Sensitivity of survival to migration routes used by juvenileChinook salmon to negotiate the Sacramento-San JoaquinRiver Delta

Russell W. Perry & Patricia L. Brandes &

Jon R. Burau & A. Peter Klimley &

Bruce MacFarlane & Cyril Michel & John R. Skalski

Received: 28 February 2011 /Accepted: 24 January 2012# Springer Science+Business Media B.V. 2012

Abstract Populations of juvenile salmon emigratingfrom natal rivers to the ocean must often traverse differ-ent migratory pathways that may influence survival. Inregulated rivers, migration routes may consist of a net-work of channels such as in the Sacramento-San Joa-quin River Delta, or of different passage structures athydroelectric dams (e.g., turbines or spillways). To in-crease overall survival, management actions in suchsystems often focus on altering the migration routingof fish to divert them away from low-survival routes andtowards high-survival routes. Here, we use a 3-year dataset of route-specific survival and movement of juvenileChinook salmon in the Sacramento-San Joaquin Deltato quantify the sensitivity of survival to changes inmigration routing at two major river junctions in theSacramento River. Our analysis revealed that changes in

overall survival in response to migration routing at oneriver junction depended not only differences in survivalamong alternative routes, but also on migration routingat the other river junction. Diverting fish away from alow-survival route at the downstream river junctionincreased population survival by less than expected,given the difference in survival among routes, becausepart of the population used an alternative migrationroute at the upstream river junction. We also show thatmanagement actions that influence only migration rout-ing will likely increase survival by less than actions thatalter both migration routing and route-specific survival.Our analysis provides an analytical framework to helpfisheries managers quantify the suite of managementactions likely to maximize increases in population levelsurvival.

Environ Biol FishDOI 10.1007/s10641-012-9984-6

R. W. Perry : J. R. SkalskiSchool of Aquatic and Fishery Sciences,University of Washington,Seattle, WA 98103, USA

P. L. BrandesUS Fish and Wildlife Service,4001 N. Wilson Way,Stockton, CA 95205, USA

J. R. BurauUS Geological Survey, California Water Sciences Center,6000 J Street,Sacramento, CA 95819, USA

A. P. KlimleyBiotelemetry Laboratory, Department of Wildlife Fish &Conservation Biology, University of California,Davis, CA 95616, USA

B. MacFarlane :C. MichelNOAA Fisheries, Southwest Fisheries Science Center,Fisheries Ecology Division,Santa Cruz, CA 95060, USA

Present Address:R. W. Perry (*)US Geological Survey, Western Fisheries Research Center,Columbia River Research Laboratory,5501-A Cook-Underwood Road,Cook, WA 98605, USAe-mail: rperry@usgs.gov

Keywords Migration . Telemetry . Juvenile salmon .

Sacramento-San Joaquin Delta . Survival

Introduction

Population dynamics of migrating fish depend on howthey use space over time. Populations may traversedifferent migratory pathways en route to their finaldestination. For example, variation in ocean currentsmay affect migration pathways of adult salmon return-ing to their natal rivers (Bracis 2010). In regulatedrivers, migrating juvenile salmon may negotiate damsvia alternative pathways such as spillways or turbines(Skalski et al. 2002, 2009). In estuaries and river deltas,complex channel networks offer an array of possiblemigration routes (Perry et al. 2010). In each of theseexamples, survival rates may vary among migrationroutes due to differences in migration timing, foodresources, environmental conditions, or predator abun-dance. Thus, understanding variation in survival amongmigration routes can provide important insights aboutpopulation dynamics.

The Sacramento-San Joaquin River Delta (hereaf-ter, the Delta) is a complex network of natural andman-made channels through which juvenile salmonmust navigate on their journey to the ocean (Fig. 1).As juvenile salmon enter the Delta from natal streams,they disperse among the Delta’s complex channelnetwork. This dispersal process is driven by the rela-tive quantities of discharge entering each channel, thehorizontal distribution of fish in the water column asthey pass a channel junction (a main channel splittinginto two or more channels), and by tidal cycles thatalter flow patterns at river junctions. Once fish enter agiven channel, they are subject to channel-specificprocesses that affect their rate of migration, vulnera-bility to predation, feeding success, growth rates, andultimately, survival. Eventually, alternative migrationroutes converge at the exit of the Delta and the popu-lation once again comes together to migrate throughSan Francisco Bay.

Movement of juvenile salmon among migrationpathways in the Delta is influenced by water manage-ment actions that route water from the Sacramento andSan Joaquin Rivers into pumping stations in the south-ern Delta. In this paper, we focus on the influence ofwater management actions on juvenile salmon emi-grating from the Sacramento River. Specifically, the

Delta Cross Channel is a man-made gated channel thatdiverts water from the Sacramento River into the inte-rior Delta, where it then flows towards the pumpingstations to be exported for agricultural and domesticuses (Fig. 1). Juvenile salmon entering the interiorDelta exhibit lower survival probabilities than othermigration routes, presumably due to longer migrationtimes, entrainment at the pumping stations, and expo-sure to predators (Brandes and McLain 2001; Newmanand Brandes 2010; Perry 2010). Furthermore, overallsurvival through the Delta (the fraction survivingthrough all routes) has averaged less than 33% formigration years 2007–2009 (Perry 2010).

Recovering endangered salmon populations in theCentral Valley requires actions that mitigate the effectsof water management on juvenile salmon. Increasingjuvenile salmon survival in the Delta may consist ofactions aimed at either reducing mortality within mi-gration routes or directing the population away fromlow-survival migration routes such as the interior Del-ta. Quantifying potential benefits of implementing re-covery actions can help fisheries managers weigh thecosts of a given action against benefits measured interms of increasing overall survival. In this study, weexamine how altering migration routing can influencethe overall survival of juvenile salmon.

In the Delta, migration routing of juvenile salmoncan be altered in at least three ways. First, physicalbarriers, such as closure of the Delta Cross Channelgates, keep fish from entering a given migration route.However, physical barriers also alter the distributionof water flow, which can have unforeseen consequen-ces on both fisheries and water resources. For exam-ple, closure of the Delta Cross Channel gatessignificantly alters the flows of many channels bothupstream and downstream of the Delta Cross Channel,which in turn may affect entrainment and survivalrates of multiple migration pathways. Closing thecross-channel gates can also increase the rate of salin-ity intrusion into the central Delta, ultimately reducingwater exports in order to comply with mandated salin-ity standards. As this example shows, simply closingoff a channel in the Delta is nontrivial, which hasspurred investigation of alternative approaches foraltering migration routing of salmon. For instance,non-physical behavioral barriers such as bubble cur-tains and strobe lights can elicit an avoidance responsefrom juvenile salmon (Coutant 2001) while allowingwater to flow unrestricted into a given channel.

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Finally, behavioral responses to the hydrodynamics atjunctions may play a role in the entrainment rates at agiven river junction. Thus, structural changes in chan-nel geometry at a river junction may provide a meansof altering migration routing without changing thedistribution of water flow. Currently, both physicaland non-physical behavioral barriers are being inves-tigated in the Delta in attempt to guide fish away fromlow-survival migration routes.

To quantify the influence of migration routing onoverall survival, we used estimates of movement andreach-specific survival obtained from acousticallytagged juvenile salmon collected over 3 years.

Biotelemetry techniques combined with mark-recapture statistical models provide a powerful toolto simultaneously quantify dispersal and survival ofjuvenile salmon migrating through the Delta. Unique-ly identifiable transmitters provided detailed informa-tion about the temporal and spatial movements ofindividuals migrating through a series of monitoringstations in the Delta. This information was then syn-thesized using a multistate mark-recapture model thatquantified dispersal of the population among migra-tion routes and survival within these routes (Perry etal. 2010). Simultaneously estimating these quantitiesallowed overall survival to be derived from each of

Route B:

Sutter and Steamboatsloughs

Route A:

SacramentoRiver

Route D:

GeorgianaSlough

Route C:

Delta CrossChannel

12km0

N

Fig. 1 Maps of the Sacra-mento–San Joaquin RiverDelta with shaded areasshowing regions comprisingsurvival through the Delta forfour different migrationroutes. For each route,survival was estimated fromFreeport on the SacramentoRiver (the northern mostextent of the shaded area) toChipps Island at the exit ofthe Delta (the western-mostextent of the shaded area). InRoute A, arrows show thetwo river junctions wheremigration routes divergefrom the Sacramento River.For routes C and D, the inte-rior Delta is the large shadedregion to the south of theSacramento River. The loca-tion of the Delta CrossChannel is indicated by thearrow in Route C. TheSacramento River release site(off the map) is 19 river kilo-meters upstream of Freeport,and the Georgiana Sloughrelease site is shown by thearrow in Route D

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these components. For this exercise, we examined thesensitivity of overall survival to migration routing byaltering the distribution of fish at critical river junc-tions and then used the observed route-specific surviv-al estimates to quantify how such actions would affectoverall survival in the Delta.

Methods

To examine how migration routing influences overallsurvival of juvenile Chinook salmon in the Delta(SDelta), we used estimates of survival and routingprobabilities provided by Perry et al. (2010) for the2007 migration year and Perry (2010) for the 2008 and2009 migration years. Route-specific survival, thefraction of fish migrating through each route, andoverall survival were estimated from acoustic-taggedjuvenile salmon using a multistate mark-recapturemodel applied to detection data from a system oftelemetry stations situated throughout the Delta.

Telemetry system

Telemetry stations monitored movement of tagged fishamong four primary migration routes through the Del-ta (Fig. 1): the mainstem Sacramento River (Route A);Sutter and Steamboat sloughs (Route B); the interiorDelta via the Delta Cross Channel (Route C); and theinterior Delta via Georgiana Slough (Route D). Eachtelemetry station consisted of single or multiple mon-itors (Vemco Ltd., Model VR2), depending on thenumber of monitors needed to maximize detectionprobabilities at each station. The number of telemetrystations varied among years (14, 23, and 20 stations in2007, 2008, and 2009, respectively), but stations need-ed to estimate migration routing and survival to theterminus of the Delta remained constant among years.Detailed maps of the each year’s telemetry system canbe found in Perry (2010).

Fish tagging and release

Juvenile late fall Chinook salmon were obtained fromand surgically tagged at the Coleman National FishHatchery in Anderson, California. For the first releasein December 2006, a 1.44-g tag (Vemco Ltd., ModelV7-1L-R64K, 40-d expected battery life) was used.For all other releases, we used a 1.6-g tag (Vemco

Ltd., Model V7-2L-R64K, 70-d expected battery life).Fish above 140 mm fork length were randomly select-ed for tagging. Transmitters were surgically implantedinto fish using methods described by Perry et al.(2010).

To release tagged fish, they were first transported torelease sites at either the Sacramento River near Sac-ramento, CA (all years) or Georgiana Slough (2008and 2009; Fig. 1). The Georgiana Slough release sitewas added for 2008 and 2009 to increase the numberof fish entering the interior Delta. In 2007 and 2008,fish were transferred to net pens (3-m square holdingnets supported by pontoons) at the release site andheld for 24 h in the Sacramento River prior to releaseto allow recovery from the transportation process. For2009, fish were transferred to perforated 121-L con-tainers (2 fish per bucket) and held for 24 h in-riverprior to release. Each release was carried out over a24-h period to distribute tagged fish over the tidal anddiel cycle. Two releases were performed in each mi-gration year; one in December and another in January.For example, in migration year 2007, fish were re-leased in December, 2006 when the Delta Cross Chan-nel was open, and again in January, 2007 when theDelta Cross Channel was closed.

Linking migration routing to overall survival

The mark-recapture model described by Perry et al.(2010) estimates three sets of parameters: detection(Phi), survival (Shi), and route entrainment probabilities(Ψhl; Perry 2010; Perry et al. 2010). Detection probabil-ities (Phi) estimate the probability of detecting a trans-mitter given a fish is alive and the transmitteroperational at telemetry station i within route h (h0A,B, C, D). Survival probabilities (Shi) estimate the prob-ability of surviving from telemetry station i to i+1within route h, conditional on surviving to station i.Route entrainment probabilities (Ψhl) estimate the prob-ability of a fish entering route h at junction l (l01, 2),conditional on fish surviving to junction l. Estimates ofthese parameters can be found in Perry (2010).

The first river junction was modeled as a two-branch junction where the entrance to Sutter andSteamboat Slough was pooled to estimate a singleroute entrainment probability. The parameter ΨB1 esti-mates the probability of being entrained into eitherSutter or Steamboat Slough at the first river junction(Fig. 2). Conversely, 1 – ΨB1 0 ΨA1 is the probability

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of remaining in the Sacramento River at the firstjunction. The second junction was modeled as athree-branch junction where ΨA2, ΨC2, and 1� ΨA2 �ΨC2 ¼ ΨD2 estimate the probabilities of remaining inthe Sacramento River (Route A), being entrained intothe Delta Cross Channel (Route C), and enteringGeorgiana Slough (Route D) at junction 2.

The mark-recapture model estimates the individualcomponents that comprise survival of the populationmigrating through the Delta, defined as survival oftagged fish from the entrance to the Delta at Freeport(rkm 73) to the exit of the Delta at station ChippsIsland (rkm -9), a distance of 82 km by way of theSacramento River. Overall survival through the Deltawas estimated from the individual components as:

SDelta ¼XD

h¼A

ΨhSh ð1Þ

where Sh is the probability of surviving the Deltagiven the specific migration route used to negotiatethe Delta, and Ψh is the probability of migratingthrough the Delta via one of four migration routes(A0Sacramento River, B0Sutter and Steamboatsloughs, C0Delta Cross Channel, D0GeorgianaSlough). Overall survival through theDelta is a weighted

average of the route-specific survival probabilities withweights equal to the fraction of fish migrating througheach route.

Migration route probabilities are a function of theroute entrainment probabilities at each of the two riverjunctions:

ΨA ¼ ΨA1ΨA2 ð2Þ

ΨB ¼ ΨB1 ð3Þ

ΨC ¼ ΨA1ΨC2 ð4Þ

ΨD ¼ ΨA1ΨD2 ð5ÞFor instance, consider a fish that migrates through

the Delta via the Delta Cross Channel (Route C). Toenter the Delta Cross Channel, this fish first remains inthe Sacramento River at junction 1 with probabilityΨA1, after which it enters the Delta Cross Channel atthe second river junction with probability ΨC2. Thus,the probability of a fish migrating through the Deltavia the Delta Cross Channel (ΨC) is the product ofthese route entrainment probabilities, ΨA1ΨC2.

Survival through the Delta for a given migrationroute (Sh) is the product of the reach-specific survivalprobabilities (Shi) that trace each migration path be-tween the entrance to the Delta and its terminus atChipps Island. Thus, Sh is comparable among yearseven though annual differences in the telemetry sys-tem resulted in different reaches over which Shi wasestimated. Furthermore, Sh is directly comparableamong routes because it estimates survival betweenthe same starting and ending locations, but for fishmigrating through different routes.

For our analysis, we focused on the probability ofentering the interior Delta (ΨID), which is the sum of theroute entrainment probabilities for the Delta Cross Chan-nel (ΨC2) and Georgiana Slough (ΨD2, Fig. 2). Survivalthrough the interior Delta was estimated as the averagesurvival of fish entering Routes C and D, weighted bythe entrainment probabilities for each route. We aggre-gated Routes C and D for this analysis because survivalestimates for fish entering the interior Delta were consis-tently lower than other routes (Fig. 3) regardless ofwhether fish entered the interior Delta via the DeltaCross Channel or Georgiana Slough. Thus, the specific

ΨB1 =1-ΨA1 ΨA1

ΨID = ΨC2 +ΨD2 = 1-ΨA2ΨA2

Route A:Sacramento River

Route B:Sutter andSteamboatSlough

Routes C and D:Interior Delta viaDelta Cross Channeland Georgiana Slough

San Francisco Bay

Fig. 2 Schematic showing the simplified routing structure androute entrainment probabilities (Ψhl) at each river junction

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route used to enter the interior Delta is immaterial withrespect to the sensitivity of overall survival to ΨID.

Influence of migration routing on SDelta

To quantify the influence of migration routing onSDelta, we examined the change in SDelta caused byvarying route entrainment probabilities while holdingconstant the route-specific survival probabilities. Spe-cifically, we examined the change in SDelta when vary-ing 1) the probability of fish entering Sutter andSteamboat sloughs (ΨB1), and 2) the conditional prob-ability of entering the interior Delta (ΨID), given fishthat remained in the Sacramento River at its junctionwith Sutter and Steamboat Slough (Fig. 2). For each

release group, we varied entrainment probabilities be-tween zero and one at each river junction, and thenrecalculated SDelta. We then quantified the predictedchange in SDelta relative to the observed estimate ofSDelta as both the absolute (i.e., additive) and relative(i.e., proportional) difference. This approach providesan understanding of how SDelta might have changedhad survival probabilities been the same but migrationrouting different for each release group.

To understand the response of SDelta to changes inΨhl, we also used demographic analysis techniques formatrix population models, which can be generalized toany transition matrix. For a Leslie matrix, sensitivity andelasticity measure the additive and proportional changein λ, the finite rate of population change, with respect toeach demographic parameter in the model (Caswell2001). In our case, SDelta is analogous to λ in that itmeasures the rate of population change between thebeginning and ending points of the Delta. Applyingthese techniques to our model, sensitivity is calculatedas

sΨhl ¼@SDelta@Ψhl

ð6Þ

and elasticity as

eΨhl ¼Ψhl

SDelta

@SDelta@Ψhl

; ð7Þ

where sΨhl and eΨhl are sensitivity and elasticity withrespect to a given route entrainment probability, Ψhl.

Sensitivity and elasticity can be interpreted in anumber of ways to provide insights into how routeentrainment probabilities affect SDelta. First, sensitivitymeasures the slope of the relationship between abso-lute changes in SDelta and Ψhl, while elasticity meas-ures the slope of proportional changes in SDelta. Thesteeper the slope, the larger will be the effect on SDeltafrom a given change in Ψhl. Positive estimates indicatethat increasing Ψhl will increase SDelta, whereas nega-tive values indicate that increasing Ψhl will reduceSDelta. Second, sensitivity and elasticity can be inter-preted as the additive and proportional change inSDelta, respectively, when increasing Ψhl from zero toone. For example, if sΨ ID ¼ �0:20 then increasing ΨID

from zero to one will reduce SDelta by 20 percentagepoints (e.g., from 0.50 to 0.30). In contrast, eΨ ID ¼�0:20 indicates a 20% change in SDelta (e.g., from0.50 to 0.40). Last, applying Eq. 6 to SDelta Eq. 1

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0.39 0.34 0.12 0.15 0.49 0.20 0.31

0.39 0.32 0.120.17 0.46 0.25 0.29

Dec. 2008 Jan. 2009

Fig. 3 Route-specific survival and the fraction of the popula-tion migrating through each migration route in the Sacramento –San Joaquin River Delta (from Perry et al. 2010; Perry 2010).Migration routes are labeled as follows: A0Sacramento River,B0Sutter and Steamboat sloughs, C0Delta Cross Channel, D0Georgiana Slough. Error bars show ±1 standard error

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yields a formula for the slope as a function of the routesurvival and entrainment parameters, elucidatingwhich parameters affect the sensitivity of SDelta toroute entrainment probabilities. Although differencesin survival among routes will certainly influence sen-sitivity of SDelta to migration routing, sensitivity willalso be a function of routing at both river junctions.

Last, we predicted SDelta by varying both ΨB1 andΨID simultaneously to quantify the range in overallsurvival that could be obtained by altering entrainmentat both river junctions. Such insights will help fisher-ies managers better understand how to target manage-ment actions aimed at altering route entrainmentprobabilities in order to maximize overall survival inthe Delta.

Results

Interannual patterns in route-specific survivaland migration probabilities

We observed substantial variation in the magnitudeof within-route survival among years, yet stablepatterns of survival across routes over all years(Perry 2010; Perry et al. 2010). Among migrationyears, 2008 stands out as having the lowest sur-vival at both the route scale and the Delta scale(Fig. 3). Survival through the Delta was <0.20 for2008, but >0.33 for all other years and releases(Table 1). Over all years, estimates of SDelta

exceeded 0.40 for only one release group (Jan.2007), and only during migration year 2007 didobserved estimates of SDelta differ considerably

between releases (Table 1). For all releases, detec-tion probabilities (Phi) were high at most sites(median01.0, mean00.915, minimum00.385),leading to favorable precision of survival probabil-ities relative to releases sample sizes (Table 1,Fig. 3).

Although rankings of route-specific survivalvary somewhat across release groups, one patternremained consistent: survival probabilities for theSacramento River were always greater than surviv-al for migration routes through the interior Delta(via Georgiana Slough and the Delta Cross Chan-nel; Fig. 3). In addition, Sutter and Steamboatsloughs exhibited either similar survival to theSacramento River (typically for January releases)or lower survival than the Sacramento River (typ-ically for December releases; Fig. 1). Except forthe Dec. 2007 release group, observed survivalestimates for Sutter and Steamboat Sloughs weregreater than for routes leading to the interiorDelta.

Sensitivity of SDelta to route entrainment probabilities

The effect of varying route entrainment probabil-ities on overall survival differed among river junc-tions. At the first river junction, sensitivity ofSDelta to entrainment into Sutter and SteamboatSlough (ΨB1) followed no consistent trend amongreleases. Increasing ΨB1 decreased SDelta for twoof the releases, increased it for two releases, andresulted in a slight positive change in SDelta fortwo releases (Table 1; Fig. 4a, b). In addition, thestandard errors for sensitivity and elasticity of ΨB1

indicate that the 95% confidence intervals overlap

Table 1 Sensitivity of SDelta to route entrainment probabilitiesfor Sutter and Steamboat sloughs and the interior Delta. Alsoshown is sample size and estimates of SDelta for each release

group (from Perry et al. 2010, Perry 2010). Standard errors aregiven in parentheses and were based on variances estimatedusing the Delta method

Release group Number released SDelta Sutter and Steamboat Slough, ΨB1 Interior Delta, ΨID 0 ΨC2+ΨD2

Sensitivity Elasticity Sensitivity Elasticity

Dec. 2006 64 0.351 (0.101) −0.125 (0.116) −0.105 (0.098) −0.078 (0.123) −0.111 (0.175)

Jan. 2007 80 0.543 (0.070) 0.030 (0.101) 0.023 (0.077) −0.129 (0.126) −0.036 (0.038)

Dec. 2007 208 0.174 (0.031) −0.059 (0.042) −0.117 (0.085) −0.142 (0.038) −0.331 (0.085)

Jan. 2008 211 0.195 (0.034) 0.062 (0.051) 0.063 (0.052) −0.127 (0.041) −0.252 (0.073)

Dec. 2008 292 0.368 (0.037) 0.038 (0.058) 0.033 (0.050) −0.148 (0.045) −0.170 (0.053)

Jan. 2009 292 0.339 (0.035) 0.125 (0.071) 0.093 (0.054) −0.176 (0.044) −0.200 (0.054)

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zero for all release groups (95% confidence inter-val0estimate ± 1.96*SE). In contrast, at the sec-ond river junction, increasing entrainment into theinterior Delta (ΨB1) decreased SDelta for everyrelease group, and the confidence intervals forfour of the six releases exclude zero (Table 1;Fig. 4c, d).

Changes in SDelta in response to migration routingat a given junction are driven partly by differences insurvival among migration routes and partly by entrain-ment probabilities at other river junctions. For exam-ple, for the two releases where SDelta declined whenincreasing ΨB1 (Dec. 2006 and Dec. 2007; Fig. 4a, b),the negative slope was driven by lower survival inSutter and Steamboat Sloughs than in the Sacramento

River (Fig. 3). For all other releases, survival wassimilar between the Sutter and Steamboat Sloughs(Route B) and the Sacramento River (Route A,Fig. 3), yet SDelta responded positively to increasingthe proportion of fish entering Sutter and SteamboatSlough (Table 1; Fig. 4a, 4a). Examining the equationfor sensitivity of SDelta with respect to ΨB1 revealswhy this pattern emerges:

sΨB1 ¼ SB � SAð Þ þ Ψ ID SA � SIDð Þ:

The first term shows that sensitivity is partly a func-tion of the difference in survival between the Sacra-mento River and Sutter and Steamboat sloughs (SB-SA). However, the second term in the equation shows

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d

Probability of enteringinterior Delta (ΨC1 + ΨD2)

Fig. 4 Predicted change in estimates of SDelta for each release group in response to varying route entrainment probabilities between zero and one

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that sensitivity is also driven by 1) the probability ofentrainment into the interior Delta (ΨID), and 2) thedifference in survival between the Sacramento Riverand interior Delta (SA-SID). Consequently, when sur-vival for Sutter and Steamboat sloughs is on par withthe Sacramento River (SB - SA ≈ 0), increasing ΨB1

increases SDelta by routing fish away from the interiorDelta where survival was lower than the SacramentoRiver.

At the second river junction, increasing entrainmentinto the interior Delta always reduced SDelta becausesurvival for the interior Delta (Routes C and D) waslower than the Sacramento River (Route A) for allrelease groups (Fig. 3). However, the magnitude ofchange in SDelta depends on not only differences insurvival between these routes, but also on the fractionof the population remaining in the Sacramento Riverat the first river junction:

sΨ ID ¼ ΨA1 SID � SAð Þ:

Although the difference in survival between theseroutes determines the direction of change in SDelta,ΨA1 scales the magnitude of change. For example,for the Jan. 2009 release group, survival of fish enter-ing the interior Delta was 0.235 less than the Sacra-mento River (i.e., SID – SA00.163–0.398). Butbecause 25% of the tagged population entered Sutterand Steamboat Slough at the first river junction(Fig. 3), the maximum possible change in SDelta isonly 0.175 when changing ΨID from one to zero(Table 1). These findings illustrate how the magni-tude of change in SDelta from altering entrainment atone river junction depends not only on differencesin survival between alternative routes, but also onthe fraction of the population passing the riverjunction.

Eliminating entrainment into the interior Delta isexpected to result in a 2–7 percentage point increase inoverall survival (Fig. 4c). As discussed above, themagnitude of this change is, in part, due to only afraction of the tagged population passing by this riverjunction. However, the small absolute increase in sur-vival is also due to low survival probabilities observedin all routes. Route-specific survival for all routes was<0.5 for most release groups (Fig. 3). Thus, while shift-ing the distribution of fish among routes influencesoverall survival, the magnitude of absolute change inSDelta is constrained by maximum survival observed in

any given route. Further increases in SDelta would re-quire management actions that affect not only migrationrouting, but also survival within migration routes.

In contrast, proportional changes in SDelta provideinsight into the relative change in survival in responseto altering route entrainment probabilities. SDelta var-ied considerably among years (Table 1) even thoughrelative differences in survival between the Sacra-mento River and interior Delta remained consistentamong years (Fig. 3). Therefore, given interannualvariation in overall survival, proportional changes inSDelta allow comparison among release groups on acommon relative scale. From this perspective, therelative change in SDelta is considerably larger thanthe absolute change, increasing by 10–35% for fiveof the six releases in response to eliminating entrain-ment into the interior Delta. This analysis shows howunderstanding changes in SDelta on both absolute andrelative scales is important, particularly when overallsurvival is low and varies through time.

Altering entrainment at both river junctions simulta-neously revealed that 1) overall survival could varyconsiderably in response to migration routing, 2) theoptimal strategy for maximizing survival varied amongreleases, and 3) sensitivity of overall survival to entrain-ment at one junction depended the value of entrainmentat the other river junction. Depending on release group,maximum SDelta was 1.5 to 2.4 times the minimumsurvival (Fig. 5). Although survival can be maximizedsimply by directing fish to the highest-survival route, theset of entrainment probabilities that maximize survivalvaried among release groups. For December releases,since the Sacramento River (Route A) exhibited highersurvival than other routes, overall survival is maximizedwhen all fish remain in the Sacramento River (i.e., whenΨB100 and ΨID00; Fig. 5). However, for January re-lease groups, overall survival is maximized by minimiz-ing entrainment into the interior Delta but maximizingentrainment in Sutter and Steamboat Slough. Becausesurvival in the Sacramento River was similar to Sutterand Steamboat Slough during January releases, divert-ing fish into Sutter and Steamboat Slough maximizesoverall survival by routing fish away from the secondriver junction where they become exposed to enteringthe interior Delta.

Simultaneously altering entrainment probabilities atboth river junctions illustrated how sensitivity of SDeltato entrainment at one junction depends on the value ofentrainment at the other river junction (Fig. 5). Vertical

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contour lines in Fig. 5 indicate regions where SDelta isinsensitive toΨB1, horizontal contour lines reveal insen-sitivity to ΨID, and closely-spaced contour lines revealregions of high sensitivity. For example, as entrainmentinto Sutter and Steamboat Slough increases, SDeltabecomes less sensitive to changes in ΨID because mostof the population is diverted away from the second riverjunction. For January releases, SDelta is insensitive toΨB1 when ΨID is low, as is indicated by the wide range

of ΨB1 that yields similar overall survival. These rela-tionships help to understand how survival through Deltavaries in response to migration routing.

Discussion

Our analysis reveals the magnitude of change in over-all survival that might be expected from management

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Fig. 5 Contour plot showingoverall survival through theSacramento – San JoaquinRiver Delta (SDelta) predictedas a function of entrainmentprobabilities into the interiorDelta and Sutter and Steam-boat Slough. Filled circlesshow the observed overallsurvival and route entrain-ment probabilities for eachrelease group

Environ Biol Fish

actions that alter migration routing through the Delta.Given the substantial difference in survival betweenthe interior Delta and the Sacramento River, we mighthave expected a larger boost in survival from elimi-nating entrainment into the interior Delta. In a simplersystem with only one branching junction (e.g., a dam),change in overall survival with respect to migrationrouting is directly proportional to the difference insurvival among migration routes. However, due tothe channel complexity of the Delta, altering migrationrouting at one river junction yields changes in SDeltathat are less than proportional to the difference insurvival between alternative migration routes. Weshowed that changes in SDelta with respect to migrationrouting at one river junction depends also on migrationrouting at other river junctions. Therefore, by consid-ering how management actions at multiple river junc-tions affect SDelta, managers may be able to optimizethe suite of actions required to maximize the expectedincrease in SDelta. These are important insights aboutthe magnitude of increase in SDelta expected frommanagement actions to alter migration routing.

The strength of inferences from acoustic tag data tothe untagged population depend on whether survivalestimates are viewed from a relative or absolute pointof view. Potential tag effects on survival (Adams et al.1998) or differences in survival between hatchery andwild fish (Reisenbichler and McIntyre 1977; Kostow2004) could result in lower absolute survival of taggedfish relative to untagged fish. In our study, although it isunknown whether tagged fish of hatchery origin exhibitlower survival than untagged fish of wild origin, abso-lute changes in survival should be interpreted with cau-tion (i.e., Fig. 4a, c). Regardless of the absolutemagnitude of survival, however, differences amongroutes that influence survival should act similarly onall populations of salmon smolts migrating through theDelta. For example, both tagged and untagged fishmigrating through the interior Delta likely experiencedlower survival relative to fish migrating within the Sac-ramento River. Therefore, relative changes in survival inresponse to altering migration routing (i.e., Fig. 4c, d)should provide stronger inferences to untagged popula-tions than will absolute change in survival probabilities.

We focused our analysis on river junctions wheremanagement actions are likely to have the largest influ-ence on population survival. For example, we showedthat Steamboat and Sutter Slough is an important mi-gration route because fish using this route avoid entering

the interior Delta where survival is lower than otherroutes. The Delta’s channel geometry is hierarchical innature such that secondary (and finer level) migrationroutes are nested within primary routes. At each second-ary and tertiary river junction, the population dividesinto a smaller and smaller fraction of the whole. There-fore, management actions focused at secondary junc-tions will have less population-level influence than atprimary river junctions simply because a small fractionof the population will be influenced. In contrast, man-agement actions have the potential for influencing muchof the population at the two primary river junctionsexamined in our analysis.

Sensitivity and elasticity measure changes in SDeltawith respect to migration routing at a junction whileholding all other parameters constant. Thus, our analysisassumes that management actions alter only migrationrouting but not route-specific survival probabilities. Thisassumption may be violated in two ways. First, chang-ing migration routing will alter the abundance of juve-nile salmon in each route, which could cause a densitydependent predator response. At very low prey densi-ties, increasing smolt abundance within a route couldincrease predation rates via the predator’s numerical orfunctional response to prey. In contrast, increasing smoltabundance to high levels within a route could reducepredation rates through predator swamping. Second,management actions that affect water routing at a par-ticular junction (e.g., physical barriers) could influenceroute-specific survival or entrainment at other junctionsby changing discharge and hydrodynamics within amigration route. For example, physical barriers alterdischarge entering each channel, and juvenile salmonsurvival has been positively correlated with discharge inthe Delta (Newman and Rice 2002; Perry 2010). Suchsimultaneous changes in migration routing and route-specific survival are not captured by our analysis.

In terms of the magnitude of change in populationsurvival, managers must consider both the expectedchange in migration routing and the expected changein route-specific survival caused by implementation ofphysical and non-physical barriers. With respect tomigration routing, physical barriers are 100% effectivewhereas non-physical barriers typically divert lessthan 100% of fish. Therefore, under the assumptionof constant route-specific survival, non-physical bar-riers would realize only a fraction of the maximumpossible increase in population survival. With respectto route-specific survival, physical barriers may yield

Environ Biol Fish

a larger change in survival than non-physical barriersbecause physical barriers alter discharge and hydrody-namics of each migration route. However, the direc-tion and magnitude of change in route-specificsurvival in response to physical and non-physical bar-riers is poorly understood. This uncertainty highlightsthe importance of quantifying simultaneous changes inboth migration routing and route-specific survival infield studies evaluating physical and non-physical bar-riers in the Delta.

Our sensitivity analysis has application to otherregulated river systems where managers must balancethe costs of water management actions against benefitsto fish populations. On the Columbia River, for exam-ple, millions of dollars are spent annually to evaluatesurvival of juvenile salmon migrating past dams. Man-agement actions such as spilling water over damsresults in foregone power generation but improvespopulation survival of juvenile salmon by divertingthem away from turbines. Our analytical approachcould be used to quantify expected changes in popu-lation survival by implementing such actions, helpingmanagers to better design dam operations to achieverecovery targets at minimum cost. More importantly,in the Delta and other regulated river systems, ouranalytical approach can be used to help design recov-ery actions before such actions are implemented. Giv-en scarce resources with which to recover endangeredsalmon populations, such analyses can help directresources towards actions most likely to yield thelargest improvement in survival.

Acknowledgements Funding for R.W.P’s involvement withthis project was provided by a CALFED Science Fellowship,Agreement No. U-04-SC-005 with the California Bay-Delta Au-thority. Tagging of juvenile salmon, ultrasonic station deploymentand interrogation, and tag-detection database maintenance weresupported by a grant from the California Bay-Delta Authority byAgreement No. U-05-SC-047. We thank the staff of ColemanNational Fish Hatchery for providing the late-fall Chinook andlogistical support for this study. Staff of the Stockton U.S. Fish andWildlife Office gratefully assisted with fish transportation andrelease. We thank two anonymous reviewers for comments thatsubstantially improved this manuscript.

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