LSZ based on the three-dimensional UnTRIM hydrodynamic model for the upper SF Estuary [24,75], and baseline knowledge of the modeled ecosystem (e.g., [6,10,39,40,54,55,63,76,77]).
- (2)
- Consideration of dynamic and stationary factors for developing conceptual models of estuarine communities [78], where dynamic factors include physico-chemical and biological characteristics of the low salinity habitat corresponding to the LSZ each X2 position, and stationary factors include geographically fixed habitat features at each X2 position such as substrate, erodible sediment, and bathymetry in the low salinity habitat [24,38].
- (3)
- Refinement of conceptual models into different subsystems describing the essential community variables influencing subadult delta smelt based on ecological syntheses of long-term field data and studies [24,38]. Community variables selected for each of the three modeled subsystems were based on functional groups (e.g., [74,79]), and their predominant spatio-temporal overlap with dynamic and stationary abiotic and biotic factors. Except for delta smelt and species with significant ecological impacts (the cyanobacterium M. aeruginosa [80], the clams P. amurensis and C. fluminea [56], and the macrophyte E. densa [58], Table 1), other functional groups included trophic levels to minimize redundant species interactions (e.g., [74,81]), (Table 1).
- (4)
- Reformulation of conceptual models into signed digraphs based on qualitative model guidelines (e.g., [71,79,93]). Negative self-effect (self-damping) was assumed to arise for each variable from density-dependent growth rate or a limited source, as in the case of nutrients [71]. Each community variable was then implicitly connected to other variables or abiotic factors through negative feedback [71,74]. Reported community interactions considered for the modeled subsystem included: predation (+, −); interference competition (−, −); and amensalism (0, −), (Appendix A).
- (5)
- Estimation of the direction of change of community variables (+, 0, −) in response to increased outflow (Table 1). Four outflow input scenarios were modeled, with the first scenario accounting for the effect of outflow on the previously referred species having significant ecological impacts. The outflow inputs for the three subsequent scenarios were used to evaluate whether cumulative outflow inputs in each subsystem could reinforce or reverse potential responses on delta smelt and other community variables. These scenarios included: scenario 1 + phytoplankton (scenario 2), scenario 2 + zooplankton (scenario 3), and scenario 3 + delta smelt (scenario 4).

#### 2.4. Qualitative Analyses

_{h}), on the rate of change of a hth variable corresponding to the jth variable in the community matrix was predicted assuming an ecosystem in moving equilibrium [29,71]. Such input could result in positive, negative, or no effect on the equilibrium magnitude or carrying capacity (N

_{i}

^{*}) of a species. The inverse of the negative community matrix (−A

_{ij}

^{−1}) provides an estimate of change in the equilibrium level of variable N

_{i}

^{*}carrying capacity due to change in parameter C

_{h}[95].

_{ji}

^{T}is the adjoint of the negative community matrix (Adj − A

_{ij}), and |−A

_{ij}| is the determinant of the negative community matrix. Since |−A

_{ij}| is constant and positive for each element of −A

^{−1}in stable ecosystems, the predicted response under local equilibrium was inferred from the Adj − A:

_{k}) due to a disturbance k acting directly upon two or more variables, the combined effect of P

_{k}on the direction of change for community variable i and their corresponding uncertainty level was computed from the corresponding matrix element Ws

_{ik}(Equation (5)) and these were derived from a modified community matrix specifying press inputs (${A}^{P}$):

_{11}to a

_{nn}represent the interaction elements a

_{ij}of community matrix A

^{o}, and P

_{ik}denotes the press input k on community variable i, which in a qualitatively defined ecosystem is specified as having positive (1), negative (−1) or no effect (0). The last row of matrix ${A}^{P}$ includes zero elements to denote no effect of community variables on P

_{k}, and a negative element (−1) to preserve the stability of matrix ${A}^{P}$ provided the community matrix A

^{o}is stable. Qualitative analyses were conducted in Maple 18 [47].

#### 2.5. Quantitative Simulations

_{ik})* and f(−Adj − A

_{ik})* respectively denote the absolute frequencies of positive and negative Adj − A

_{ik}in stable matrices, and N is the total number of simulations for each perturbation scenario, including stable and non-stable matrices (N = 10,000). As in the case of Ws, the value of Δ$\hat{p}$ provided both the overall direction of change and its uncertainty for each community variable, with extreme potential values (Δ$\hat{p}$ = −1, negative response and Δ$\hat{p}$ = 1, positive response) both indicating no uncertainty in the direction of change among simulations, Δ$\hat{p}$ ≥ |0.5| and < |1|indicating low uncertainty, and Δ$\hat{p}$ = 0 denoting total uncertainty. Quantitative simulations were performed in a program written in C# version 3.0 [96].

#### 2.6. Statistical Analyses

## 3. Results

#### 3.1. Community Stability

#### 3.2. Community Response to Outflow

#### 3.3. Delta Smelt Abundance and X2

## 4. Discussion

#### 4.1. Community Stability

#### 4.2. Community Model Predictions

#### 4.3. Delta Smelt Abundance under Different Ranges of X2

#### 4.4. Community Models and Prediction Metrics

#### 4.5. Management Implications

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Table A1.**Qualitative interactions for modeled community variables defined in Table 1 at the high-, mid-, and low-X2 positions in the upper San Francisco Estuary. (References shown in parentheses).

High-X2 Variables | DS | ZO | PH | ED | PR | CF | MA |

DS | −1 [71] | 1 [41] | 0 | −1 [64] | −1 [92] | 0 | −1 [70] |

ZO | −1 [41] | −1 [71] | 1 [113] | −1 [114] | 0 | 0 | −1 [69] |

PH | 0 | −1 [113] | −1 [71] | −1 [85] | 0 | −1 [115] | −1 [80] |

ED | 0 | 0 | 0 | −1 [71] | 0 | 1 [116] | −1 [117] |

PR | 1 [92] | 0 | 0 | 0 | −1 [71] | 0 | −1 [80] |

CF | 0 | 0 | 1 [115] | −1 [100] | 0 | −1 [71] | −1 [118] |

MA | 0 | 0 | 0 | −1 [119] | 0 | −1 [120] | −1 [71] |

Mid-X2 Variables | DS | ZO | PH | PA | PR | CF | MA |

DS | −1 [71] | 1 [41] | 0 | 0 | −1 [92] | 0 | −1 [70] |

ZO | −1 [41] | −1 [71] | 1 [113] | −1 [66,88] | 0 | 0 | −1 [69] |

PH | 0 | −1 [113] | −1 [71] | −1 [60] | 0 | −1 [115] | −1 [80] |

PA | 0 | 1 [66,88] | 1 [60] | −1 [71] | 0 | 0 | −1 [118] |

PR | 1 [92] | 0 | 0 | 0 | −1 [71] | 0 | −1 [80] |

CF | 0 | 0 | 1 [115] | 0 | 0 | −1 [71] | −1 [118] |

MA | 0 | 0 | 0 | 0 | 0 | −1 [120] | −1 [71] |

Low-X2 Variables | DS | ZO | PH | PA | PR | ||

DS | −1 [71] | 1 [41] | 0 | 0 | −1 [92] | ||

ZO | −1 [41] | −1 [71] | 1 [113] | −1 [66,88] | 0 | ||

PH | 0 | −1 [113] | −1 [71] | −1 [60] | 0 | ||

PA | 0 | 1 [66,88] | 1 [60] | −1 [71] | 0 | ||

PR | 1 [92] | 0 | 0 | 0 | −1 [71] |

## References

- Townend, I.H. Identifying change in estuaries. J. Coast. Conserv.
**2004**, 10, 5–12. [Google Scholar] [CrossRef] - Lotze, H.K.; Lenihan, H.S.; Bourque, B.J.; Bradbury, R.H.; Cooke, R.G.; Kay, M.C.; Kidwell, S.M.; Kirby, M.X.; Peterson, C.H.; Jackson, J.B.C. Depletion, degradation, and recovery potential of estuaries and coastal seas. Science
**2006**, 312, 1806–1809. [Google Scholar] [CrossRef] - Borja, A.; Dauer, D.M.; Elliott, M.; Simenstad, C.A. Medium- and long-term recovery of estuarine and coastal ecosystems: Patterns, rates and restoration effectiveness. Estuaries Coasts
**2010**, 33, 1249–1260. [Google Scholar] [CrossRef] - Gillson, J. Freshwater flow and fisheries production in estuarine and coastal systems: Where a drop of rain is not lost. Rev. Fish. Sci.
**2011**, 19, 168–186. [Google Scholar] [CrossRef] - Grimaldo, L.F.; Sommer, T.; Van Ark, N.; Jones, G.; Holland, E.; Moyle, P.B.; Herbold, B.; Smith, P. Factors affecting fish entrainment into massive water diversions in a tidal freshwater estuary: Can fish losses be managed? N. Am. J. Fish. Manag.
**2009**, 29, 1253–1270. [Google Scholar] [CrossRef] - Cloern, J.E.; Jassby, A.D. Drivers of change in estuarine-coastal ecosystems: Discoveries from four decades of study in San Francisco Bay. Rev. Geophys.
**2012**, 50. [Google Scholar] [CrossRef] [Green Version] - Hobbs, J.A.; Moyle, P.B.; Fangue, N.; Connon, R.E. Is extinction inevitable for delta smelt and longfin smelt? An opinion and recommendations for recovery. SFEWS
**2017**, 15. [Google Scholar] [CrossRef] - Cohen, A.N.; Carlton, J.T. Accelerating invasion rate in a highly invaded estuary. Science
**1998**, 279, 555–558. [Google Scholar] [CrossRef] [PubMed] - Castillo, G.C.; Damon, L.J.; Hobbs, J.A. Community patterns and environmental associations for pelagic fishes in a highly modified estuary. Mar. Coast. Fish.
**2018**, 10, 508–524. [Google Scholar] [CrossRef] - Feyrer, F.; Newman, K.; Nobriga, M.; Sommer, T. Modeling the effects of future outflow on the abiotic habitat of an imperiled estuarine fish. Estuaries Coasts
**2011**, 34, 120–128. [Google Scholar] [CrossRef] - Komoroske, L.M.; Connon, R.E.; Lindberg, J.; Cheng, B.S.; Castillo, G.; Hasenbein, M.; Fangue, N.A. Ontogeny influences sensitivity to climate change stressors in an endangered fish. Conserv. Physiol.
**2014**, 2, cou008. [Google Scholar] [CrossRef] [PubMed] - Schlacher, T.A.; Wooldridge, T.H. Ecological responses to reductions in freshwater supply and quality in South Africa’s estuaries: Lessons for management and conservation. J. Coast. Conserv.
**1996**, 2, 115–130. [Google Scholar] [CrossRef] - Moyle, P.B.; Bennett, W.A.; Fleenor, W.E.; Lund, J.R. Habitat variability and complexity in the upper San Francisco Estuary. SFEWS
**2010**, 8. [Google Scholar] [CrossRef] - Reinert, T.R.; Peterson, J.T. Modeling the effects of potential salinity shifts on the recovery of striped bass in the Savannah River Estuary, Georgia-South Carolina, United States. Environ. Manag.
**2008**, 41, 753–765. [Google Scholar] [CrossRef] [PubMed] - Guenther, C.B.; MacDonald, T.C. Comparison of estuarine salinity gradients and associated nekton community change in the Lower St. Johns River Estuary. Estuaries Coasts
**2012**, 35, 1443–1452. [Google Scholar] [CrossRef] - Wissel, B.; Fry, B. Tracing Mississippi River influences in estuarine food webs of coastal Louisiana. Oecologia
**2005**, 144, 659–672. [Google Scholar] [CrossRef] [PubMed] - Vinagre, C.; Salgado, J.; Cabral, H.N.; Costa, M.J. Food web structure and habitat connectivity in fish estuarine nurseries—Impact of river flow. Estuaries Coasts
**2011**, 34, 663–674. [Google Scholar] [CrossRef] - Estevez, E.D. Review and assessment of biotic variables and analytical methods used in estuarine inflow studies. Estuaries
**2002**, 25, 1291–1303. [Google Scholar] [CrossRef] - Sakaris, P.C. A review of the effects of hydrologic alteration on fisheries and biodiversity and the management and conservation of natural resources in regulated river systems. In Current Perspectives in Contaminant Hydrology and Water Resources Sustainability; Bradley, P.M., Ed.; Tech: Rijeka, Croatia, 2013; pp. 273–297. [Google Scholar]
- Rowell, K.; Flessa, K.W.; Dettmana, D.L.; Román, M.J.; Gerberc, L.R.; Findley, L.T. Diverting the Colorado River leads to a dramatic life history shift in an endangered marine fish. Biol. Conserv.
**2008**, 141, 1138–1148. [Google Scholar] [CrossRef] - Purtlebaugh, C.H.; Allen, M.C. Relative abundance, growth, and mortality of five Age-0 estuarine fishes in relation to discharge of the Suwannee River, Florida. Trans. Am. Fish. Soc.
**2010**, 139, 1233–1246. [Google Scholar] [CrossRef] - Livingston, R.J. Trophic response of estuarine fishes to long-term changes of river runoff. Bull. Mar. Sci.
**1997**, 60, 984–1004. [Google Scholar] - Kimmerer, W.J. Effects of freshwater flow on abundance of estuarine organisms: Physical effects or trophic linkages? Mar. Ecol. Prog. Ser.
**2002**, 243, 39–55. [Google Scholar] [CrossRef] - Brown, L.R.; Baxter, R.; Castillo, G.; Conrad, L.; Culberson, S.; Erickson, G.; Feyrer, F.; Fong, S.; Gehrts, K.; Grimaldo, L.; et al. Synthesis of Studies in the Fall Low-Salinity Zone of the San Francisco Estuary, September–December 2011; US Geological Survey Scientific Investigations Report 2014–5041; US Geological Survey: Reston, VA, USA, 2014.
- Wootton, J.T.; Emmerson, M. Measurement of interaction strength in nature. Annu. Rev. Ecol. Evol. Syst.
**2005**, 36, 419–444. [Google Scholar] [CrossRef] - Lane, P.; Levins, R. The dynamics of aquatic systems. The effects of nutrient enrichment on model plankton communities. Limnol. Oceanogr.
**1977**, 22, 454–471. [Google Scholar] - Dambacher, J.M.; Li, H.W.; Rossignol, P.A. Qualitative predictions in model ecosystems. Ecol. Model.
**2003**, 161, 79–93. [Google Scholar] [CrossRef] - Fox, J.W. Current food web models cannot explain the overall topological structure of observed food webs. Oikos
**2006**, 115, 97–109. [Google Scholar] [CrossRef] - Levins, R. The qualitative analysis of partially specified systems. Ann. N. Y. Acad. Sci.
**1974**, 231, 123–138. [Google Scholar] [CrossRef] [PubMed] - Li, H.W.; Moyle, P.B. Ecological analysis of species introductions into aquatic ecosystems. Trans. Am. Fish. Soc.
**1981**, 110, 772–782. [Google Scholar] [CrossRef] - Dambacher, J.M.; Luh, H.K.; Li, H.W.; Rossignol, P.A. Qualitative stability and ambiguity in model ecosystems. Am. Nat.
**2003**, 161, 876–888. [Google Scholar] [CrossRef] - Hosack, G.R.; Hayes, K.R.; Dambacher, J.M. Assessing model structure uncertainty through an analysis of system feedback and Bayesian networks. Ecol. Appl.
**2008**, 18, 1070–1082. [Google Scholar] [CrossRef] - Li, H.W.; Rossignol, P.A.; Castillo, G. Risk analysis of species introduction: Insights from qualitative modeling. In Non-Indigenous Fresh Water Organisms in North America; Vectors of Introduction, Biology and Impact; Claudi, R., Leach, J., Eds.; Lewis Press: Boca Raton, FL, USA, 1999; pp. 431–447. [Google Scholar]
- Montano-Moctezuma, G.; Li, H.W.; Rossignol, P.A. Alternative community structures in a kelp-urchin community: A qualitative modeling approach. Ecol. Model.
**2007**, 205, 343–354. [Google Scholar] [CrossRef] - Dambacher, J.M.; Brewer, D.T.; Dennis, D.M.; Macintyre, M.; Foale, S. Qualitative modelling of gold mine impacts on Lihir Island’s socioeconomic system and reef-edge fish community. Environ. Sci. Technol.
**2007**, 41, 555–562. [Google Scholar] [CrossRef] - Ramos-Jiliberto, R.; Garay-Narváez, L.; Medina, M.H. Retrospective qualitative analysis of ecological networks under environmental perturbation: A copper-polluted intertidal community as a case study. Ecotoxicology
**2012**, 21, 234–243. [Google Scholar] [CrossRef] [PubMed] - Reum, J.C.P.; Ferriss, B.E.; McDonald, P.S.; Farrell, D.M.; Harvey, C.J.; Klinger, T.; Levin, P.S. Evaluating community impacts of ocean acidification using qualitative network models. Mar. Ecol. Prog. Ser.
**2015**, 536, 11–24. [Google Scholar] [CrossRef] - IEP (Interagency Ecological Program). An Updated Conceptual Model of Delta Smelt Biology: Our Evolving Understanding of an Estuarine Fish; Interagency Ecological Program for the San Francisco Bay/Delta Estuary. Technical Report 90; IEP: Sacramento, CA, USA, 2015. [Google Scholar]
- Jassby, A.D.; Kimmerer, W.J.; Monismith, S.G.; Armor, C.; Cloern, J.E.; Powell, T.M.; Schubel, J.R.; Vendlinski, T.J. Isohaline position as a habitat indicator for estuarine populations. Ecol. Appl.
**1995**, 5, 272–289. [Google Scholar] [CrossRef] - Bennett, W.A. Critical assessment of the delta smelt population in the San Francisco Estuary, California. SFEWS
**2005**, 3. [Google Scholar] [CrossRef] - Slater, S.B.; Baxter, R.D. Diet, prey selection, and body condition of age-0 delta smelt, Hypomesus transpacificus, in the Upper San Francisco Estuary. SFEWS
**2014**, 12. [Google Scholar] [CrossRef] - Department of Fish and Wildlife. State and Federally Listed endangered and Threatened Animals of California; State of California, Natural Resources Agency, Department of Fish and Wildlife, Biogeographic Data Branch, California Natural Diversity Database: Sacramento, CA, USA, 2018.
- U.S. Fish and Wildlife Service. Formal Endangered Species Act Consultation on the Proposed Coordinated Operations of the Central Valley Project (CVP) and State Water Project (SWP); U.S. Fish and Wildlife Service, California and Nevada Region: Sacramento, CA, USA, 2008.
- Kimmerer, W.J.; MacWilliams, M.L.; Gross, E.S. Variation of fish habitat and extent of the low-salinity zone with freshwater flow in the San Francisco Estuary. SFEWS
**2013**, 11. [Google Scholar] [CrossRef] - Sommer, T.; Mejia, F.H.; Nobriga, M.L.; Feyrer, F.; Grimaldo, L. The spawning migration of delta smelt in the upper San Francisco Estuary. SFEWS
**2011**, 9. [Google Scholar] [CrossRef] - Moyle, P.B.; Brown, L.R.; Durand, J.R.; Hobbs, J.A. Delta smelt: Life history and decline of a once-abundant species in the San Francisco Estuary. SFEWS
**2016**, 14. [Google Scholar] [CrossRef] - Dambacher, J.M.; Li, H.W.; Rossignol, P.A. Relevance of community structure in assessing indeterminacy of ecological predictions. Ecology
**2002**, 83, 1372–1385. [Google Scholar] [CrossRef] - Cloern, J.E. Habitat connectivity and ecosystem productivity: Implications from a simple model. Am. Nat.
**2007**, 169, E21–E33. [Google Scholar] [CrossRef] [PubMed] - Sommer, T.; Armor, C.; Baxter, R.; Breuer, R.; Brown, L.; Chotkowski, M.; Culberson, S.; Feyrer, F.; Gingras, M.; Herbold, B.; et al. The collapse of pelagic fishes in the upper San Francisco Estuary. Fisheries
**2007**, 32, 270–277. [Google Scholar] [CrossRef] - Arthur, J.F.; Ball, M.D.; Baughman, S.Y. Summary of federal and state water project environmental impacts in the San Francisco Bay-Delta estuary, California. In The San Francisco Bay: The Ecosystem. Further Investigations into the Natural History of San Francisco Bay and Delta with Reference to the Influence of Man; Hollibaugh, J.T., Ed.; Friesen Printers: Altona, MB, Canada, 1996; pp. 445–495. [Google Scholar]
- California Department of Water Resources. Dayflow Data. Available online: https://water.ca.gov/Programs/Environmental-Services/Compliance-Monitoring-And-Assessment/Dayflow-Data (accessed on 14 May 2019).
- CDEC (California Data Exchange Center). The California Data Exchange Center. California Department of Water Resources. Available online: http://cdec.water.ca.gov (accessed on 29 April 2019).
- IEP (Interagency Ecological Program). Portal to IEP Data and Metadata. Available online: https://water.ca.gov/Programs/Environmental-Services/Interagency-Ecological-Program/Data-Portal (accessed on 29 April 2019).
- Feyrer, F.; Nobriga, M.L.; Sommer, T.R. Multidecadal trends for three declining fish species: Habitat patterns and mechanisms in the San Francisco Estuary, California, USA. Can. J. Fish. Aquat. Sci.
**2007**, 64, 723–734. [Google Scholar] [CrossRef] - MacNally, R.; Thomson, J.R.; Kimmerer, W.J.; Feyrer, F.; Newman, K.B.; Sih, A.; Bennett, W.A.; Brown, L.; Fleishman, E.; Culberson, S.D.; et al. Analysis of pelagic species decline in the upper San Francisco Estuary using multivariate autoregressive modeling (MAR). Ecol. Appl.
**2010**, 20, 1417–1430. [Google Scholar] [CrossRef] [Green Version] - Peterson, H.A.; Vayssieres, M. Benthic assemblage variability in the upper San Francisco Estuary: A 27-year retrospective. SFEWS
**2010**, 8. [Google Scholar] [CrossRef] - Kratina, P.; MacNally, R.; Kimmerer, W.J.; Thomson, J.R.; Winder, M. Human-induced biotic invasions and changes in plankton interaction networks. J. Appl. Ecol.
**2014**, 51, 1066–1074. [Google Scholar] [CrossRef] - Santos, M.J.; Anderson, L.W.; Ustin, S.L. Effects of invasive species on plant communities: An example using submersed aquatic plants at the regional scale. Biol. Invasions
**2011**, 13, 443–457. [Google Scholar] [CrossRef] - Durand, J.; Fleenor, W.; McElreath, R.; Santos, M.J.; Moyle, P. Physical controls on the distribution of the submersed aquatic weed Egeria densa in the Sacramento–San Joaquin Delta and implications for habitat restoration. SFEWS
**2016**, 14. [Google Scholar] [CrossRef] - Nichols, F.H.; Thompson, J.K.; Schemmel, L.E. Remarkable invasion of San Francisco Bay (California, USA) by the Asian clam Potamocorbula amurensis. II. Displacement of a former community. Mar. Ecol. Prog. Ser.
**1990**, 66, 95–101. [Google Scholar] [CrossRef] - Winder, M.; Jassby, A.D. Shifts in zooplankton community structure: Implications for food web processes in the Upper San Francisco Estuary. Estuaries Coasts
**2011**, 34, 675–690. [Google Scholar] [CrossRef] - Nobriga, M.L.; Feyrer, F.; Baxter, R.D.; Chotkowski, M. Fish community ecology in an altered river delta: Species composition, life history strategies, and biomass. Estuaries
**2005**, 28, 776–785. [Google Scholar] [CrossRef] - Light, T.; Grosholz, T.; Moyle, P. Delta Ecological Survey (Phase I): Nonindigenous Aquatic Species in the Sacramento-San Joaquin Delta, a Literature Review; U.S. Fish and Wildlife Service: Stockton CA, USA, 2005. [Google Scholar]
- Ferrari, M.C.; Ranåker, L.; Weinersmith, K.L.; Young, M.J.; Sih, A.; Conrad, J.L. Effects of turbidity and an invasive waterweed on predation by introduced largemouth bass. Environ. Biol. Fishes
**2014**, 97, 79–90. [Google Scholar] [CrossRef] - Hestir, E.L.; Schoellhamer, D.H.; Greenberg, J.; Morgan-King, T.; Ustin, S.L. The Effect of submerged aquatic vegetation expansion on a declining turbidity trend in the Sacramento-San Joaquin River Delta. Estuaries Coasts
**2016**, 39, 1110–1112. [Google Scholar] [CrossRef] - Kimmerer, W.J. Response of anchovies dampens effects of the invasive bivalve Corbula amurensis on the San Francisco Estuary foodweb. Mar. Ecol. Prog. Ser.
**2006**, 324, 207–218. [Google Scholar] [CrossRef] - Carlton, J.T.; Thompson, J.K.; Schemel, L.E.; Nichols, F.H. Remarkable invasion of San Francisco Bay (California, USA) by the Asian clam Potamocorbula amurensis. I. Introduction and dispersal. Mar. Ecol. Prog. Ser.
**1990**, 66, 81–94. [Google Scholar] [CrossRef] - Lehman, P.W.; Boyer, G.; Hall, C.; Waller, S.; Gehrts, K. Distribution and toxicity of a new colonial Microcystis aeruginosa bloom in the San Francisco Bay Estuary, California. Hydrobiologia
**2005**, 541, 87–90. [Google Scholar] [CrossRef] - Ger, K.A.; Teh, S.J.; Goldman, C.R. Microcystin-LR toxicity on dominant copepods Eurytemora affinis and Pseudodiaptomus forbesi of the upper San Francisco Estuary. Sci. Total Environ.
**2009**, 407, 4852–4857. [Google Scholar] [CrossRef] [PubMed] - Acuña, S.; Baxa, D.; Teh, S. Sublethal dietary effects of microcystin producing Microcystis on threadfin shad, Dorosoma petenense. Toxicon
**2014**, 60, 1191–1202. [Google Scholar] [CrossRef] - Puccia, C.J.; Levins, R. Qualitative Modeling of Complex Systems. An Introduction to Loop Analysis and Time Averaging; Harvard University Press: Cambridge, MA, USA, 1985. [Google Scholar]
- Levins, R. Evolution in Changing Environments. Some Theoretical Explorations. Monographs in Population Biology; McArthur, R.H., Ed.; Princeton University Press: Princeton, NJ, USA, 1968. [Google Scholar]
- Puccia, C.J.; Levins, R. Qualitative Modeling in Ecology: Loop Analysis, Signed Digraphs and Time Averaging. In Qualitative Simulation Modeling and Analysis; Fishwick, P.A., Luker, P.A., Eds.; Advances in Simulation; Springer: New York, NY, USA, 1991; pp. 119–143. [Google Scholar]
- Castillo, G.C.; Li, H.W.; Rossignol, P.A. Absence of overall feedback in a benthic estuarine community: A system potentially buffered from impacts of biological invasions. Estuaries
**2000**, 23, 275–291. [Google Scholar] [CrossRef] - MacWilliams, M.L.; Bever, A.J.; Gross, E.S.; Ketefian, G.S.; Kimmerer, W.J. Three-dimensional modeling of hydrodynamics and salinity in the San Francisco Estuary: An evaluation of model accuracy, X2, and the low–salinity zone. SFEWS
**2015**, 13. [Google Scholar] [CrossRef] - Castillo, G. Annotated Bibliography of the Delta Smelt (Hypomesus transpacificus). Programmatic Review of Delta Smelt Program Elements (2005–06). Interagency Ecological Program. Available online: https://www.researchgate.net/publication/332725919 (accessed on 28 April 2019).
- Sommer, T.; Mejia, F.H. A place to call home: A synthesis of delta smelt habitat in the upper San Francisco Estuary. SFEWS
**2013**, 11. [Google Scholar] [CrossRef] - Peterson, M.S. A conceptual view of environment-habitat-production linkages in tidal river estuaries. Rev. Fish. Sci.
**2003**, 11, 291–313. [Google Scholar] [CrossRef] - Lane, P.A. Preparing Marine Plankton Data Sets for Loop Analysis. ESA Supplement. Available online: http://esapubs.org/archive/ecol/E067/001/suppl-1B.pdf (accessed on 29 April 2019).
- Lehman, P.W.; Teh, S.J.; Boyer, G.L.; Nobriga, M.L.; Bass, E.; Hogle, C. Initial impacts of Microcystis aeruginosa blooms on the aquatic food web in the San Francisco Estuary. Hydrobiologia
**2010**, 637, 229–248. [Google Scholar] [CrossRef] - Simberloff, D.; Dayan, T. The guild concept and the structure of ecological communities. Annu. Rev. Ecol. Syst.
**1991**, 22, 115–143. [Google Scholar] [CrossRef] - Lucas, L.V.; Cloern, J.E.; Thompson, J.K.; Monsen, N.E. Functional variability of habitats within the Sacramento-San Joaquin Delta: Restoration implications. Ecol. Appl.
**2002**, 12, 1528–1547. [Google Scholar] - Lopez, C.B.; Cloern, J.E.; Schraga, T.S.; Little, A.J.; Lucas, L.V.; Thompson, J.K.; Burau, J.R. Ecological values of shallow-water habitats: Implications for restoration of disturbed ecosystems. Ecosystems
**2006**, 9, 422–440. [Google Scholar] [CrossRef] - Brown, L.R.; Michniuk, D. Littoral fish assemblages of the alien-dominated Sacramento–San Joaquin Delta, California, 1980–1983 and 2001–2003. Estuaries Coasts
**2007**, 30, 186–200. [Google Scholar] [CrossRef] - Yarrow, M.; Marin, V.H.; Finlayson, M.; Tironi, A.; Delgado, L.E.; Fisher, F. The ecology of Egeria densa Planchón (Liliopsida: Alismatales): A wetland ecosystem engineer? Rev. Chil. Hist. Nat.
**2009**, 82, 299–313. [Google Scholar] [CrossRef] - Lehman, P.W.; Boyer, G.; Satchwell, M.; Waller, S. The influence of environmental conditions on the seasonal variation of Microcystis cell density and microcystins concentration in San Francisco Estuary. Hydrobiologia
**2008**, 600, 187–204. [Google Scholar] [CrossRef] - Alpine, A.E.; Cloern, J.E. Trophic interactions and direct physical effects control phytoplankton biomass and production in an estuary. Limnol. Oceanogr.
**1992**, 37, 946–955. [Google Scholar] [CrossRef] - Kimmerer, W.J.; Gartside, E.; Orsi, J.J. Predation by an introduced clam as the probable cause of substantial declines in zooplankton in San Francisco Bay. Mar. Ecol. Prog. Ser.
**1994**, 113, 81–93. [Google Scholar] [CrossRef] - Kimmerer, W.J.; Parker, A.E.; Lidström, U.; Carpenter, E.J. Short-term and interannual variability in primary production in the low-salinity zone of the San Francisco Estuary. Estuaries Coasts
**2012**, 35, 913–929. [Google Scholar] [CrossRef] - Sobczak, W.V.; Cloern, J.E.; Jassby, A.D.; Muller-Solger, A.B. Bioavailability of organic matter in a highly disturbed estuary: The role of detrital and algal resources. Proc. Natl. Acad. Sci. USA
**2002**, 99, 8101–8105. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Jassby, A.D. Phytoplankton in the upper San Francisco Estuary: Recent biomass trends, their causes and their trophic significance. SFEWS
**2008**, 6. [Google Scholar] [CrossRef] - Nobriga, M.L.; Loboschefsky, E.; Feyrer, F. Common predator, rare prey: Exploring juvenile striped bass predation on delta smelt in California’s San Francisco Estuary. Trans. Am. Fish. Soc.
**2014**, 142, 1563–1575. [Google Scholar] [CrossRef] - Novak, M.; Wootton, J.T.; Doak, D.F.; Emmerson, M.; Estes, J.A.; Tinker, M.T. Predicting community responses to perturbations in the face of imperfect knowledge and network complexity. Ecology
**2011**, 92, 836–846. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Gantmacher, F.R. Applications of the Theory of Matrices; Dover Publications. Inc.: Mineola, NY, USA, 2005. [Google Scholar]
- Nakajima, H. Sensitivity and stability of flow networks. Ecol. Model.
**1992**, 62, 123–133. [Google Scholar] [CrossRef] - Luh, H.K. Oregon State University. Loop Analysis Program in Microsoft.NET 3.5 Framework. Available online: http://ipmnet.org/loop/loopanalysis.aspx (accessed on 12 March 2019).
- California Department of Fish and Wildlife. Fall Midwater Trawl Index. Available online: http://www.dfg.ca.gov/delta/data/fmwt/indices.asp (accessed on 12 March 2019).
- Maceda-Veiga, A. Towards the conservation of freshwater fish: Iberian Rivers as an example of threats and management practices. Rev. Fish. Biol. Fisher.
**2013**, 23, 1–22. [Google Scholar] [CrossRef] - Nobriga, M.L.; Sommer, T.R.; Feyrer, F.; Fleming, K. Long-term trends in summertime habitat suitability for delta smelt, Hypomesus transpacificus. SFEWS
**2008**, 6, 6. [Google Scholar] [CrossRef] - Yamamuro, M. Herbicide-induced macrophyte-to-phytoplankton shifts in Japanese lagoons during the last 50 years: Consequences for ecosystem services and fisheries. Hydrobiologia
**2012**, 699, 5–19. [Google Scholar] [CrossRef] - Kimmerer, W.J.; Thompson, J.K. Phytoplankton growth balanced by clam and zooplankton grazing and net transport into the low-salinity zone of the San Francisco Estuary. Estuaries Coasts
**2014**, 37, 1202–1218. [Google Scholar] [CrossRef] - Bennett, W.A.; Moyle, P.B. Where have all the fishes gone? Interactive factors producing fish declines in the Sacramento-San Joaquin Estuary. In The San Francisco Bay: The Ecosystem. Further Investigations into the Natural History of San Francisco Bay and Delta with Reference to the Influence of Man; Hollibaugh, J.T., Ed.; Friesen Printers: Altona, MB, Canada, 1996; pp. 519–542. [Google Scholar]
- Rose, K.A.; Kimmerer, W.J.; Edwards, K.P.; Bennett, W.A. Individual-based modeling of delta smelt population dynamics in the upper San Francisco Estuary I. Model description and baseline results. Trans. Am. Fish. Soc.
**2013**, 142, 1238–1259. [Google Scholar] [CrossRef] - Rose, K.A.; Kimmerer, W.J.; Edwards, K.P.; Bennett, W.A. Individual-based modeling of delta smelt population dynamics in the upper San Francisco Estuary II. Alternative baselines and good versus bad years. Trans. Am. Fish. Soc.
**2013**, 142, 1260–1272. [Google Scholar] [CrossRef] - Kimmerer, W.J.; Rose, K.A. Individual-based modeling of delta smelt population dynamics in the upper San Francisco Estuary III. Effects of entrainment mortality and changes in prey. Trans. Am. Fish. Soc.
**2018**, 147, 223–243. [Google Scholar] [CrossRef] - Hammock, B.G.; Moose, S.P.; Sandoval Solis, S.; Goharian, E.; Swee, J.T. Hydrodynamic modeling coupled with long-term field data provide evidence for suppression of phytoplankton by invasive clams and freshwater exports in the San Francisco Estuary. J. Environ. Manag.
**2019**, 63, 703–717. [Google Scholar] [CrossRef] [PubMed] - Cottingham, A.; Huang, P.; Hipsey, M.R.; Hall, N.G.; Ashworth, E.; Williams, J.; Potter, I.C. Growth, condition, and maturity schedules of an estuarine fish species change in estuaries following increased hypoxia due to climate change. Ecol. Evol.
**2018**, 8, 7111–7130. [Google Scholar] [CrossRef] [Green Version] - Baustian, M.M.; Clark, F.R.; Jerabek, A.S.; Wang, Y.; Bienn, H.C.; White, E.D. Modeling current and future freshwater inflow needs of a subtropical estuary to manage and maintain forested wetland ecological conditions. Ecol. Indic.
**2018**, 85, 791–807. [Google Scholar] [CrossRef] - Martins, I.; Antunes, C.; Dias, E.; Campuzano, F.J.; Pinto, L.; Santos, M.M.; Antunes, C. Antagonistic effects of multiple stressors on macroinvertebrate biomass from a temperate estuary (Minho estuary, NW Iberian Peninsula). Ecol. Indic.
**2019**, 101, 792–803. [Google Scholar] [CrossRef] - Allen, C.R.; Gunderson, L.H. Pathology and failure in the design and implementation of adaptive management. J. Environ. Manag.
**2011**, 92, 1379–1384. [Google Scholar] [CrossRef] [Green Version] - Cartwright, J.; Caldwell, C.; Nebiker, S.; Knight, R. Putting flow-ecology relationships into practice: A decision-support system to assess fish community response to water-management scenarios. Water
**2017**, 9, 196. [Google Scholar] [CrossRef] - Arthington, A.H.; Bhaduri, A.; Bunn, S.E.; Jackson, S.E.; Tharme, R.E.; Tickner, D.; Young, B.; Acreman, B.; Baker, N.; Capon, S.; et al. The Brisbane declaration and global action agenda on environmental flows. Front. Environ. Sci.
**2018**, 6, 45. [Google Scholar] [CrossRef] - Gifford, S.M.; Rollwagen Bollens, G.C.; Bollens, S.M. Mesozooplankton omnivory in the upper San Francisco Estuary. Mar. Ecol. Prog. Ser.
**2007**, 348, 33–46. [Google Scholar] [CrossRef] - Burks, R.L.; Jeppesen, E.; Lodge, D.M. Macrophyte and fish chemicals suppress Daphnia growth and alter life-history traits. Oikos
**2000**, 88, 139–148. [Google Scholar] [CrossRef] - Lucy, F.E.; Karatayev, A.Y.; Burlakova, L.E. Predictions for the spread, population density, and impacts of Corbicula fluminea in Ireland. Aquat. Invasions
**2012**, 7, 465–474. [Google Scholar] [CrossRef] - Sousa, R.; Gutierrez, J.L.; Aldridge, D.C. Non-indigenous invasive bivalves as ecosystem engineers. Biol. Invasions
**2009**, 11, 2367–2385. [Google Scholar] [CrossRef] - Pflugmacher, S. Promotion of oxidative stress in the aquatic macrophyte Ceratophyllum demersum during biotransformation of the cyanobacterial toxin microcystin-LR. Aquat. Toxicol.
**2004**, 70, 169–178. [Google Scholar] [CrossRef] - Hwang, S.J.; Kim, H.S.; Park, J.H.; Kim, B.H. Effects of cyanobacterium Microcystis aeruginosa on the filtration rate and mortality of the freshwater bivalve Corbicula leana. J. Environ. Biol.
**2010**, 31, 483–488. [Google Scholar] - Gao, Y.N.; Dong, J.; Fu, Q.Q.; Wang, Y.P.; Chen, C.; Li, J.H.; Li, R.; Zhou, C.J. Allelopathic effects of submerged macrophytes on phytoplankton. Allelopath. J.
**2017**, 40, 1–22. [Google Scholar] [Green Version] - Liu, Y.; Xie, P.; Wu, X.P. Grazing on toxic and non-toxic Microcystis aeruginosa PCC7820 by Unio douglasiae and Corbicula fluminea. Limnology
**2009**, 10, 1–5. [Google Scholar] [CrossRef]

**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].

**Figure 2.**Example of (

**A**) a 3 × 3 community matrix (A

^{o}) showing qualitative interaction terms for 3 variables such as species or trophic groups, with diagonal matrix elements −a

_{11}, −a

_{22}, and −a

_{33}representing negative self-effects of each variable and zero denoting no effect, and (

**B**) its corresponding signed-digraph. Open circles denote variables (N

_{i}), with lines between variables ending in arrows and bubbles respectively denoting positive and negative effects, and curved lines originating and ending in the same variable denoting self-effects, after [29].

**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].

**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 (+, −) in response to sustained outflow input. Direction of change without parentheses is unconditional. Direction of change in parentheses denote high-certainty (asterisk) and low-conditional certainly (no asterisk), and ? denotes complete ambiguity.

**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$\hat{p}$). Acronyms represent species or trophic groups (Table 1, Figure 3) and legend denotes the four outflow input scenarios (Figure 4). Values of |Δ$\hat{p}$| can range between 1 (unconditional sign determinacy) and 0 (complete uncertainty), with |Δ$\hat{p}$| 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$\hat{p}$) 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.

**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).

**Table 1.**Variables considered in qualitative community models for the upper San Francisco Estuary. Black circles denote community variables included in the low salinity zone at three positions of the 2 psu isohaline (X2).

Variable Type | Variable Code (Description) | Low X2 74 km | Mid X2 81 km | High X2 85 km | Functional Role | Community Response to Outflow |
---|---|---|---|---|---|---|

Explanatory | FL (Delta outflow, m ^{3} s^{−1}) | 323 [24] | 227 [24] | 142 [24] | Major abiotic forcing factor controlling the overlap between dynamic and stationary factors in the upper San Francisco Estuary, the position and size of the low salinity zone and the low salinity habitat of delta smelt and community interactions [24,38]. | |

Response (Community variables) | CF (Corbicula fluminea, Asian clam) ^{1} | ● [24] | ● [24] | Filter feeder exerting grazing pressure on phytoplankton [82,83]. | (+) [56] | |

DS (Hypomesus transpacificus, delta smelt) | ● [38,45] | ● [38,45] | ● [38,45] | Zooplanktivorous preying primarily on copepods, mysids, and cladocerans [40,41]. | (+) [10,54] | |

ED (Egeria densa, Brazilian waterweed) ^{1} | ● [58,59] | Primary producer of dense submersed vegetation beds which reduce open water habitat, alter the habitat for other aquatic plants [58,65] and provide habitat for centrarchids [84]. | (−) [59,85] | |||

MA (Microcystis aeruginosa, cyanobacterium) ^{2} | ● [24,86] | ● [24,86] | Biological contaminant due to its poor nutritional value and transfer of toxic microcystins into the aquatic food web [24,69,70,80]. | (−) [86] | ||

PA (Potamocorbula amurensis, overbite clam) ^{1} | ● [24] | ● [24] | Filter feeder exerting grazing pressure on phytoplankton and zooplankton [87,88]. | (−) [56] | ||

PH (Phytoplankton) | ● [38,89,90] | ● [38,89,90] | ● [38,89,90] | Primary producer fueling higher trophic levels of the food web in the open waters of the Delta and Suisun Bay [89,90]. | (+) [38,91] | |

PR (Predators of delta smelt) | ● [24,38] | ● [24,38] | ● [24,38] | Piscivores deemed to exert predation pressure on delta smelt throughout the Delta and Suisun Bay [24], including two introduced species, striped bass Morone saxatilis [62,92] and largemouth bass Micropterus salmoides [64,84]. | (0) ^{3} [38] | |

ZO (Zooplankton) | ● [24,38] | ● [24,38] | ● [24,38] | Primary and secondary consumer supporting pelagic and benthic food webs [41,88]. | (+) [55] |

**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).

R–H Criteria | Low-X2 (74 km) | Mid-X2 (81 km) | High-X2 (85 km) |
---|---|---|---|

None | 2.7 | 39.9 | 48.2 |

Only I | 0.3 | 3.5 | 10.6 |

Only II | 0.0 | 0.0 | 0.0 |

Both | 97 | 56.6 | 41.2 |

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**MDPI and ACS Style**

Castillo, G.C.
Modeling the Influence of Outflow and Community Structure on an Endangered Fish Population in the Upper San Francisco Estuary. *Water* **2019**, *11*, 1162.
https://doi.org/10.3390/w11061162

**AMA Style**

Castillo GC.
Modeling the Influence of Outflow and Community Structure on an Endangered Fish Population in the Upper San Francisco Estuary. *Water*. 2019; 11(6):1162.
https://doi.org/10.3390/w11061162

**Chicago/Turabian Style**

Castillo, Gonzalo C.
2019. "Modeling the Influence of Outflow and Community Structure on an Endangered Fish Population in the Upper San Francisco Estuary" *Water* 11, no. 6: 1162.
https://doi.org/10.3390/w11061162