https://orcid.org/0000-0002-4402-638X
Abstract
Trade‐offs among objectives in natural resource management can be exacerbated in altered ecosystems and when there is uncertainty in predicted management outcomes. Multi‐criteria decision analysis and value of information (VOI) are underutilized decision tools that can assist fisheries managers in handling trade‐offs and evaluating the importance of uncertainty. We demonstrate the use of these tools using a case study in the Sacramento River, California, USA, where two imperiled species with different temperature requirements, winter‐run Chinook Salmon Oncorhynchus tshawytscha and Green Sturgeon Acipenser medirostris, spawn and rear in the artificially cold Shasta Dam tailwater. A temperature‐control device installed on Shasta Dam maintains cool water for Chinook Salmon; however, uncertainties exist related to the effects of temperatures on the spawning and rearing of both species. We consider four alternative hypotheses in models of early life‐stage dynamics to evaluate the effects of alternative temperature management strategies on Chinook Salmon and Green Sturgeon management objectives. We used VOI to quantify the increase in management performance that can be expected by resolving hypothesis‐based uncertainties as a function of the weight assigned to species‐specific objectives. We found the decision was hindered by uncertainty; the best performing alternative depends on which hypothesis is true, with warmer or cooler alternative management strategies recommended when weights favor Green Sturgeon or Chinook Salmon objectives, respectively. The value of reducing uncertainty was highest when Green Sturgeon was slightly favored, highlighting the interaction between scientific uncertainty and decision makers' values. Our demonstration features multi‐criteria decision analysis and VOI as transparent, deliberative tools that can assist fisheries managers in confronting value conflicts, prioritizing resolution of uncertainty, and optimally managing aquatic ecosystems.
INTRODUCTION
Natural resource managers face many challenges, including navigating difficult trade‐offs among competing management objectives or stakeholder values. Managers may need to consider outcomes of their decisions with regard to opposing and diverse values. Fisheries managers may often contend with social–ecological mismatches between native and nonnative species (Beever et al. 2019), or intractable conflicts among a suite of stakeholder and economically driven values in heavily managed systems (e.g., regulated rivers, Schmidt et al. 1998; estuaries, Moyle et al. 2018). For example, harvest decisions for Atlantic horseshoe crab Limulus polyphemus not only affect harvest‐dependent fisheries, but also wildlife viewers valuing migratory shorebirds that depend on crab eggs as a critical food source, and the biomedical industry harvesting crab blood for medical products (McGowan et al. 2015). In many cases, a single management strategy may not appease the diverse concerns of stakeholders; for example, in Grand Canyon National Park, where operations of the Glen Canyon Dam cause divergent outcomes for recreational uses, hydropower generation, traditional cultural values, and habitat for endangered fishes, among others (Schmidt et al. 1998; Runge et al. 2011a). Fisheries management in such socio‐ecologically complex settings may benefit from structured and formalized approaches to decision making that recognize the diverse values of the public and Indigenous groups, while addressing agency mandates (Runge et al. 2011a; Gregory et al. 2012; Colvin and Peterson 2016).
Migrating Chinook Salmon Oncorhynchus tshawytscha. Photo credit: David Herasimtschuk, Freshwater Illustrated.
Structured decision making (SDM) can assist fisheries managers in formulating enduring and repeatable decisions with the transparency the public may increasingly demand (Conroy and Peterson 2013; Colvin and Peterson 2016; Hemming et al. 2022). Formal decision analyses such as SDM emphasize the recognition of values (i.e., value‐focused thinking) important to a decision maker and the decomposition of a decision into logical and tractable components, including the problem definition, objectives, alternative management actions, performance (consequences) of management alternatives, and trade‐offs (PrOACT; Hammond et al. 1999). Multi‐criteria decision analysis (MCDA) can be a useful SDM tool for deliberative and transparent decision making involving interspecific biological interactions in single‐ or multispecies management contexts (Smyth and Drake 2022), or where multiple management objectives compete (Gregory et al. 2012; Converse 2020). Structured processes can be used to elicit management objectives from fisheries managers or a group of stakeholders, then MCDA methods can incorporate predictions of objective‐specific consequences of alternative management actions, allowing for trade‐offs to be made according to the decision maker's objectives (Runge et al. 2011a; Smith et al. 2015). Ultimately, desirable outcomes of management actions may depend on how fishery objectives are weighted and how trade‐offs are considered (Costello et al. 2010; Smith et al. 2015).
Uncertainties in the predicted consequences of management alternatives also plague decision making, particularly when the ranking of management alternatives depends on which competing hypothesis best describes how a system functions (Runge et al. 2011b; Smith 2020). Knowing which factors influence juvenile fish survival, for example, may help managers prioritize research and restoration alternatives to maximize adult fish populations (Peterson and Duarte 2020). Managers may elect to delay a decision until additional information is gathered; however, timely decisions in fisheries management are particularly relevant when facing rapid declines in imperiled or economically important species (Dauwalter et al. 2020), or when responding to a species invasion (Healy et al. 2023). Value of information (VOI) tools can help managers confront trade‐offs between delaying a decision until additional information is gathered and making an immediate decision with an uncertain outcome, and include quantitative methods to prioritize sources of uncertainty for research or monitoring (Runge et al. 2011b; Bolam et al. 2019). The expected value of perfect information (EVPI) is a measure of the improvement in management that can be achieved with respect to all management objectives if uncertainty is fully reduced (Runge et al. 2011b; Smith 2020). For example, if EVPI is zero, uncertainty would have no effect on the decision‐making process and selection of a management strategy (additional information would not improve management performance). The expected value of partial information (EVPXI) quantifies the value of addressing specific sources of uncertainty, which can then be used to prioritize research or monitoring to maximize improvement in management performance. Despite the apparent benefit of MCDA and VOI tools in addressing trade‐offs and uncertainty prevalent in decision‐making processes and their potential for improving management, these tools are generally underutilized (Hansen and Jones 2008; Bolam et al. 2019; Smyth and Drake 2022), especially in a fisheries management context (but for recent fisheries applications, see Fielder et al. 2016; Peterson and Duarte 2020).
Herein, we demonstrate the use of MCDA and VOI tools through a simplified case study that evaluates four alternative river temperature management strategies with important implications for two U.S. Endangered Species Act (ESA)‐listed fishes in the Sacramento River, California, downstream of Shasta Dam (Figure 1). We assessed how varying a fisheries manager's objective weights (priorities) and the importance of different sources of uncertainty surrounding species‐specific temperature requirements influence ranking of alternative temperature management strategies for conserving these imperiled fishes. This decision context is particularly challenging because post‐dam habitat conditions may support one species of conservation value, while existing single‐species temperature management strategies may have negative implications for another. Endangered winter‐run Chinook Salmon Oncorhynchus tshawytscha spawn in the artificially cold tailwater below Shasta Dam and threatened Green Sturgeon Acipenser medirostris require warmer (natural) conditions for spawning and rearing in this same river reach (Rodgers et al. 2019; Zarri et al. 2019). A temperature‐control device was installed on Shasta Dam in 1997 to provide cool water to the Sacramento River at key times for Chinook Salmon spawning; however, potential uncertainties exist related to effects of temperature on winter‐run Chinook Salmon egg‐to‐fry survival and Green Sturgeon spawning and rearing. Value of information may also vary across objective weights, which may influence research priorities (Costello et al. 2010). We demonstrate how these uncertainties challenge the development of optimal temperature management strategies and quantify improvements in management that may be achieved using VOI tools.
The location of study area on the Sacramento River in California, including approximate spawning habitat under current temperature management regimes for winter‐run Chinook Salmon and Green Sturgeon, and areas of spawning habitat overlap. Data source: U.S. Geological Survey (https://bit.ly/4cH7MXN).
Ecological, Legal, and Regulatory Context
Multiple stressors have driven declines in native fishes in the Sacramento River and the San Francisco Bay‐Delta (Moyle 1995). In the years following the 1848 California gold rush, most riverine, floodplain, and estuarine aquatic habitats between the Sierra Nevada Mountains and Pacific coast of California were destroyed, disconnected, and altered. The construction and operation of California's Central Valley dams as part of the Central Valley Project (CVP) eliminated access to suitable higher‐elevation tributary spawning habitat, and modified the hydrologic, thermal, and sediment transport regimes that maintained spawning, egg incubation, or rearing habitats for both anadromous winter‐run Chinook Salmon (Yoshiyama et al. 1998), and Green Sturgeon (Mora et al. 2009).
The relationship between dam management and effects of invasive species, habitat quality, and availability on ESA‐listed species is complex and confounded by interacting factors (Moyle 1995; Moyle et al. 2018; Zarri et al. 2019). Persistence of winter‐run Chinook Salmon now partly relies on reproduction occurring solely in the main‐stem Sacramento River downstream of Shasta and Keswick dams (Figure 1; Yates et al. 2008). Hatchery production has also been a critically important reason for the continued persistence of winter‐run Chinook Salmon (NMFS 2014). Historically, winter‐run Chinook Salmon spawned in cool high‐elevation tributaries to which access was blocked with the construction of Shasta Dam (Yoshiyama et al. 1998). Shasta Dam and Reservoir operations attempt to maintain a coldwater pool to facilitate discharge temperatures (discharge volume is regulated by Keswick Dam) sufficient to minimize temperature‐dependent egg‐to‐fry mortality downstream of Keswick Dam to the confluence of Clear Creek (Sacramento River kms 483–470; Figure 1) from approximately May 15 to October 31 (NMFS 2019). However, information derived from laboratory and field studies suggests there are discrepancies in temperature sensitivity of Chinook Salmon eggs and fry; field‐derived estimates, which may be more realistic, suggest optimum temperatures could be 3°C lower than those derived from laboratory studies (Martin et al. 2017; Anderson et al. 2022).
Green Sturgeon spawning habitat was eliminated in the upper Sacramento River by Shasta Dam, and degraded in the main stem downstream, which were primary factors leading to the species' decline and continue to inhibit recovery (reviewed in NMFS 2018). Chinook Salmon and Green Sturgeon are now relegated to the main‐stem Sacramento River downstream of Shasta Dam, increasing the overlap in their spawning and early life stage rearing (Miller et al. 2020). Temperature management below Shasta Dam meant to benefit winter‐run Chinook Salmon may be less than optimal for Green Sturgeon spawning and development of eggs, larvae, and young‐of‐year (age‐0) juvenile (hereafter “juvenile”) life stages (Moser et al. 2016; Rodgers et al. 2019; Zarri et al. 2019; Poytress et al. 2024); however, the distribution and habitat use of juvenile Green Sturgeon is unclear given limited sampling of juveniles (Poytress et al. 2014) until recently (Poytress et al. 2024). Limited knowledge exists regarding Green Sturgeon early life stage temperature requirements and relationships with population demographic rates (Moser et al. 2016). Optimum temperatures for Green Sturgeon larval production may be ~14–17°C, whereas higher temperatures may provide optimal conditions for juvenile life stages (up to ~24°C; Moser et al. 2016; Rodgers et al. 2019). For example, age‐0 Green Sturgeon developing from larval to juvenile life stages reared at 11°C or 13°C showed negligible or slower growth relative to those reared at 16°C or 19°C (Poletto et al. 2018). The spawning and egg incubation period for Green Sturgeon is approximately April–June (Colborne et al. 2022), and larval to juvenile development and juvenile rearing occurs in the Sacramento River during summer and fall (June–November or later; Poytress et al. 2024), which overlaps with winter‐run Chinook Salmon critical spawning and egg‐to‐fry development periods (Zarri et al. 2019). The cooling effects of coldwater releases on Sacramento River temperatures can extend far beyond critical reaches for winter‐run Chinook Salmon egg‐to‐fry development (Daniels and Danner 2020), which may affect Green Sturgeon early life stages beyond areas of spatial overlap between spawning areas for the two species. For this analysis, we assume spawning adults, including eggs, and juvenile Green Sturgeon would inhabit reaches further upstream toward Shasta and Keswick dams if temperatures were optimal.
In summary, decision making regarding temperature management strategies is hampered by uncertainty about potential conflicts between water temperature needs for Green Sturgeon and winter‐run Chinook Salmon, which have temporally and spatially overlapping spawning ranges in the Central Valley. Sacramento River streamflow and water temperatures vary annually and seasonally (Figure 2). During dry years (e.g., 2015, 2022; Figure 2), the limited coldwater pool volume above Shasta Dam may constrain managers' options to meet ecological requirements for winter‐run Chinook Salmon spawning and rearing (Sapin et al. 2017), but warmer discharge temperatures resulting from low reservoir levels may support Green Sturgeon early life stage development.
![Hydrology and water temperature by calendar day (January 1–December 31) for the Sacramento River below Keswick (top panel; 1990–2022, range in daily mean streamflow 43.8–2,211.6 m3/s; Sacramento River at Keswick, California, U.S. Geological Survey [USGS] gaging station 11370500, USGS 2023a), and at Red Bluff, California (bottom panel; 1988–2022, range in daily mean streamflow 102.8–2,996.0 m3/s; USGS gaging station 11377100, USGS 2023b; water temperature data source: CBR 2023). Horizontal lines indicate daily mean streamflow (m3/s), colors reflect daily mean temperatures (°C), and reference lines approximate the winter‐run Chinook Salmon spawning/incubation period (May 1 – August 31).](https://oup.silverchair-cdn.com/oup/backfile/Content_public/Journal/fisheries/49/11/10.1002_fsh.11174/2/m_fsh11174-fig-0002-m.jpeg?Expires=1747979751&Signature=O5aC8dlTtLvUSik6LV52ReVlhufnv5VVV23qtMZpSjYkUc0CDWzBtFn97jspK-WmMRdbGAhU3t45PeMbu1faJyPNcSw-I-GYGVSjry-1PY8DLUarPO6A4GcA3imYDPAXisjbYNFoqFlrZyFbN9h~0dDv9sjABaTu9UBkdTHhh7GjQK5HBMWjpz9m~CUCPVf4ZIoyBXPbPMLe2Xaq~AcNZ4drqUAjudorStWzqGnGsVxfPUlYw0orVdurcaHXRUlUtssk~70prWt7gYvp5mHRsu3Guxqj1BclWtrlmvZY8JF2rko7HtiWpJjcFPgpIVORMYDx0KGqwYM3VaHqeslp3Q__&Key-Pair-Id=APKAIE5G5CRDK6RD3PGA)
Hydrology and water temperature by calendar day (January 1–December 31) for the Sacramento River below Keswick (top panel; 1990–2022, range in daily mean streamflow 43.8–2,211.6 m3/s; Sacramento River at Keswick, California, U.S. Geological Survey [USGS] gaging station 11370500, USGS 2023a), and at Red Bluff, California (bottom panel; 1988–2022, range in daily mean streamflow 102.8–2,996.0 m3/s; USGS gaging station 11377100, USGS 2023b; water temperature data source: CBR 2023). Horizontal lines indicate daily mean streamflow (m3/s), colors reflect daily mean temperatures (°C), and reference lines approximate the winter‐run Chinook Salmon spawning/incubation period (May 1 – August 31).
The U.S. Bureau of Reclamation (hereafter “Reclamation”) operates the CVP, a complex water storage and delivery system involving multiple California reservoirs, including Shasta Reservoir, the largest reservoir in the state. Water availability to meet the demands of water users or the need for flood‐control operations depends upon uncertain and variable annual precipitation and snowmelt and streamflow patterns (e.g., Figure 2) that drive runoff into the reservoirs. Statewide reservoir storage capacity, including Shasta, is typically sufficient for multiyear water management planning, but irreducible uncertainty related to climate change on water availability, water rights, and regulatory requirements have strained operations during recent droughts (Herbold et al. 2022).
METHODS
Decision Structure
For this demonstration of MCDA and VOI tools, we created a prototype decision structure, motivated by a Reclamation management context in the Sacramento River, but focused only on a few simplified elements of the decision setting. We have focused on temperature management but note that both temperature and streamflow may influence key life history events and habitat suitability for Green Sturgeon and Chinook Salmon. We also assumed the consumptive water use objectives were met by our alternative management strategies described below. Overall persistence of both anadromous species depends on factors outside of the Sacramento River in both marine and fresh waters—the broader problem facing CVP managers involves interconnected water management decisions related to several ESA‐listed fish species distributed throughout the Central Valley and San Francisco Bay‐Delta. Nonetheless, we posit that there is pedagogical value in this focused analysis involving a limited set of key elements embedded in the broader and more complex Central Valley decision context. We defined Reclamation's decision space for this analysis as reservoir and temperature management in the Sacramento River downstream of Shasta Dam to approximately Red Bluff (Figure 1), which encompasses much of the known spawning habitat for winter‐run Chinook Salmon and Green Sturgeon.
Objectives and Performance Measures
Fundamental objectives represent a decision maker's long‐term desired outcomes that are relevant to the decision at hand and, thus, are an expression of the decision maker's values (or, in the case of public agencies, the values of the legislative body that gave the decision maker statutory authority to act). We identified two fundamental objectives related to operations of Shasta Dam based on a review of ESA recovery plans (NMFS 2014, 2018), the 2019 biological opinion (NMFS 2019), and other documents to maximize the probability of persistence of winter‐run Chinook Salmon and to maximize the probability of persistence of Green Sturgeon. Assuming the temperatures of Shasta Dam releases have a strong link to survival and development of early life stages of both species during the spring and summer seasons, and because consequences may differ due to species' life history strategies (e.g., semelparity versus iteroparity), we focused on objectives that would reflect early life stage dynamics of Chinook Salmon and also link to population growth of long‐lived Green Sturgeon. Thus, we defined the objectives for this analysis as “to maximize the survival of early life stages of winter‐run Chinook Salmon” and “to maximize the minimum population abundance of Green Sturgeon.” Minimum population abundance is indicative of a population's propensity to decline, and, thus, maximizing this measure would lead to a higher likelihood of Green Sturgeon persistence (McCarthy and Thompson 2001). We defined performance measures, which quantify how well objectives are met by the temperature management strategies (Hemming et al. 2022), for these objectives as (1) annual winter‐run Chinook Salmon egg‐to‐fry survival probability in the Sacramento River reach between Keswick Dam and the confluence with Clear Creek, and (2) the expected minimum population abundance for Green Sturgeon between Keswick Dam and Red Bluff over a simulated 32‐year simulated period.
Hypotheses
Critical uncertainties are limitations in our knowledge that have the potential to affect the ranking of alternative management strategies (Runge et al. 2011b). To calculate VOI, an articulation of uncertainty (alternative hypotheses about how a system functions) and a priori weights (relative belief in the alternative models) on alternative hypotheses are required (Runge et al. 2011b; Canessa et al. 2015; Bolam et al. 2019). Based on field‐derived estimates (see figure 3 in Martin et al. 2017), we assumed 11°C and 12.5°C were reasonable lower and upper bounds (Figure 3) to represent the uncertainty in winter‐run Chinook Salmon egg‐to‐fry critical temperature (Tcrit). Critical temperature represents the threshold below which temperature‐dependent mortality is assumed not to occur (Martin et al. 2017). For Green Sturgeon, egg incubation success, growth, and survival related to water temperature is uncertain, particularly for early and postlarval juvenile life stages (Mayfield and Cech 2004; Moser et al. 2016; Rodgers et al. 2019). Evidence suggests a wider and somewhat warmer optimum temperature range for postlarval juvenile life stages of Green Sturgeon (Poletto et al. 2018; Zarri and Palkovacs 2019), compared to eggs or larvae (Rodgers et al. 2019; Figure 3). We assumed the performance of alternative temperature management strategies in maintaining positive Green Sturgeon population growth depends on either egg/larval or juvenile life stage sensitivity to temperature in spawning and rearing habitats. We represented uncertainty in our analysis through four competing and mutually exclusive hypotheses (Table 1).
Temperature suitability curves (top) for Green Sturgeon egg–larva and young‐of year juvenile life stages derived from the literature and used in Green Sturgeon metapopulation viabillity models to predict expected minimum abundance, and winter‐run Chinook Salmon critical temperature thresholds (bottom) for Shasta Reservoir release temperature alternatives in the Sacramento River, California. Temperature suitability curves represent a range in temperatures that are unsuitable (0) to optimum (1) for Green Sturgeon egg development or juvenile growth.
Hypotheses considered to represent relationships between Green Sturgeon and winter‐run Chinook Salmon and temperatures in the analysis of temperature management below Shasta Dam on the Sacramento River, California.
| Hypothesis number | Species specific hypothesis | |
| Green Sturgeon population growth (λ) dependency | Chinook Salmon critical temperature (Tcrit) | |
| 1 | Spawning and egg incubation temperatures (April–June) | 11.0°C |
| 2 | Spawning and egg incubation temperatures (April–June) | 12.5°C |
| 3 | Young‐of‐year juvenile rearing temperatures (June–October) | 11.0°C |
| 4 | Young‐of‐year juvenile rearing temperatures (June–October) | 12.5°C |
| Hypothesis number | Species specific hypothesis | |
| Green Sturgeon population growth (λ) dependency | Chinook Salmon critical temperature (Tcrit) | |
| 1 | Spawning and egg incubation temperatures (April–June) | 11.0°C |
| 2 | Spawning and egg incubation temperatures (April–June) | 12.5°C |
| 3 | Young‐of‐year juvenile rearing temperatures (June–October) | 11.0°C |
| 4 | Young‐of‐year juvenile rearing temperatures (June–October) | 12.5°C |
Hypotheses considered to represent relationships between Green Sturgeon and winter‐run Chinook Salmon and temperatures in the analysis of temperature management below Shasta Dam on the Sacramento River, California.
| Hypothesis number | Species specific hypothesis | |
| Green Sturgeon population growth (λ) dependency | Chinook Salmon critical temperature (Tcrit) | |
| 1 | Spawning and egg incubation temperatures (April–June) | 11.0°C |
| 2 | Spawning and egg incubation temperatures (April–June) | 12.5°C |
| 3 | Young‐of‐year juvenile rearing temperatures (June–October) | 11.0°C |
| 4 | Young‐of‐year juvenile rearing temperatures (June–October) | 12.5°C |
| Hypothesis number | Species specific hypothesis | |
| Green Sturgeon population growth (λ) dependency | Chinook Salmon critical temperature (Tcrit) | |
| 1 | Spawning and egg incubation temperatures (April–June) | 11.0°C |
| 2 | Spawning and egg incubation temperatures (April–June) | 12.5°C |
| 3 | Young‐of‐year juvenile rearing temperatures (June–October) | 11.0°C |
| 4 | Young‐of‐year juvenile rearing temperatures (June–October) | 12.5°C |
Alternative Temperature Management Strategies
We developed a range of alternative temperature management strategies for spring (April–May) and summer (June–October) seasons in the Sacramento River that align with early life history stages of Green Sturgeon and winter‐run Chinook Salmon to explore strategies that may balance trade‐offs between objectives (Gregory et al. 2012). Seasonal temperatures simulated in our alternative management strategies are based on observed average seasonal water temperatures between 1990 and 2022 (CBR 2023) or observed wet (2017) and dry (2015) years in the Sacramento River below Keswick Dam and at Red Bluff during spring and summer, and modeled using pre‐dam temperatures (Reclamation 2022). We recognize that all strategies may not be achievable in the future; additional hydrological and temperature modeling necessary to understand the feasibility of implementation is beyond the scope of this demonstrative case study. Nonetheless, based on our use of observed temperatures, we suggest that most scenarios are realistic. There is also substantial interannual variability in reservoir inflows that constrain discharge (Figure 2); however, for this prototype, we assumed average coldwater pool volumes will be available to allow for flexibility in release temperatures from May–October (i.e., coldwater pool volume >0). We verified this assumption by calculating the monthly mean volume of coldwater pool in Shasta Reservoir using a published equation (Yates et al. 2008; Supplementary Information Table S2). We found the minimum mean coldwater pool volume in Shasta Reservoir was ≥1.909 billion m3 using data from 1990 to 2022 (CBR 2023). Our set of alternative temperature management strategies included (Table 2):
Alternative 1: Long‐term average management. The release patterns are such that they match the observed seasonal mean temperature from 1990 to 2022 for spring and summer. This alternative represents baseline temperature management (status quo), including management of discharge temperatures ≤11.9°C to the extent feasible between May and October, or up to 13.3°C in dry years, using the temperature‐control device installed on Shasta Dam in 1997 (NMFS 2019).
Alternative 2: Run‐of‐river management. Based on modeled temperatures (Reclamation 2022), releases from Keswick Dam and Red Bluff would approximate a natural, pre‐dam temperature regime. The temperatures represented in this alternative are expected to be more similar to a natural condition than the other alternatives and represent the warmest conditions of the alternatives considered.
Alternative 3: Sturgeon‐focused management. We assumed Green Sturgeon early life stages (eggs to juveniles) would benefit from warmer than average dam discharge temperatures from spring spawning through summer rearing. This alternative represents temperatures observed during spring and summer of 2015 (CBR 2023), which were among the warmest years on record following the installation of the temperature control device, but cooler than the run‐of‐river alternative.
Alternative 4: Chinook Salmon‐focused management. Temperatures mimic those observed during 2017 (CBR 2023), when temperatures during summer were the coolest since 1990 and annual Chinook Salmon egg‐to‐fry survival was among the highest recorded (C. Marcinkevage, NMFS, personal communication; O'Farrell et al. 2018). Thus, we assumed similar temperatures would maximize winter‐run Chinook Salmon egg‐to‐fry survival and juvenile production.
Constant (average) water temperatures (°C) for each alternative management strategy, by season and location in the Sacramento River below Shasta Dam, California. April–June temperatures relate to Green Sturgeon spawning and egg incubation, and June–October temperatures relate to winter‐run Chinook Salmon critical egg‐to‐fry survival periods and young‐of‐year juvenile rearing periods for Green Sturgeon.
| Alternative | Keswick water temperature | Red Bluff water temperature | ||
| April–June | June–October | April–June | June–October | |
| 1. Long‐term average management | 10.5 | 11.6 | 13.9 | 14.6 |
| 2. Run of River | 12.5 | 17.3 | 15.9 | 20.6 |
| 3. Sturgeon‐focused management | 12.1 | 13.1 | 16.0 | 16.6 |
| 4. Salmon‐focused management | 10.6 | 10.9 | 13.7 | 14.2 |
| Alternative | Keswick water temperature | Red Bluff water temperature | ||
| April–June | June–October | April–June | June–October | |
| 1. Long‐term average management | 10.5 | 11.6 | 13.9 | 14.6 |
| 2. Run of River | 12.5 | 17.3 | 15.9 | 20.6 |
| 3. Sturgeon‐focused management | 12.1 | 13.1 | 16.0 | 16.6 |
| 4. Salmon‐focused management | 10.6 | 10.9 | 13.7 | 14.2 |
Constant (average) water temperatures (°C) for each alternative management strategy, by season and location in the Sacramento River below Shasta Dam, California. April–June temperatures relate to Green Sturgeon spawning and egg incubation, and June–October temperatures relate to winter‐run Chinook Salmon critical egg‐to‐fry survival periods and young‐of‐year juvenile rearing periods for Green Sturgeon.
| Alternative | Keswick water temperature | Red Bluff water temperature | ||
| April–June | June–October | April–June | June–October | |
| 1. Long‐term average management | 10.5 | 11.6 | 13.9 | 14.6 |
| 2. Run of River | 12.5 | 17.3 | 15.9 | 20.6 |
| 3. Sturgeon‐focused management | 12.1 | 13.1 | 16.0 | 16.6 |
| 4. Salmon‐focused management | 10.6 | 10.9 | 13.7 | 14.2 |
| Alternative | Keswick water temperature | Red Bluff water temperature | ||
| April–June | June–October | April–June | June–October | |
| 1. Long‐term average management | 10.5 | 11.6 | 13.9 | 14.6 |
| 2. Run of River | 12.5 | 17.3 | 15.9 | 20.6 |
| 3. Sturgeon‐focused management | 12.1 | 13.1 | 16.0 | 16.6 |
| 4. Salmon‐focused management | 10.6 | 10.9 | 13.7 | 14.2 |
To understand the sensitivity of VOI to management alternatives included in a MCDA, we also developed a post hoc optimization alternative. For the post hoc alternative, we combined the warmest observed spring water temperatures (2021) with the coolest observed summer temperatures (2017) to describe a management action that favored both species objectives (Table S3). Detailed methods and results regarding the post hoc alternative are available in the Supplementary Information.
Predictive Models
We used two species‐specific models to assess the performance of alternative temperature management strategies for Chinook Salmon and Green Sturgeon objectives. To assess consequences of summer average temperature alternatives for the reach between Keswick Dam and Clear Creek for winter‐run Chinook Salmon (Table 1), we used the Central Valley Prediction and Assessment of Salmon stage‐independent egg‐to‐fry survival model (Martin et al. 2017; CBR 2023). We modeled alternative Chinook Salmon Tcrit values that represented the temperature sensitivity hypotheses (11°C and 12.5°C) while holding other parameters constant; we applied these modifications for demonstration purposes, recognizing that more nuanced model modifications are possible. Model outputs were cumulative daily summer egg‐to‐fry survival rates, given daily water temperatures, which varied only with alternative‐based temperature‐dependent mortality.
For Green Sturgeon, we used a matrix‐based metapopulation viability model to predict life‐stage‐ and subpopulation‐specific effects of Sacramento River alternative temperature management strategies on population abundance (e.g., Murphy et al. 2020; Healy et al. 2023; Dynamic Habitat Disturbance and Ecological Resilience model). Our use of the Dynamic Habitat Disturbance and Ecological Resilience model allowed for the simulation of effects of longitudinal (reach or subpopulation‐specific) variation in river water temperatures on life‐stage‐specific demographic vital rates (reproductive rates, survival, growth, or life‐stage transition rates), while accounting for density‐dependent processes in reproductive rates and dispersal between subpopulations we assumed were also driven by habitat suitability. The model applies user‐specified life‐stage‐specific habitat suitability curves to adjust probabilistic demographic and dispersal rates when temperatures are suboptimal. After a review of available literature (Mayfield and Cech 2004; Moser et al. 2016; Poletto et al. 2018; Rodgers et al. 2019; Zarri and Palkovacs 2019), we developed Green Sturgeon temperature‐based habitat suitability curves (Figure 3) for population reproductive rates (a function of egg survival and individual female fecundity, proportion of spawning females; Beamesderfer et al. 2007) as a function of average April–June temperature, and juvenile growth (life‐stage transition rates) as a function of June–October water temperatures (Table 1; see Supplementary Information for a description of model mechanics and parametric assumptions). We simulated the effects of temperature variation across reproductive rates and juvenile life stages on the metapopulation dynamics of Green Sturgeon in two Sacramento River subpopulations. We defined Green Sturgeon subpopulations as those spawning and rearing either in the reach below Keswick Dam to the Clear Creek confluence or at Red Bluff. Dispersal between subpopulations, which is simulated prior to the calculation of abundance and projection into the next time step, was also a function of juvenile habitat (temperature) suitability. We calculated the performance measure of expected minimum population size (post‐breeding census; Murphy et al. 2020) by finding the minimum population size over a 32‐year time series (based on the available time series of temperature data to model baseline conditions) for each of 100 simulations, and averaging that value over all simulations (McCarthy and Thompson 2001).
Decision Analysis
Multi‐Criteria Decision Analysis
Expected Value of Perfect Information
Although we did not elicit weights from stakeholders or managers for this exercise (Hemming et al. 2018), we varied the objective weights to demonstrate their influence on the performance of alternatives under uncertainty, and their influence on EVPI and EVPXI. We adjusted objective weights by alternatively prioritizing Chinook Salmon and Green Sturgeon by incrementally increasing objective weights between 0 and 1 on the Chinook Salmon objective.
RESULTS
The expected minimum Green Sturgeon abundance ranged from 2,085 to 9,721 across alternative temperature management strategies (Table 3), which we used as the range for normalizing Green Sturgeon performance measure scores. Winter‐run Chinook Salmon (temperature dependent) egg‐to‐fry survival ranged from 0 to 1 (normalizing was unnecessary; Table 3). Composite alternative performance scores (Vj) varied according to objective weights (Figure 4). With equal weights on the four hypotheses, the best‐performing alternative depended on objective weights—the salmon‐focused management alternative performed best (Vj = 1.0, i.e., maximum possible score) when objective weights favored Chinook Salmon (i.e., Chinook Salmon objective weight = 1.0), whereas the run‐of‐river alternative was preferred when objective weights favored Green Sturgeon (Vj = 0.88, Chinook Salmon objective weight = 0; Figure 4). If the weight on the Chinook Salmon objective was less than 0.38, the run‐of‐river alternative was favored; if the weight on the Chinook Salmon objective exceeded 0.37, the salmon‐focused alternative was favored (Figure 4). No other alternatives were favored under objective weighting schemes with equal weights on hypotheses.
Consequences of alternative management strategies below Shasta and Keswick dams on the Sacramento River, California, for Green Sturgeon and winter‐run Chinook Salmon under two different models of the influence of temperature on life‐stage‐specific drivers of Green Sturgeon minimum abundance and Chinook Salmon critical temperature (Tcrit) for egg‐to‐fry survival. Dark green cells indicate the highest scores for each species/hypothesis, and white cells are the worst performing alternatives. Normalized scores for Green Sturgeon are in parentheses, and the average scores by alternative are displayed to demonstrate performance if objective weights entirely favored one objective or the other (see Figure 4).
| Alternative | Green Sturgeon hypotheses | Chinook Salmon hypotheses | ||||||||
| 1. Sturgeon spawning | 2. Sturgeon spawning | 3. Sturgeon juvenile | 4. Sturgeon juvenile | Average | 1. Salmon Tcrit 11°C | 2. Salmon Tcrit 12.5°C | 3. Salmon Tcrit 11°C | 4. Salmon Tcrit 12.5°C | Average | |
| 1. Long‐term average management | 2,426 (0.04) | 2,426 (0.04) | 7,149 (0.66) | 7,149 (0.66) | 4,788 (0.35) | 0.33 | 1.00 | 0.33 | 1.00 | 0.67 |
| 2. Run of river | 7,886 (0.76) | 7,886 (0.76) | 9,721 (1.00) | 9,721 (1.00) | 8,804 (0.88) | 0 | 0 | 0 | 0 | 0 |
| 3. Sturgeon‐focused management | 5,745 (0.48) | 5,745 (0.48) | 9,595 (0.98) | 9,595 (0.98) | 7,670 (0.73) | 0.02 | 0.36 | 0.02 | 0.36 | 0.19 |
| 4. Salmon‐focused management | 2,085 (0) | 2,085 (0) | 6,052 (0.52) | 6,052 (0.52) | 4,069 (0.26) | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
| Alternative | Green Sturgeon hypotheses | Chinook Salmon hypotheses | ||||||||
| 1. Sturgeon spawning | 2. Sturgeon spawning | 3. Sturgeon juvenile | 4. Sturgeon juvenile | Average | 1. Salmon Tcrit 11°C | 2. Salmon Tcrit 12.5°C | 3. Salmon Tcrit 11°C | 4. Salmon Tcrit 12.5°C | Average | |
| 1. Long‐term average management | 2,426 (0.04) | 2,426 (0.04) | 7,149 (0.66) | 7,149 (0.66) | 4,788 (0.35) | 0.33 | 1.00 | 0.33 | 1.00 | 0.67 |
| 2. Run of river | 7,886 (0.76) | 7,886 (0.76) | 9,721 (1.00) | 9,721 (1.00) | 8,804 (0.88) | 0 | 0 | 0 | 0 | 0 |
| 3. Sturgeon‐focused management | 5,745 (0.48) | 5,745 (0.48) | 9,595 (0.98) | 9,595 (0.98) | 7,670 (0.73) | 0.02 | 0.36 | 0.02 | 0.36 | 0.19 |
| 4. Salmon‐focused management | 2,085 (0) | 2,085 (0) | 6,052 (0.52) | 6,052 (0.52) | 4,069 (0.26) | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
Consequences of alternative management strategies below Shasta and Keswick dams on the Sacramento River, California, for Green Sturgeon and winter‐run Chinook Salmon under two different models of the influence of temperature on life‐stage‐specific drivers of Green Sturgeon minimum abundance and Chinook Salmon critical temperature (Tcrit) for egg‐to‐fry survival. Dark green cells indicate the highest scores for each species/hypothesis, and white cells are the worst performing alternatives. Normalized scores for Green Sturgeon are in parentheses, and the average scores by alternative are displayed to demonstrate performance if objective weights entirely favored one objective or the other (see Figure 4).
| Alternative | Green Sturgeon hypotheses | Chinook Salmon hypotheses | ||||||||
| 1. Sturgeon spawning | 2. Sturgeon spawning | 3. Sturgeon juvenile | 4. Sturgeon juvenile | Average | 1. Salmon Tcrit 11°C | 2. Salmon Tcrit 12.5°C | 3. Salmon Tcrit 11°C | 4. Salmon Tcrit 12.5°C | Average | |
| 1. Long‐term average management | 2,426 (0.04) | 2,426 (0.04) | 7,149 (0.66) | 7,149 (0.66) | 4,788 (0.35) | 0.33 | 1.00 | 0.33 | 1.00 | 0.67 |
| 2. Run of river | 7,886 (0.76) | 7,886 (0.76) | 9,721 (1.00) | 9,721 (1.00) | 8,804 (0.88) | 0 | 0 | 0 | 0 | 0 |
| 3. Sturgeon‐focused management | 5,745 (0.48) | 5,745 (0.48) | 9,595 (0.98) | 9,595 (0.98) | 7,670 (0.73) | 0.02 | 0.36 | 0.02 | 0.36 | 0.19 |
| 4. Salmon‐focused management | 2,085 (0) | 2,085 (0) | 6,052 (0.52) | 6,052 (0.52) | 4,069 (0.26) | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
| Alternative | Green Sturgeon hypotheses | Chinook Salmon hypotheses | ||||||||
| 1. Sturgeon spawning | 2. Sturgeon spawning | 3. Sturgeon juvenile | 4. Sturgeon juvenile | Average | 1. Salmon Tcrit 11°C | 2. Salmon Tcrit 12.5°C | 3. Salmon Tcrit 11°C | 4. Salmon Tcrit 12.5°C | Average | |
| 1. Long‐term average management | 2,426 (0.04) | 2,426 (0.04) | 7,149 (0.66) | 7,149 (0.66) | 4,788 (0.35) | 0.33 | 1.00 | 0.33 | 1.00 | 0.67 |
| 2. Run of river | 7,886 (0.76) | 7,886 (0.76) | 9,721 (1.00) | 9,721 (1.00) | 8,804 (0.88) | 0 | 0 | 0 | 0 | 0 |
| 3. Sturgeon‐focused management | 5,745 (0.48) | 5,745 (0.48) | 9,595 (0.98) | 9,595 (0.98) | 7,670 (0.73) | 0.02 | 0.36 | 0.02 | 0.36 | 0.19 |
| 4. Salmon‐focused management | 2,085 (0) | 2,085 (0) | 6,052 (0.52) | 6,052 (0.52) | 4,069 (0.26) | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
Composite scores for alternative temperature management strategies across a 0–1 range in Chinook Salmon objective weights, with equal weights applied to the four defined hypotheses for Shasta Reservoir temperature release alternatives for the Sacramento River, California. Corresponding Green Sturgeon objective weights are displayed in parentheses across the x‐axis.
Under equal objective and hypothesis weights, the best‐performing alternative temperature management strategy was not robust to uncertainty. The salmon‐focused alternative performed best under hypotheses 1 or 3, while the long‐term average management alternative scored the highest if hypotheses 2 or 4 were true (Vi,j; Table 4). The expected value under certainty was 0.65 and the maximum composite performance score under uncertainty was 0.63 (Table 4), which meant that reducing uncertainty under equal objective weights would lead to a VOI of 0.02 (EVPI score of 3.74%; Table 5).
Composite scores (equal objective‐ and hypothesis‐weighted average scores, Vj) by alternative temperature management strategy and hypothesis on the Sacramento River, California, and outcomes under uncertainty (Vi,j). Cells are shaded from the highest (darker) to lowest (white) scores for each objective and hypothesis. The maximum performance under each hypothesis (expected value under certainty) is given, and the maximum performance under uncertainty is displayed in bold.
| Alternative | Hypothesis specific score (Vj,k) | Composite score (Vj) | |||
| 1. Sturgeon spawning/salmon Tcrit 11°C | 2. Sturgeon spawning/salmon Tcrit 12.5°C | 3. Sturgeon juvenile/salmon Tcrit 11°C | 4. Sturgeon juvenile/salmon Tcrit 12.5°C | ||
| 1. Long term average management | 0.19 | 0.52 | 0.50 | 0.83 | 0.51 |
| 2. Run of river | 0.38 | 0.38 | 0.50 | 0.50 | 0.44 |
| 3. Sturgeon‐focused management | 0.25 | 0.42 | 0.50 | 0.67 | 0.46 |
| 4. Salmon‐focused management | 0.50 | 0.50 | 0.76 | 0.76 | 0.63 |
| Expected values under certainty | Hypothesis‐weighted average of maximum performance | ||||
| Maximum performance by hypothesis | 0.50 | 0.52 | 0.76 | 0.83 | 0.65 |
| Alternative | Hypothesis specific score (Vj,k) | Composite score (Vj) | |||
| 1. Sturgeon spawning/salmon Tcrit 11°C | 2. Sturgeon spawning/salmon Tcrit 12.5°C | 3. Sturgeon juvenile/salmon Tcrit 11°C | 4. Sturgeon juvenile/salmon Tcrit 12.5°C | ||
| 1. Long term average management | 0.19 | 0.52 | 0.50 | 0.83 | 0.51 |
| 2. Run of river | 0.38 | 0.38 | 0.50 | 0.50 | 0.44 |
| 3. Sturgeon‐focused management | 0.25 | 0.42 | 0.50 | 0.67 | 0.46 |
| 4. Salmon‐focused management | 0.50 | 0.50 | 0.76 | 0.76 | 0.63 |
| Expected values under certainty | Hypothesis‐weighted average of maximum performance | ||||
| Maximum performance by hypothesis | 0.50 | 0.52 | 0.76 | 0.83 | 0.65 |
Composite scores (equal objective‐ and hypothesis‐weighted average scores, Vj) by alternative temperature management strategy and hypothesis on the Sacramento River, California, and outcomes under uncertainty (Vi,j). Cells are shaded from the highest (darker) to lowest (white) scores for each objective and hypothesis. The maximum performance under each hypothesis (expected value under certainty) is given, and the maximum performance under uncertainty is displayed in bold.
| Alternative | Hypothesis specific score (Vj,k) | Composite score (Vj) | |||
| 1. Sturgeon spawning/salmon Tcrit 11°C | 2. Sturgeon spawning/salmon Tcrit 12.5°C | 3. Sturgeon juvenile/salmon Tcrit 11°C | 4. Sturgeon juvenile/salmon Tcrit 12.5°C | ||
| 1. Long term average management | 0.19 | 0.52 | 0.50 | 0.83 | 0.51 |
| 2. Run of river | 0.38 | 0.38 | 0.50 | 0.50 | 0.44 |
| 3. Sturgeon‐focused management | 0.25 | 0.42 | 0.50 | 0.67 | 0.46 |
| 4. Salmon‐focused management | 0.50 | 0.50 | 0.76 | 0.76 | 0.63 |
| Expected values under certainty | Hypothesis‐weighted average of maximum performance | ||||
| Maximum performance by hypothesis | 0.50 | 0.52 | 0.76 | 0.83 | 0.65 |
| Alternative | Hypothesis specific score (Vj,k) | Composite score (Vj) | |||
| 1. Sturgeon spawning/salmon Tcrit 11°C | 2. Sturgeon spawning/salmon Tcrit 12.5°C | 3. Sturgeon juvenile/salmon Tcrit 11°C | 4. Sturgeon juvenile/salmon Tcrit 12.5°C | ||
| 1. Long term average management | 0.19 | 0.52 | 0.50 | 0.83 | 0.51 |
| 2. Run of river | 0.38 | 0.38 | 0.50 | 0.50 | 0.44 |
| 3. Sturgeon‐focused management | 0.25 | 0.42 | 0.50 | 0.67 | 0.46 |
| 4. Salmon‐focused management | 0.50 | 0.50 | 0.76 | 0.76 | 0.63 |
| Expected values under certainty | Hypothesis‐weighted average of maximum performance | ||||
| Maximum performance by hypothesis | 0.50 | 0.52 | 0.76 | 0.83 | 0.65 |
Expected value of perfect information (EVPI) and expected value of partial information (EVPXI) for the set of four alternative temperature management strategies for Shasta Reservoir releases to the Sacramento River, California, under varying objective weights and equal hypothesis weights, for Chinook Salmon critical temperature egg‐to‐fry survival hypotheses and Green Sturgeon spawning and rearing hypotheses. Cells are shaded across EVPXI columns from least to greatest EVPXI scores (11.6% at Chinook objective weight = 0.38), and EVPI cells are shaded from least (light) to greatest values (dark green).
| Chinook Salmon objective weight | EVPI (%) | Hypotheses | |
| Chinook Salmon critical temperature − EVPXI (%) | Green Sturgeon spawning/rearing − EVPXI (%) | ||
| 0 | 0 | 0 | 0 |
| 0.25 | 2.94 | 5.53 | 2.70 |
| 0.38 | 11.60 | 5.83 | 7.52 |
| 0.50 | 3.74 | 3.74 | 0 |
| 0.75 | 1.44 | 1.44 | 0 |
| 1 | 0 | 0 | 0 |
| Chinook Salmon objective weight | EVPI (%) | Hypotheses | |
| Chinook Salmon critical temperature − EVPXI (%) | Green Sturgeon spawning/rearing − EVPXI (%) | ||
| 0 | 0 | 0 | 0 |
| 0.25 | 2.94 | 5.53 | 2.70 |
| 0.38 | 11.60 | 5.83 | 7.52 |
| 0.50 | 3.74 | 3.74 | 0 |
| 0.75 | 1.44 | 1.44 | 0 |
| 1 | 0 | 0 | 0 |
Expected value of perfect information (EVPI) and expected value of partial information (EVPXI) for the set of four alternative temperature management strategies for Shasta Reservoir releases to the Sacramento River, California, under varying objective weights and equal hypothesis weights, for Chinook Salmon critical temperature egg‐to‐fry survival hypotheses and Green Sturgeon spawning and rearing hypotheses. Cells are shaded across EVPXI columns from least to greatest EVPXI scores (11.6% at Chinook objective weight = 0.38), and EVPI cells are shaded from least (light) to greatest values (dark green).
| Chinook Salmon objective weight | EVPI (%) | Hypotheses | |
| Chinook Salmon critical temperature − EVPXI (%) | Green Sturgeon spawning/rearing − EVPXI (%) | ||
| 0 | 0 | 0 | 0 |
| 0.25 | 2.94 | 5.53 | 2.70 |
| 0.38 | 11.60 | 5.83 | 7.52 |
| 0.50 | 3.74 | 3.74 | 0 |
| 0.75 | 1.44 | 1.44 | 0 |
| 1 | 0 | 0 | 0 |
| Chinook Salmon objective weight | EVPI (%) | Hypotheses | |
| Chinook Salmon critical temperature − EVPXI (%) | Green Sturgeon spawning/rearing − EVPXI (%) | ||
| 0 | 0 | 0 | 0 |
| 0.25 | 2.94 | 5.53 | 2.70 |
| 0.38 | 11.60 | 5.83 | 7.52 |
| 0.50 | 3.74 | 3.74 | 0 |
| 0.75 | 1.44 | 1.44 | 0 |
| 1 | 0 | 0 | 0 |
When varying both hypothesis and objective weights, it becomes clear that the performance of the alternative temperature strategies depends on both sets of weights (Figures 5 and 6). As the relative weight on the Chinook Salmon objective increases, the Green Sturgeon rearing period hypotheses become less important to alternative performance (Figure 5). At weights higher than 0.63 on the Green Sturgeon objective (<0.37 on Chinook Salmon), the uncertainty related to Green Sturgeon spawning and rearing becomes more important to choosing between the run‐of‐river and sturgeon‐focused management as a preferred management strategy (Figure 5A–D). Uncertainty in Chinook Salmon temperature sensitivity becomes more important in differentiating between alternative temperature management strategies when Chinook Salmon objective weights are between 0.25 and 0.75, as the salmon‐focused management alternative dominates the other alternative temperature management strategies at higher Chinook Salmon objective weights (Figure 6B–E).
Variation in composite alternative Shasta Dam temperature management strategy scores by objective weight (varied across panels) and weighted by Green Sturgeon spawning and young‐of‐year juvenile rearing temperature sensitivity hypotheses for the Sacramento River, California.
Variation in composite alternative temperature management strategy scores by objective weight (varied across panels) and weighted by temperature sensitivity hypotheses for winter‐run Chinook Salmon egg‐to‐fry survival in the Sacramento River, California.
The EVPI also varied depending on the weights on objectives and hypotheses. Under equal objective weights, the percent EVPI ranged from 0 to 6.0%, depending on the weight placed on hypotheses, and EVPI ranged from 0 to 11.6% across all objective and hypothesis weights (Figure 7). This represents a 11.6% maximum gain in management performance, or composite score, reflecting an increase in Chinook Salmon egg‐to‐fry survival and Green Sturgeon minimum abundance, if all uncertainty was reduced prior to decision making. Conversely, our analysis indicated less influence of uncertainty on management performance with increasing weight on either objective (uncertainty matters less to the decision; Figure 7). Of course, there was no advantage in reducing uncertainty if 100% of the weight was placed on either objective (see EVPI in Figure 7; EVPI and EVPXIs = 0%, Table 5).
Variation in expected value of perfect information (%) by Chinook Salmon objective weight and (top) weight on the critical temperature hypothesis (12.5°C), and (bottom panel) weight on the Green Sturgeon summer young‐of‐year juvenile rearing period hypothesis related to Shasta Reservoir alternative temperature management strategies for the Sacramento River, California. Lines are colored according to hypothesis weight.
We demonstrate the EVPI calculations in a decision tree, using equally weighted hypotheses and objective weights that maximize EVPI (Chinook Salmon and Green Sturgeon objective weights of 0.38 and 0.62, respectively), and illustrate the relationships between objectives, hypotheses, and alternative management strategies (Figure 8; cf. Conroy and Peterson 2013; Smith 2020). In the lower branch of the decision tree, a decision maker chooses to implement the run‐of‐river temperature management strategy, because that action has the highest expected performance under uncertainty (0.5458, equation 2). If, on the other hand, the decision maker chooses to resolve uncertainty prior to committing an action (top branch of the decision tree), the expected performance is higher (0.6091). Although the realized management performance will depend on which hypothesis was true, an 11.6% increase in the Chinook Salmon and Green Sturgeon objectives would be expected once uncertainty was resolved (i.e., equation 3: EVPI = 0.6091–0.5458 = 0.0633 or 11.6% increase in management performance). In Figure 8, we also include a demonstration of the composite performance score calculations (Valternative 1, hypothesis 1; Equation 1).
A decision tree showing an example of the calculation of the expected value of perfect information (EVPI) for resolving uncertainties that influence selection of a temperature management strategy, with weights favoring Green Sturgeon and maximizing EVPI (Wsturgeon = 0.62, WChinook = 0.38). The bottom branch shows the expected value under uncertainty (0.5458; equation 2) and the top branch chooses the expected management performance after uncertainty is resolved (expected value under certainty = 0.6091); the difference is the EVPI (bottom left inset; equation 3). Decision points are represented by squares, uncertainties are represented by ovals, and outcomes are represented by hexagons. The outcomes (hexagons) are the composite performance scores weighted across objectives (W, far right), for each combination of action and hypothesis. At each uncertainty node, expected values are taken across the values associated with the possible hypotheses. At each decision node, the strategy with the maximum expected performance value is chosen (shown in bold text and shaded in green).
Our calculation of EVPXI, using an objective weighting scheme maximizing EVPI (11.6%), showed that reducing uncertainty in just the Green Sturgeon life‐stage‐specific temperature sensitivity would result in a greater gain in management performance (EVPXISturgeon = 7.52%) than reducing uncertainty in just the Chinook Salmon temperature sensitivity hypotheses (EVPXIChinook = 5.83%; Table 5).
DISCUSSION
We demonstrated the use of MCDA and VOI tools for decision making in the context of habitat management for two imperiled species with uncertain and potentially conflicting early life‐stage temperature requirements in California. We approached this decision analysis assuming adequate reservoir storage volume would exist, which allowed for flexibility in temperature management and a demonstration of uncertainties and trade‐offs that may be confronted in an average year. Our results suggest that run‐of‐river temperature releases from Shasta Dam would create ideal temperatures for Green Sturgeon but would result in very low winter‐run Chinook Salmon egg‐to‐fry survival. The salmon‐focused management alternative had the poorest performance for Green Sturgeon and best for Chinook Salmon (see Table 2) but would be the best choice under equal objective and hypothesis weights, as indicated by the composite scores for alternative temperature management strategies. However, the decision is hindered by uncertainty—if Chinook Salmon Tcrit is in fact warmer (12.5°C) and Green Sturgeon population growth is driven by summer juvenile rearing period temperatures (hypothesis 4), long‐term average management would provide optimal temperatures for both species. This uncertainty in predicted outcomes could become more or less important to the decision, depending upon a decision maker's values.
By varying weights across Green Sturgeon and Chinook Salmon objectives in our analysis, the sensitivity of alternative performance to a decision maker's values (e.g., Costello et al. 2010; Smith et al. 2015), and to uncertainty in species' temperature requirements became apparent. For example, performance of all alternatives was sensitive to Green Sturgeon uncertainty at objective weights favoring Green Sturgeon (e.g., slope of lines in Figure 5A–D), but the run‐of‐river alternative dominates the others, regardless of uncertainty, if all a decision maker cared about was Green Sturgeon (Figure 5A). When the Chinook Salmon objective was increasingly favored, the relationship between the performance of the long‐term average management alternative and Chinook Salmon uncertainty became stronger. However, this uncertainty would matter little to the decision maker at Chinook Salmon objective weights of ~0.8–1.0 because salmon‐focused management was insensitive to uncertainties in Tcrit and dominated the other alternative temperature management strategies. These results provide insights into interactions between uncertainty, values, and alternative management strategy performance.
Combining disparate metrics of different objectives (e.g., Chinook Salmon egg‐to‐fry survival with expected minimum Green Sturgeon population size) into a multi‐criteria value function can be disconcerting, but this is precisely the strength of MCDA—to allow the comparison of apples to oranges in a way that reflects the decision maker's values (Esmail and Geneletti 2018; Martin and Mazzotta 2018; Converse 2020). Nevertheless, it is important to understand several underlying assumptions of such an analysis. First, we assume that the performance metrics are measures of the decision maker's fundamental objectives. In our case study, for example, egg‐to‐fry survival is an expedient measure of a key life history parameter, but it might not be the outcome that the decision maker fundamentally cares about. Careful work with the decision maker is warranted to ensure the objectives are captured accurately. Second, the MCDA method we have used assumes that the decision maker cares about the performance metric in a linear manner. If this is not the case, then there are methods for generating a nonlinear value function that captures the preferences of the decision maker (Esmail and Geneletti 2018; Runge and Converse 2020). In our case study, for example, if there is a threshold in egg‐to‐fry survival rate below which the outcome is unacceptable to the decision maker, a nonlinear value function that reflects that threshold could be included in the analysis. Third, we have assumed that the multi‐attribute value is an additive function of the objective measures, such that the relative contribution of one objective to the overall performance does not depend on the performance of the other objectives. This need not be the case, and there are more detailed techniques for accommodating this type of dependence in the preferences. While these more advanced decision analysis tools were beyond the scope of our study, we point the reader to Gregory et al. (2012), Hemming et al. (2018, 2022), Converse (2020), and other literature referenced for more information.
Research and monitoring can improve understanding of ecosystem dynamics; however, not all sources of uncertainty resulting from incomplete knowledge are equally important to decision making (Hansen and Jones 2008; Runge et al. 2011b). The calculation of EVPI and EVPXI facilitates a direct link between management objectives and the importance of specific uncertainties (Bolam et al. 2019). The relative improvement in management performance of up to ~12%, as measured by an expected increase in (normalized) Green Sturgeon abundance and Chinook Salmon egg‐to‐fry survival and reflected in composite scores for management strategies, may be achieved if research, conducted before the decision maker commits to a decision, clarifies the relationships between demographic rates and temperatures. Although VOI varied across objective weights, when comparing the relative importance of specific sources of uncertainty (EVPXI), maximum improvements in the management performance could be achieved if research was focused on Green Sturgeon spawning and rearing temperatures. However, outcomes could be improved across a broader range of objective weights if future research was focused on addressing uncertainties related to Chinook Salmon Tcrit. Ultimately, a manager must decide when the VOI is high enough to forgo taking an action and pursue acquiring information to reduce the relevant uncertainty. The decision is easy when VOI is zero—an action should be taken because delaying the action to reduce uncertainty will not change which alternative is best from the set considered. Alternatively, as the VOI increases or the cost of reducing remaining uncertainty increases, the decision becomes more difficult, particularly if resources for research and monitoring come at the expense of other species recovery actions (Hansen and Jones 2008; Buxton et al. 2020). To reduce uncertainties in our case study, researchers could consider expanding lab‐ and field‐based temperature studies across species' life stages (Rodgers et al. 2019) and life stage transitions. For example, monitoring Green Sturgeon egg survival in spring, and young‐of‐year Green Sturgeon survival and Chinook Salmon egg‐to‐fry survival or juvenile production through the summer (Nelson et al. 2022), under spatiotemporally variable temperatures, could lead to improved management for both species.
Fisheries management downstream of Shasta Dam in the Central Valley, and in other altered systems, is likely influenced by a complex interaction of disparate uncertainties, and multiple objectives and constraints that could be included in a comprehensive MCDA. Scientists may tend toward ecologically realistic but complicated and unfocused system models, but in reality, it is often the case that few sources of uncertainty are important to decision making (Peterson and Duarte 2020). Within MCDA, the roles of scientists (charged with making hypothesis‐driven predictions about management performance) and fisheries managers (responsible for decision making) are separate—involving both in the process helps ensure key uncertainties that affect the decision are identified (Runge et al. 2011b; Peterson and Duarte 2020; Smith 2020). Using VOI methods to evaluate the importance of uncertainty through expert elicitation, for example, before implementing formal experiments, can help inform trade‐offs between investing in information gathering or implementing management actions like habitat restoration (Hansen and Jones 2008). Our analysis demonstrates that uncertainty may complicate decision making (Runge et al. 2011a, 2011b) and management performance ultimately depends on the interaction between a decision makers' values and biological uncertainty. Ultimately, MCDA and VOI are transparent and deliberative tools that can assist fisheries managers in confronting value conflicts that are becoming increasingly difficult, improving resource allocation, and optimally managing aquatic ecosystems.
ACKNOWLEDGMENTS
The Bay‐Delta Reclamation Office provided funding for this work, and R code to facilitate the use of the SacPAS model was developed by W. N. Beer, University of Washington, and provided to Reclamation. We appreciate Michael E. Colvin, U.S. Geological Survey Columbia Environmental Research Center, and four anonymous reviewers for constructive peer reviews that improved our manuscript. Any use of trade, firm, or product names is for descriptive purposes only and does not imply endorsement by the U.S. Government. The views expressed are those of the authors and do not represent the views of the U.S. Bureau of Reclamation. There is no conflict of interest declared in this article.
