Review of Decade-Old Misdirection on Delta Smelt

For several decades, scientific literature and state and federal permits have documented the decline in Delta smelt and promoted actions designed to slow the Delta smelt’s demise or even reverse it. However, that soundly based and widely promoted recovery strategy has often been undermined by some scientists and engineers funded by water-related industries and users intent on minimizing constraints on their water operations. The undermining of traditional science and regulatory institutions has been insidious and aggressive, to the point of nearly destroying the Central Valley and Bay-Delta ecosystem and many of its public trust resources. I know this from working nearly 50 years on these conflicts.

A recent interest takes me back to some of these undermining efforts from a decade ago. In this post, I evaluate past theories from such efforts and further characterize the “science” used to support them. I believe such hindsight reviews of these historical efforts helps to daylight and counteract similar present and future attempts to undermine institutional protections. I focus on unsubstantiated conclusions, on misuse of data or analytical tools, and on the authors’ general strategy of promoting misinformation to argue their points.

The “scientific paper” I review in this post on Delta smelt is William J. Miller, Bryan F. J. Manly, Dennis D. Murphy, David Fullerton & Rob Roy Ramey (Miller et al.) (2012): An Investigation of Factors Affecting the Decline of Delta Smelt (Hypomesus transpacificus) in the Sacramento-San Joaquin Estuary, Reviews in Fisheries Science, 20:1, 1-19, DOI: 10.1080/10641262.2011.634930.1

In commenting below, I show quotations from the paper in quotes and italics.

Comments on the Authors’ Major Conclusion in the Abstract

  • “Strong evidence was found of density-dependent population regulation.” The authors made no attempt to describe such “regulation” of the Delta smelt population. First, the meaning of “strong” is unclear. I assume the authors mean that two variables appear closely related. I found a “density-dependent” relationship (see my Figure 1, below), wherein summer abundance is positively related to previous fall abundance. Second, the meaning of “regulation” is unclear. I assume by “regulation” they mean that at very high numbers of adults, recruitment tails off, as implied in the blue curve in Figure 1. But as shown in the figure, the inference is far from a “strong evidence” of “population regulation” due to density.

  • “The density of prey was the most important environmental factor explaining variations in delta smelt abundance from 1972 to 2006 and over the recent period of decline in the abundance of the fish.” Association does not necessarily mean cause and effect. In Figure 1, I show that wet years have, on average, ten times more recruitment than dry years. That could be why prey appears important, because smelt prey densities (and feeding habitat conditions) tend to be better in wet years. However, water temperatures are also higher in dry years, as is entrainment of smelt in the south Delta. Just because prey has the highest correlation does not mean it is the cause or has any direct effect. These variables are not independent from one another.

  • “Predation and water temperature showed possible effects.” The authors also noted other positive relationships. The problem with such statistical analyses is that the “independent variables” being tested against smelt abundance are not independent from each other. Therefore, no judgement can be made as to cause and relationship, only inferences.

  • “Entrainment of delta smelt at south Delta pumping plants showed statistically significant effects on adult-to-juvenile survival but not over the fish’s life cycle.” Here again, cause and effect are inferred. The authors state the fact that recruitment is related to the number of adult spawners, yet they immediately state otherwise. Entrainment of adult smelt is something that has been measured – as salvage at the south Delta pumping plants. It is a variable that can readily be compared to the fall trawl index. But entrainment of larvae and early juveniles (6-25 mm young) is not measured, and thus this part of the “fish’s life cycle” cannot be statistically related to any smelt index.

  • “Neither the volume of water with suitable abiotic attributes nor other factors with indirect effects, including the location of the 2 ppt isohaline in the Delta in the previous fall (“fall X2”), explained delta smelt population trends beyond those accounted for by prey density.” When a variable shows minimal relationship, it cannot be concluded that it has no effect, or compared in strength to another “independent” variable (another potential factor). Fall X2 may only be important in some years, and thus its effect relationship may be non-linear.2 The relationships being studied may also change with time (as indicated in Figure 1). Relationships are also often complicated by factors that act in complex ways. Posts on my own reviews generally support the Fall X2 action for a variety of reasons.3 Thus, the authors’ conclusion or implication that Fall X2 is not important is not reasonable. The prey factor simply takes up more of the variability in the multi-factor statistical analysis, and thus masks the role of Fall X2.

Comments on the Introduction

  • The need for immediate conservation responses is acute, but that need confronts another unfortunate delta smelt reality—perhaps less is known about the habitat of delta smelt, resources essential to its persistence, and the environmental stressors causing its low population numbers than is known about any other listed species.” This statement has no basis and is simply untrue. Delta smelt are one of the most studied fish on Earth.

  • “The life cycle of the tiny estuarine fish takes place in turbid, open waters, making it impossible to observe its behavior and account for many of its vital ecological relationships.” Over the past five decades, there have been numerous studies and volumes of monitoring data on Delta smelt “ecological relationships”. One only has to look at Figure 1. As for behavior, Delta smelt have been raised and observed in labs and hatcheries for over two decades. Two decades ago, I could literally smell them and their prime habitat. I could also tell where they would be by measuring salinity and water temperature.

  • “Several candidate factors have plausible mechanisms of effect on delta smelt numbers, but previous attempts to relate environmental stressors to the decline of this fish were not able to identify the factors responsible for the recent declines in the abundance index to near-extinction levels.” The evidence from the 1987-1992 drought (see Figure 1 for one of many examples) was quite compelling, enough to get the species listed under the Endangered Species Act, first as threatened (1993), then as endangered (2010). All the “plausible factors” could be related to drought conditions that had become worse with ever-increasing effects of water management (increasing exports year after year). Protections instituted in the aftermath of the drought and listing4 included designation of critical habitat (1994) and a recovery plan (1996), as well as multiple federal biological opinions and habitat conservation plans, and state incidental take permits over the next two decades. Recovery programs, including the Central Valley Project Improvement Program (CVPIA) and CALFED Bay-Delta Ecosystem Restoration Program (ERP), focused on Delta smelt recovery. Those efforts led directly to significant progress in 2010-2011; however, weakened protections during the 2012-2015 drought ended the potential for further progress.

  • “No field data have been derived from experimnts that directly relate delta smelt population responses to variation in physical and biotic conditions.” This statement is a gross untruth. The data that support Figure 1 are “field data.” Many of the various monitoring surveys (e.g., Larval Survey, 20-mm survey, Townet Survey) yield indices that show such relationships.

Comments on the Discussion

I could go on in the same -vein through the paper’s introduction, methods, results, and discussion, but I will skip to the paper’s primary conclusions as presented in the discussion section.

  • [E]ntrainment was not a statistically significant factor in survival from fall to fall”. First, entrainment of early smelt life stages into the federal and state south-Delta export facilities is not monitored. Second, monitoring that does help assess entrainment risk shows the inherent risk (Figures 2 and 3). Third, the fall midwater trawl survey includes the fall period of high adult salvage losses that contributed to the population decline, a data feature that compromises the fall-to-fall survival-factor analysis.

  • “Changes in prey density appear to best explain the sharp drop in delta smelt abundance in this century”. First, Delta-smelt prey density is also directly and indirectly related to south Delta exports. Second, an annual index of smelt prey is a very crude way to analyze the effects of prey through the various life stages of smelt or its annual abundance indices.

  • “Density dependence was an important factor affecting survival from fall to summer, summer to fall, and fall to fall.” First, there is little or no evidence that high densities reduce recruitment or survival, at least in the period of record. Historically, available habitat had to limit the population size and recruitment near their highest abundance levels. Second, there is also no evidence that very low population levels lead to higher survival, growth, or abundance (from less crowding and competition). These are the two features that generally contribute to density-dependent population regulation. What the authors term density-dependence is simply the fact that more adults lead to more young, and more young lead to more adults. Water management and use lead to fewer adults and young – density independent population regulation controls population abundance.

  • “This finding indicates that density dependence must be accounted for in analyses directed at identifying factors that are important to the abundance of delta smelt.” This only means that any factors that lead to fewer adults or young damages the population, and that those losses are compounded across life stages. There are no remaining compensatory density-dependent capacity reserves in the population to absorb or counter such added mortality.

  • “There was some indication that average water temperature and calanoid copepod biomass (a general measure of prey density) in April–June were important contributors to survival of delta smelt from fall to summer.” Again, these are factors affected by water management. Delta exports pull warm water and invertebrates into the south Delta. These are density-independent factors.

  • “Furthermore, predation in April–June, representing the combined effects of water clarity and abundance of the predators, inland silversides, largemouth bass, crappie, and sunfish, was important to delta smelt survival from fall to fall.” Again, the effects of predation are increased by the warmer, clearer water pulled into the interior Delta by south Delta exports.

  • “Furthermore, in the case of delta smelt, not only does an effects hierarchy suggest the use of simple linear regression models, but the low sampling errors in abundance relative to process errors indicates that this simple and transparent method of analysis is an appropriate method for identifying environmental factors with direct effects. Therefore, at least for delta smelt and perhaps for other fish for which sampling errors in abundance are relatively low, simple linear regression, as an alternative to more complex life-cycle models, can produce informative results.” Such analyses have been inappropriately used to confuse interpretations of long-term environmental and fish population dynamics data, and to misinform and misdirect environmental resource management and regulatory processes, institutional and public awareness, and the public’s confidence in these societal and cultural institutions.

Summary and Conclusions

Miller et al. (2012), the “scientific” paper referenced in this post, is an example of efforts on the part of state and federal water contractors to point the blame for resource declines on factors other than water operations that overuse and abuse public trust resources. It is important not only in itself, but also because it combines with similar efforts to become part of a body of alternative “science” that is cited by water suppliers and managers in repetition of the narrative that water operations have minimal effect on the Delta smelt’s decline.

I recognize that such efforts may appear in “peer reviewed” journals, and can be sincere efforts to contribute to the understanding of the science underlying resource management. I am simply registering the need for caution and consideration of the source and the content of all analytical and interpretive efforts related to information used by those responsible for protecting our public trust resources.

Figure 1. Delta smelt spawner-recruit relationship. Figure generated by Tom Cannon.

Figure 2. Delta smelt survey catch pattern from mid-June 2012, one of the last surveys with an abundance of larval smelt produced from the strong 2011 brood spawning population. The red lines show the approximate location of the upstream location of X2 (low salinity zone).

Figure 3. Typical dry year spring-summer tidally-filtered (net) or daily-average hydrology for the Delta, showing net flow rates toward south Delta export pumps.

Cache Slough Tidal Wetland Restoration – Update More misguided resource-damaging habitat restoration for an already highly altered and compromised Delta

Cache Slough Complex Restoration

The Cache Slough Complex is in the lower (southern) Yolo Bypass in the north Delta region (Figure 1). It is the focus of the state’s tidal wetland restoration EcoRestore Program that spans 16,000 acres in the Cache Slough region of the Sacramento-San Joaquin Delta.

The 53,000-acre Cache Slough Complex is located in the northwest corner of the Sacramento-San Joaquin River Delta in Solano and Yolo counties (Figure 1). The Yolo Bypass receives inflow directly from the Sacramento River (Fremont Weir), the Colusa Basin Drain, Putah and Cache creeks, and agricultural and municipal discharges. The Cache Slough Complex exits the Yolo Bypass via Cache Slough, first connecting to the outlets of Miner and Steamboat Sloughs, before entering the tidal Sacramento River channel near Rio Vista.

The Cache Slough Complex has been identified as an area with great potential for tidal restoration as a result of its connectivity with the Yolo Bypass floodplain, suitable elevations, high turbidity, high primary and secondary productivity, and use by Delta smelt (Hypomesus transpacificus), Chinook salmon (Oncorhynchus tshawytscha), and other native fishes. Both federal and state wildlife agencies consider the Cache Slough Complex to be a prime area to advance habitat conservation to benefit endangered species in the Sacramento-San Joaquin Delta and incorporate improvements to the regional flood management system.

The latest project approved for construction is the Lookout Slough Project, a 3000-acre tidal marsh restoration immediately to the west of Liberty Island. The Project was certified by DWR in 2020 as mitigation/compensation for the Delta Tunnel Project. The Delta Stewardship Council recently denied appeals1 to the state’s certification of the Lookout Slough tidal marsh restoration project. Once completed, Lookout Slough will be the Delta’s largest single tidal habitat restoration project to date.

The Problem

Most of the tidal “restoration projects” in the Cache Slough Complex involve breeching leveed tracts of agricultural land to create subtidal or intertidal habitat. Tidal waters once confined to narrow floodplain channel are now allowed to pour through breaches onto over 10,000 acres of formerly diked farmlands. The process started between 1980 and 2000 when Little Holland Tract (1456 acres) and Liberty Island (4340 acres) levees failed and were not repaired, leaving these lands open to the tides. Because these reclaimed wetlands had subsided during active farming, most of the “restored tidelands” became sub-tidal, year-round, warm, shallow, open-water habitat. Such habitat is too warm for Delta native fishes except during the winter.

The enhanced tidal exchange and warm productive winter and early-spring habitat attracts migratory Delta native fishes like smelt, splittail, and salmon to the Cache Slough Complex. While such habitat is considered beneficial in winter, it warms excessively in spring and summer, reducing the period of quality rearing, and can reduce overall survival and production. Native fishes have succumbed to the heat, stranding in the uneven landforms, and predation by non-native warm-water fish.

The latest projects, Lower Yolo Ranch (1749 acres), Yolo Flyway Farms (300 acres), and Lookout Slough (3000 acres), will add 5000 acres of mostly shallow intertidal habitat. Tidewater will flood onto these lands twice a day to warm in the California sun and then return to cooler deep, shaded, sub-tidal sloughs long considered prime Delta smelt and salmon rearing habitat. Not only will the new inter-tidal “wetlands” be too warm, but they will contribute to warming adjacent sub-tidal sloughs that convey water to and from other parts of the north Delta. This water quality degradation gets worse with each new project and has resulted in the degradation of the entire north Delta as a viable spawning, rearing, and critical habitat of Delta smelt. The effect has measurably contributed to the near extinction of Delta smelt.

The Evidence

The United States Geological Service has many water quality and flow monitoring gages in the Cache Slough Complex (Figure 2) that provide considerable evidence of the above-described problem. Specific gages with pertinent data records reviewed for this post are highlighted in Figure 2.

Waters in the northern Cache Slough Complex become too warm for salmon and smelt (>20ºC) by spring (Figure 3). In summer (Figure 4), water tidally flooded into subtidal island-tracts can warm 5-7ºC over a day before draining back into adjacent sloughs. Water temperatures in the northern sloughs of the Cache Slough Complex reach 25ºC (lethal to smelt) or higher in summer, even in wet and normal water years (2016-2018, Figure 5). Water temperatures in the southern Cache Slough Complex are only slightly lower (Figure 6). Over the past decade, water temperatures in the Cache Slough Complex overall have been gradually increasing (Figures 7 and 8), to the detriment of Delta native fishes.

The Solution

The problem can be lessened or even reversed at existing and future restoration projects by:

  1. Limiting tidal access to sub-tidal sites to winter, when water and air temperatures are colder.
  2. Building projects with flow-through tidal channel features rather than a single opening.
  3. Ensuring that projects are inter-tidal with small, narrow, shaded channels, or tule benches.
  4. Narrowing, deepening, and shading connecting tidal sloughs.
  5. Limiting discharge of warm agricultural wastewater into tidal channels.
  6. Providing supplementary inflow of Sacramento River water from the Fremont Weir, from the entrance gates of the Sacramento Deepwater Shipping Channel, or from other locations.
  7. Retrofitting existing restoration sites and designing future projects as outlined above.


Figure 2. USGS gage locations in the Cache Slough Complex.

Figure 3. Water temperatures recorded at Little Holland Tract in 2015-16.

Figure 4. Water temperatures and water surface elevation (gage height) recorded at Little Holland Tract in July 2017. Note higher water temperature spikes occurred with strongest ebb (draining) tides.

Figure 5. Water temperature in Liberty Cut adjacent to Little Holland Tract, 2016-18.

Figure 6. Water temperature and tidally-filtered flow rate in Sacramento Deepwater Ship Channel, April-September 2021.

Figure 7. Water temperature in lower Cache Slough, 2011-2016.

Figure 8. Water temperature in the lower Sacramento River channel near Rio Vista, 2010-2019.

Yolo Flyway Farms Tidal Wetland Restoration Project

Yolo Flyway Farms

The Yolo Flyway Farms project is a new element of the state’s EcoRestore program to fulfill requirements of federal biological opinions for the State Water Project and Central Valley Project. The 300-acre tidal wetland restoration project is located in the southern Yolo Bypass in what is commonly referred to as the Cache Slough Complex (Figure 1). The Project’s design entails allowing tidal access to excavated upland irrigated pasture land by opening levees along Prospect Slough (Figure 2). The Project is in a known area of concentration for Delta smelt as determined by nearby CDWR screw trap sampling in Prospect Slough (Figure 3). Project sponsors submitted a certification of consistency with the Delta Plan to the Delta Stewardship Council.1

Are such projects in the best interest of the Delta smelt population? A close look at project attributes may help answer the question.

Positive attributes:

  1. Replacement of the existing tide gate irrigation system with open levee breaches eliminates existing entrainment and loss of Delta smelt and other fishes into the irrigated pasture lands.
  2. New tidal channels and tidal wetlands would provide rearing habitat for young smelt, salmon, and splittail. Plankton and benthic invertebrate food sources for fish would likely increase.
  3. Hard surfaces may provide smelt spawning habitat.

Negative attributes:

  1. Tidal channels would provide new habitat for predatory birds and fish , which could increase loss of young smelt and salmon. Prospect Slough is deep, turbid, strong- current habitat unfavorable to predators. Tidal channels of project would be dead end, low velocity, less turbid habitats favorable to predators of fish.
  2. The southern Yolo Bypass aquatic habitats are warm from spring through fall, at times exceeding the thermal optimum for Delta smelt. Proposed shallow-water dead-end sloughs and flooded wetlands would warm and increase warming of Prospect Slough and other lower Bypass waters. While a positive attribute in winter and at times in late fall and early spring, this would be detrimental at other times.

Despite the potential positive benefits of such restoration in general, the potential negative aspects of the Project are a real concern. Some of the potential negative effects could be reduced through changes in project design and operations. At a minimum, the project should be considered an adaptive management experiment where potential positive and negative attributes are studied to determine the overall benefit of the action and whether it fulfills the objectives of the biological opinions.

Figure 1. Yolo Flyway Farms Project location (red circle) in southern Yolo Bypass.

Figure 3. Prospect Slough adjacent to Deepwater Shipping Channel and Liberty Island in southern Yolo Bypass. CDWR screw trap in yellow circle.

Smelt Status – Spring 2022

Initial 2022 late winter surveys indicate modest improvement in longfin and Delta smelt populations. Previous posts outlined the grim status of the two species.1

Delta Smelt

Five larval Delta smelt were captured in the first 20-mm survey of 2022. They were captured in the Cache Slough Complex in late March (Figure 1). After more of the survey is processed, further numbers of recently hatched larvae may be noted, indicating a slight improvement in the nearly extinct population.

Longfin Smelt

Larval longfin smelt were widely collected in the late February Smelt Larva Survey (Figure 2). Highest densities were in the low-salinity zone (Figures 2 and 3). Numbers were higher than in recent years, likely reflecting good early winter condition after high December Valley-wide precipitation.

These modest improvements in the endangered smelt populations will likely be short-lived as the State Board enacts the Temporary Urgency Change Petition (TUCP) of the Department of Water Resources and the Bureau of Reclamation in response to the winter 2022 drought. The TUCP will further reduce freshwater outflow and move the low-salinity zone upstream into the Delta (Figure 4 and 5). Depleted reservoir storage resulting from excessive storage releases to water contractors in 2020 and 2021 created the need for the petition. Despite the depleted reservoir storage, less extreme measures are possible that would provide some protection for the smelt, as discussed in an April 5 post.

Figure 1. Partial results of late March 2022 20-mm Survey, showing location of 5 identified Delta smelt larvae in Cache Slough Complex.

Figure 2. Results of late February 2022 Smelt Larva Survey, showing density of longfin smelt larvae collected in Bay-Delta survey region. Red outline is area of low-salinity zone (2000-8000 EC).

Figure 3. Plot of longfin smelt larvae catch per 1000 cubic meters sampled in late February Smelt Larva Survey (shown in Figure 2). Red curve shows that larvae were concentrated in the low-salinity zone (2000-8000 EC).

Figure 4. Salinity at confluence of Sacramento and San Joaquin Delta channels in eastern Suisun Bay in late winter – early spring 2022.

Figure 5. Calculated Delta outflow in late winter – early spring 2022.

A Simplified Look at the Complex World of Fish Population Dynamics

I have a simplified approach in analyzing fish population dynamics from which I review the status of populations of smelt and salmon. It looks at the dynamics of the relationship between the number of spawning adults and their returning adult recruits one to several years later (Figure 1). In the fish science vernacular, it is sometimes referred to as the “spawner-recruit curve” or “stock-recruitment relationship” or simply “S/R relationship”. The major features of a S/R relationship are shown in Figure 1 (A, B, and C):

A. The blue and red curves show a standard spawner-recruit relationship, with higher spawners bringing more recruits – more eggs, more young, more smolts, more returning spawners, etc. It tails off when too many adults result in competition for food or spawning habitat, or higher rates of communicable disease – density-dependent effects.

B. The variability around the blue and red curves, shown by the vertical lines through the curves, is caused by density-independent effects such as drought, fishing harvest, or pollution that vary from year to year.

C. The difference between the blue and red curves, shown in the example as a yellow arrow, is a shift in the S/R curve that is a result in a fundamental shift in the relationship. Examples of such changes are the amount or quality of habitat from a dam being built, watershed destruction from a fire, loss of streamflow from new water diversions, loss of prey base, etc. The blue curve shows the S/R relationship before a fundamental shift; the red curve shows the S/R relationship after the fundamental shift.

Some environmental factors can affect one or more of the three features. For example, hatcheries can increase recruits (A and B), or they can cause a fundamental shift in the relationship (C) by imposing genetic changes in the population. Hatcheries benefit egg viability and fry survival, producing more smolts to the ocean per spawner in salmon populations, but may alter the wild component’s genetic viability.

The winter-run salmon population’s S/R relationship (Figure 2) exhibits these features, as well as the overall complexity in the relationship. Hatchery smolt introductions have propped up the population over the past two decades and increased its variability (red curve and vertical line), especially during periods of drought.

For longfin smelt, a state-listed species, there is a strong S/R relationship (Figure 3) to the features described in A-C above. There is a strong positive S/R relationship (A). There is a strong effect of the climate (B). And there appears to be a fundamental shift in recent years (C).

For Delta smelt (Figure 4), a state- and federally-listed species, which I consider nearly extinct at least in the wild, there was a strong S/R relationship (A), a climate effect (B), and a fundamental shift (C). The latter proved simply not sustainable, leading to a population crash that is not recoverable without supplementation (hatchery inputs) or drastic changes In environmental conditions.1 Note that 2016 is the last year in this figure, because the population since 2017 has been too close to zero to evaluate.

The largest salmon population, the Sacramento fall-run salmon, long sustained by hatchery inputs, is mainly controlled by feature B (Figure 5). Climate and water management are the dominant control of survival of hatchery and naturally-produced smolts reaching the ocean.

In conclusion, I recognize that S/R relationships represent a simplified view of extremely complex and changing relationships in the real world. Estimates of the number of spawners and recruits are often crude. But the relationships are real and statistically significant. It is up to us to interpret them by relating causal factors and developing hypotheses that can be tested with further scientific study and experiments. Unfortunately, managing fishery resources in the face of complex ecology, difficulty monitoring, natural variability, and statistical measurement errors is inherently difficult, even before political and economic factors get into the mix.

Figure 1. Spawner-Recruit relationships with three main features (A-C). See text for explanation of the features. In figures 2-4 below, the blue curve represents the historical S/R relationship. The red curve represents the new historical S/R relationship following a fundamental shift in the relationship, including long-term drought. The vertical lines through the curves show the range of the annual variability of the S/R relationship attached to each curve, excluding the density-dependent variability that is incorporated into the curve. In this example figure, the yellow curve tracks a fundamental shift in the S/R relationship. Spawners are shown on the x-axis; recruits are shown on the y-axis. The numbers on the axes are log transformed in order to make size of the figures manageable; log transformation does not alter the statistical relationships.

Figure 2. Spawner-Recruit relationship for winter-run Chinook salmon in the Sacramento River. Numbers shown represent the brood year of recruits (number of returning adults) for year displayed. For example, “11” represents fish produced in wet year 2011. The color of the number shows the conditions when brood was spawned and reared in the upper Sacramento River below Shasta Dam before emigrating to the ocean. A red number shows a dry year during spawning and early rearing. A blue number designates wet year spawning and rearing conditions. A green number designates normal water year conditions. For example, 15 represents brood-year 2015 recruits that returned in 2018, while its red color designates drought conditions in 2015. In this figure, numbers on axes are log-2 transformed.

Figure 3. The longfin smelt S/R relationship. The number and color represents the brood year’s fall index (recruits) and its water year type during its spawning run and first year of rearing. The spawners are the index from two years earlier. For example, the red number 15 represents the fall index for brood-year 2015 under water-year 2015 drought conditions, with spawners being the recruits from 2013. In this figure, numbers on axes are log-log transformed.

Figure 4. The Delta Smelt S/R relationship. I added two curves and a vertical line to an original figure to show the hypothesized S/R relationship; there is too little variability in the red curve for a vertical line to be meaningful.

Figure 5. Spawner-Recruit relationship for upper Sacramento River mainstem fall-run Chinook salmon. Number is recruitment year (escapement). Spawners are recruits from three years prior. Numbers are log minus 3 transformed. A red number shows a dry water year two years prior during rearing and emigration. A blue number shows a wet year two years prior. A green number shows for a normal water year two years prior. For example: red 17 represents 2017 run that reared in drought year 2015, with spawners (parents) being the 2014 green run number. Note that only one curve is shown. in gray, for this run of salmon, which is almost entirely dependent on hatchery production.