Application of a Life Cycle Simulation Model to Evaluate Impacts of Water Management and Conservation Actions on an Endangered Population of Chinook Salmon

Abstract

Fisheries and water resource managers are challenged to maintain stable or increasing populations of Chinook salmon in the face of increasing demand on the water resources and habitats that salmon depend on to complete their life cycle. Alternative management plans are often selected using professional opinion or piecemeal observations in place of integrated quantitative information that could reduce uncertainty in the effects of management plans on population dynamics. We developed a stochastic life cycle simulation model for an endangered population of winter-run Chinook salmon in the Sacramento River, California, USA with the goal of providing managers a tool for more effective decision making and demonstrating the utility of life cycle models for resource management. Sensitivity analysis revealed that the input parameters that influenced variation in salmon escapement were dependent on which age class was examined and their interactions with other inputs (egg mortality, Delta survival, ocean survival). Certain parameters (river migration survival, harvest) that were hypothesized to be important drivers of population dynamics were not identified in sensitivity analysis; however, there was a large amount of uncertainty in the value of these inputs and their error distributions. Thus, the model also was useful in identifying future research directions. Simulation of variation in environmental inputs indicated that escapement was significantly influenced by a 10% change in temperature whereas larger changes in other inputs would be required to influence escapement. The model presented provides an effective demonstration of the utility of life cycle simulation models for decision making and provides fisheries and water managers in the Sacramento system with a quantitative tool to compare the impact of different resource use scenarios.

Full text

1 23
Environmental Modeling &
Assessment
ISSN 1420-2026
Volume 17
Number 5
Environ Model Assess (2012) 17:455-467
DOI 10.1007/s10666-012-9306-6
Application of a Life Cycle Simulation
Model to Evaluate Impacts of Water
Management and Conservation Actions
on an Endangered Population of Chinook
Salmon
Steven C.Zeug, Paul S.Bergman,
Bradley J.Cavallo & Kristopher S.Jones

1 23
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Application of a Life Cycle Simulation Model to Evaluate
Impacts of Water Management and Conservation Actions
on an Endangered Population of Chinook Salmon
Steven C. Zeug &Paul S. Bergman &Bradley J. Cavallo &
Kristopher S. Jones
Received: 3 August 2011 / Accepted: 3 January 2012 / Published online: 19 February 2012
#Springer Science+Business Media B.V. 2012
Abstract Fisheries and water resource managers are chal-
lenged to maintain stable or increasing populations of Chinook
salmon in the face of increasing demand on the water resources
and habitats that salmon depend on to complete their life cycle.
Alternative management plans are often selected using profes-
sional opinion or piecemeal observations in place of integrated
quantitative information that could reduce uncertainty in the
effects of management plans on population dynamics. We
developed a stochastic life cycle simulation model for an
endangered population of winter-run Chinook salmon in the
Sacramento River, California, USA with the goal of providing
managers a tool for more effective decision making and dem-
onstrating the utility of life cycle models for resource manage-
ment. Sensitivity analysis revealed that the input parameters
that influenced variation in salmon escapement were dependent
on which age class was examined and their interactions with
other inputs (egg mortality, Delta survival, ocean survival).
Certain parameters (river migration survival, harvest) that were
hypothesized to be important drivers of population dynamics
were not identified in sensitivity analysis; however, there was a
large amount of uncertainty in the value of these inputs and
their error distributions. Thus, the model also was useful in
identifying future research directions. Simulation of variation in
environmental inputs indicated that escapement was signifi-
cantly influenced by a 10% change in temperature whereas
larger changes in other inputs would be required to influence
escapement. The model presented provides an effective dem-
onstration of the utility of life cycle simulation models for
decision making and provides fisheries and water managers in
the Sacramento system with a quantitative tool to compare the
impact of different resource use scenarios.
Keywords California .Delta .Life cycle model .Sacramento
River .Simulation .Winter run Chinook salmon
1 Introduction
Understanding what drives interannual variability in Chinook
salmon (Oncorhynchus tshawytscha) populations is of consid-
erable interest to resource managers because of the large num-
ber of salmon stocks that are currently listed as threatened or
endangered [1,14]. Declines in the number of salmon return-
ing to spawn have triggered recovery plans intended to stabi-
lize or increase population sizes. The success of these plans has
varied considerably and many populations remain at risk [15].
The factors responsible for declines in Chinook salmon pop-
ulations are generally known yet, the relative importance of
each factor and the scale at which it operates is often unknown,
which complicates attempts to effectively apply management
actions to recover Chinook salmon stocks [7,31,37].
Both scientists and managers have increasingly recognized
the utility of life cycle models for evaluating salmon popula-
tion responses to management actions [28], and a recent review
of salmon recovery efforts in California’s Central Valley rec-
ommended their use [12]. Although there have been many
studies and monitoring efforts focused on the ecology of
salmon at the individual and population level, many of these
data relate only to a single life stage, habitat type, or environ-
mental variable. This has made it difficult to integrate these
data into a traditional statistical framework to estimate inter-
annual population dynamics or to identify specific bottlenecks
to population recovery. Life cycle models utilize available
time-series data as well as values taken from laboratory studies
or other sources to parameterize model relationships, thereby
utilizing the greatest amount of data available to dynamically
simulate responses of populations across multiple life stages to
changes in environmental variables or combinations of
S. C. Zeug (*):P. S. Bergman :B. J. Cavallo :K. S. Jones
Cramer Fish Sciences,
13300 New Airport Road, Suite 102,
Auburn, CA 95602, USA
e-mail: stevez@fishsciences.net
Environ Model Assess (2012) 17:455–467
DOI 10.1007/s10666-012-9306-6
Author's personal copy

environmental variables at specified times and locations.
Thus, these models are powerful tools that can be used by
managers to plan and evaluate recovery actions for Chinook
salmon. Here, we present a life cycle simulation model for an
endangered winter-run Chinook salmon population in the
Sacramento River, California, USA (Fig. 1).
Sacramento River Chinook salmon stocks have expe-
rienced severe declines over the last century resulting in
extirpation of some populations [14]andamoratorium
on commercial and sport harvest in recent years to
protect extant populations. Winter run in the Sacramento
River was listed as endangered under the Federal En-
dangered Species Act in 1994 [9]. Historically, winter
run utilized high elevation stream habitats in the Upper
Sacramento River and tributaries for holding, spawning,
and rearing [36]. However, extensive dam construction
in the early twentieth century restricted winter run to a
single reach of the lower Sacramento River below
Keswick Dam [35]. After leaving the spawning and
rearing habitat, juvenile winter run migrate down the
Sacramento River, through the Sacramento–San Joaquin
Delta (hereafter referred to as the Delta) and spend from
2 to 4 years in the ocean before returning to their natal
spawning grounds.
As pressure on Sacramento River water resources con-
tinues to increase from domestic and agricultural users,
resource managers are in need of quantitative tools to com-
pare the relative impact of future water use activities on the
winter-run population and to select relevant life stages and
environmental variables to focus on for recovery actions.
Our goals for this study were to describe a stochastic life
cycle simulation model for winter run in the Sacramento
River: the Interactive Object-Oriented Simulation Model
(IOS). Specifically, we: (1) present the structural and func-
tional relationships of the IOS model, (2) conduct a sensi-
tivity analysis that describes uncertainty in estimates of
model parameters, and uncertainty due to inherent stochas-
ticity of the population, and (3) examine the response of the
model to variability in the four environmental drivers for
which sufficient data were available including: temperature
that affects egg and fry survival during early development,
flow that affects survival and migration travel time during
freshwater migration, water exports that affect survival in
certain migration pathways, and ocean productivity that
affects survival in the ocean.
2 Methods
2.1 Model Description and Structure
The IOS model uses a systems dynamics modeling frame-
work, a technique that is used for framing and understanding
the behavior of complex systems over time [6,10]. System
dynamics models are made up of stocks (e.g., number of
fish) and flows (e.g., sources of mortality) which are in-
formed by mathematical equations [10]. IOS was imple-
mented in the software GoldSim, which enables the
simulation of complex processes through creation of simple
object relationships, while incorporating Monte Carlo sto-
chastic methods [27]. Terms used in the model description
are defined in Table 1.
The IOS model is composed of six model stages that are
arranged sequentially to account for the entire life cycle of
winter run, from eggs to returning spawners (Fig. 2). In
sequential order, the IOS model stages are: (1) spawning,
that models the number and temporal distribution of eggs
deposited in the gravel at the spawning grounds; (2) early
development, that models the impact of temperature on
maturation timing and mortality of eggs at the spawning
grounds; (3) fry rearing, that models the relationship be-
tween temperature and mortality of salmon fry during the
river rearing period; (4) river migration, that estimates mor-
tality of migrating salmon smolts in the Sacramento River
between the spawning and rearing grounds and the Delta;
(5) delta passage, that models the impact of flow, route
selection, and water exports on the survival of salmon
smolts migrating through the Delta to San Francisco Bay;
and (6) ocean survival, that estimates the impact of natural
mortality and ocean harvest to predict survival and spawning
returns (escapement) by age. Below is a detailed description of
each model stage.
Spawning For the first four simulation years, the model is
seeded with a fixed number of female spawners. In subse-
quent years, the number of spawners is determined by the
model’s probabilistic simulation of survival to this life stage.
To ensure that developing fish experience the correct envi-
ronmental conditions during each year, spawn timing
mimics the observed arrival of salmon on the spawning
grounds as determined by 8 years of carcass surveys
(2002–2009) conducted by the United States Fish and Wild-
life Service (USFWS). Winter run die after spawning which
allows the size of the spawning population to be estimated
from the number of carcasses observed. In each year, one of
the eight spawning distributions is chosen at random. Eggs
deposited on a particular date are treated as cohorts which
experience temperature and flow on a daily time step during
this stage. The daily number of spawners is calculated by
multiplying the daily proportion of the total carcasses ob-
served during the USFWS surveys by the total Jolly–Seber
estimate of spawners [24].
Sd¼CdSJS ð1Þ
where, S
d
is the daily number of spawners, C
d
is the daily
proportion of total carcasses, and S
JS
is the total Jolly–Seber
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Fig. 1 Map of the Sacramento River and the Sacramento–San Joaquin Delta, including approximate areas defined by each model-stage
Chinook Salmon Life Cycle Model 457
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estimate of spawners. In order to better match the timing of
carcass observations to the deposition of eggs, the date of
egg deposition is shifted 14 days before the carcasses were
observed (Kevin Niemela, personal communication).
To obtain an estimate of juvenile production, a Ricker
stock-recruitment curve [26] was fit between the number of
fry produced each year (R) and the number of spawners (S)
as estimated by the California Department of Fish and Game
screw trap sampling (juveniles) and USFWS carcass surveys
(spawners) for years (1996–1999, 2002–2007):
R¼aSebSþ"ð2Þ
where, Ris the estimate of juvenile recruitment, αis a
parameter that describes recruitment rate, and βis a param-
eter that measures the level of density dependence. The
density-dependent parameter (β) did not differ significantly
from zero (95% CI0−6.3 × 10
−6
−5.5×10
−6
). Therefore, β
was removed from the equation and a linear version of the
relationship was estimated. The number of spawners
explained 86% of the variation in fry production (F
1,9
0
268, p<0.001) in the data, so the value of αwas taken from
the regression:
R¼1043&Sð3Þ
This linear relationship is used to predict values for mean
fry production along with the confidence intervals for the
predicted values. These values are then used to define a
normal probability distribution, which is randomly sampled
each year to determine the annual fry production. Although
the Ricker model accounts for mortality during egg incuba-
tion, the data used to fit the Ricker model were from a
limited time period (1996–1999, 2002–2007) when water
Table 1 Glossary of
terms used to
describe model func-
tions, data sources,
and relevant locations
in the study area
Term Definition
CDFG California Department of Fish and Game
Delta A freshwater tidal estuary formed by the Sacramento and San Joaquin Rivers that salmon
juveniles must pass through on their way to the Pacific Ocean
Escapement The total number of Chinook salmon that leave the ocean and return to the Sacramento
River to spawn. This number includes 2-, 3-, and 4-year-old fish
Fry Salmon life stage that occurs from the period of emergence from spawning gravels until the
start of physiological changes in preparation for migration
Jolly_Seber estimate A statistical method of estimating the size of a population using mark and recapture data
Screwtrap A passive sampling devise that traps juvenile salmon as they migrate downstream
Smolt Salmon life stage characterized by physiological changes in preparation for migration and
ocean entry
Spawner Salmon that leaves the ocean and returns to the Sacramento River to spawn. This can occur
at age 2, 3 or 4. All fish die after spawning
USFWS United States Fish and Wildlife Service
Winter-run Chinook
salmon
A genetically distinct population of Chinook salmon that completes the freshwater portion
of their life cycle in the Sacramento River. This population has been listed as endangered
under the federal Endangered Species Act
Junction Geo/DCC The combined junction of the Sacramento River, Georgiana Slough and the Delta Cross
Channel. Both Georgiana Slough and the Delta Cross channel lead into the Interior Delta
reach
Junction SS The junction between two potential migration routes, the Sacramento River and Sutter/
Steamboat Slough
Interior Delta A reach that fish entering through Junction Geo/DCC must pass through on their way to the
ocean. This reach is a network of tidal channels and a relationship between water exports
and survival is present in this reach
Reach Geo/DCC The combined reach of Georgiana Slough and the Delta Cross Channel
Reach Sac 1 The Sacramento River between the start of the Delta at Freeport and the junction with
Steamboat/Sutter Slough
Reach Sac2 The Sacramento River between the reach Sac1 and the Junction of Georgiana Slough and
the Delta Cross Channel
Reach Sac3 The Sacramento River between Sac2 and the confluence of Steamboat/Sutter Slough and
the Sacramento River. A flow–survival relationship is present in this reach
Reach Sac4 The Sacramento River between the confluence of the Sacramento River and Sutter/
Steamboat Slough and the end of the Delta Passage model stage
Reach SS The combined reach of Sutter and Steamboat Slough. A flow–survival relationship is
present in this reach.
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temperatures during egg incubation were too cool (<14°C)
to cause significant temperature-related egg mortality [32].
Thus, additional mortality was imposed in the model when
temperatures exceeded those experienced during the years
used to construct the Ricker model.
Early Development Data from three laboratory studies was
used to estimate the relationship between temperature, egg
mortality, and development time [4,19,32]. Using data from
these experiments, a relationship was constructed between
maturation time and water temperature. First, we converted
maturation time (days) to a daily maturation rate (1/day):
daily maturation rate ¼maturation time1ð4Þ
A significant linear relationship between maturation rate
and water temperature was detected using linear regression
(F
1,15
02,188, p<0.001):
daily maturation rate ¼0:00058&Temp 0:018 ð5Þ
Each day, the mean maturation rate of the incubating eggs
is predicted from the daily temperature using the above linear
function; the predicted mean maturation rate along with the
confidence intervals of the predicted values are used to define
a normal probability distribution, which is then randomly
sampled to determine the daily maturation rate. A cohort of
eggs accumulates a percentage of total maturation each day
from the above equation until 100% maturation is reached.
Data from the USFWS [32] was used to inform the rela-
tionship between temperature and mortality of developing
winter-run eggs. This study utilized a small number of treat-
ments (three temperature treatments) and although studies
from other regions could have been used, we chose to use
data specific to winter run. Salmon populations are adapted to
local temperature regimes and use of data from outside of the
Sacramento River may not conform with the requirements of
winter run. The functional form of the temperature–mortality
relationship was similar to data from other regions suggesting
that USFWS data on winter run was sufficient to parameterize
the model-predicted mortality over the entire incubation peri-
od was converted to a daily mortality rateto apply temperature
effects in the model. This conversion was used to calculate
daily mortality using the methods described in [3]:
mortality ¼11total mortalityðÞ
ð1=development timeÞð6Þ
where, total mortality is the predicted mortality over the entire
incubation period observed for a particular water temperature
Delta exit to age 2
Survival
Age 2
Survival
Age 3
Natural
mortality
Harvest
Age 4
Harvest
Natural
mortality
Return to
spawning
grounds
8%
88%
4%
Mortality
Fry rearing
Day 60 -120
Mortality
Maturation
Early development
Day 1 -60
Survival
River migration
Day 120 - 145
Spawning
Day 1
% daily
spawners
Speed
Survival
Day 149 to ocean
Sac4
To ocean Survival
Day 150 to ocean
Interior Delta
Speed
Survival
Day 148 -150
Geo/DCC
Speed
Survival
Sac3
Day 148 -149
Speed
Survival
Day 146 -149
SS
Sac 1
Speed
Speed
Survival
Day 145
Speed
Survival
Day 146 -148
Sac2
Ocean survival
Delta passage
Fig. 2 Conceptual diagram of IOS model stages and environmental
influences on functional relationships at each stage. Colors indicate the
environmental driver influencing each relationship where red
temperature, blue flow, green water exports, and pink ocean produc-
tivity. Relationships in black indicate that values are drawn from a
normal distribution, a uniform distribution, or are constants
Chinook Salmon Life Cycle Model 459
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and development time was the time to develop from fertiliza-
tion to emergence.
The following exponential relationship was fitted between
observed daily mortality and observed water temperatures
[32]:
daily mortality ¼1:38&1015eð0:503&TempÞð7Þ
Each day, the mean mortality rate of the incubating
eggs is predicted from the daily temperature measured
at Bend Bridge on the Sacramento River using the
above exponential function. The predicted mean mortal-
ity rate along with the confidence intervals of the pre-
dicted values is used to define a normal probability
distribution, which is then randomly sampled to deter-
mine the daily egg mortality rate.
Fry Rearing Data from USFWS [32] was used to model
fry mortality during rearing as a function of water
temperature. The following exponential relationship
was fitted between observed daily mortality and ob-
served water temperatures [32]:
daily mortality ¼3:92&1012eð0:349&TempÞð8Þ
Each day, the mean proportional mortality of the
rearing fish is predicted from the daily temperature
using the above exponential relationship; the predicted
mean mortality along with the confidence intervals of
the predicted values are used to define a normal prob-
ability distribution, which is then randomly sampled to
determine daily mortality. Temperature mortality is ap-
plied to rearing fry for 60 days that is the approximate
time required for fry to transition into smolts [32]and
enter the next stage.
River Migration In this model stage, survival of smolts
from the spawning and rearing grounds to the Delta
(City of Freeport on the Sacramento River) is a normal-
ly distributed random variable with a mean of 23.5%
and a standard error of 1.7%. Mortality in this stage is
applied only once and occurs on the same day that a
cohort of smolts enters the model stage rather than
beingapplieddailyasintheEarly Development stage
because there was no data to support a relationship with
flow or temperature. Smolts are delayed from entering
the next model stage to account for travel time. Mean
travel time (20 days) is used along with the standard
error (3.6 days) to define a normal probability distribu-
tion, which is randomly sampled to determine the total
travel time of migrating smolts. Survival and travel time
means and standard deviations were acquired from an
acoustic study of late-fall run Chinook smolt migration
in the Sacramento River [18].
Delta Passage Smolt migration is evaluated based on four
major functional relationships: (1) route selection by smolts at
river junctions, that is a function of the proportion of flow
entering each route; (2) reach specific and flow-survival rela-
tionships, where survival in two reaches is a function of flow
and a normally distributed variable in all other reaches; (3)
flow–migration speed, which is a function of reach specific
flow; and (4) export mortality, which is caused by entrainment
into State and Federal water pumping facilities. Daily cohorts
of smolts enter the first reach of the Delta on a day of the year
determined by timing in the previous model stages. In reaches
with a flow–survival relationship, mean flow on the day
smolts enter the reach is used to calculate a survival value
and a migration speed for that reach. The survival value is
applied once to all smolts that entered the reach on that date.
Then, smolts are delayed from entering the next reach by a
number of days determined by the calculated migration rate
and the length of the reach. In reaches without a flow–survival
relationship, survival values are drawn from a normal proba-
bility distribution and migration speed is calculated as a func-
tion of flow on the day of entry into the reach. When smolts
reach a junction, a daily cohort will split according to the
relationships described below, based on the flow on the day
smolts reach the junction.
Fish route selection at junctions is based on acoustic
tagging studies in the Delta by Perry et al. [23]. At the
junction of the Sacramento River and Steamboat/Sutter
Slough (Junction SS, Table 1), smolts consistently entered
downstream reaches in proportion to the flow being
diverted. For the Sacramento River–Geo/DCC junction (Junc-
tion Geo/DCC, Table 1), there was a linear, nonproportional
relationship between flow and fish movement:
y¼0:22 þ0:47xð9Þ
where, yis the proportion offish diverted into Geo/DCC and x
is the proportion of flow diverted into Geo/DCC.
Reach-specific survival and associated error estimates
also were obtained from Delta acoustic tagging studies
[23] where mean reach survival is used with reach-specific
standard deviation to define a normal probability distribu-
tion sampled daily to determine the survival rate. There was
a significant relationship between survival and flow for two
Delta reaches (SS and Sac3; [23])andweusedalogit
survival function to predict mean reach survival (S) from
reach flow (flow):
S¼eb0þb1flowðÞ
1þeb0þb1flowðÞ ð10Þ
where, β
0
(SS0−0.175, Sac30−0.121) is the reach coeffi-
cient and β
1
(0.52) is the flow coefficient. All the benefits of
increased flow are accounted for the in relationships we
have applied for reaches SS and Sac3.
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Daily downstream smolt movement occurs as function of
reach-specific length and migration speed as developed
from acoustic tagging results. We used flow and migration
speeds reported by Vogel [33] to create a best-fit logarithmic
relationship:
y¼16:59lnðxÞ76:79 ð11Þ
where, yis migration speed (kilometer per day
1
) and xis
flow (cubic meter per second). Due to assumed strong tidal
influences in reach Sac4, migration speed in this reach is
independent of flow; set at 22.6 km·day
−1
, the average speed
of acoustic tagged smolts [33]. Migration speed variance
from acoustic study data is used along with mean migration
speed to define a normal probability distribution that is
sampled from each day to determine the daily migration
speed in each reach.
Fish that enter the DCC/Georgiana Slough junction enter
the interior delta that is a complex network of tidal freshwater
channels where smolts are exposed to natural mortality as well
as entrainment in large water diversions. To apply water
export-related effects, we used the export–mortality relation-
ship described by Newman and Brandes [22]:
S¼0:000024&exports þ0:625 ð12Þ
where, Sis mean survival and the slope (−0.000024) is from
the relationship between survival and Delta exports in cubic
meter per second. The intercept was adjusted from 0.58 to
0.625 so the regression line passes the point (184, 0.47), where
184 is the meanexport level (cubic meter per second) and 0.47
is the mean survival rate observed during the acoustic studies
we used to estimate survival in the Interior Delta. In effect, we
used the slope of the relationship between survival and exports
estimated by Newman and Brandes [22] as a scalar on the
survival rates observed from acoustic tagging studies. Mean
survival is then used along with the standard deviation to
inform a normal probability distribution that is sampled from
each day to determine Interior Delta survival.
As each cohort of smolts exits the final reaches of the
Delta, they accumulate until all cohorts from that year have
exited the Delta. After all smolts have arrived, they enter the
Ocean Survival stage as a single cohort and the model
begins applying mortality on an annual time step.
Ocean Survival This model stage utilizes equations for
smolt-to-age-2 mortality, winter mortality, ocean harvest,
and spawning returns to predict yearly survival and escape-
ment numbers (i.e., individuals exiting the ocean to spawn).
Ocean Survival model stage elements are listed in Table 2
and discussed below.
Relying on ocean harvest, mortality, and returning
spawner data from Grover et al. [13], we applied a uniform-
ly distributed random variable between 96% and 98%
mortality for winter run from ocean entry to age 2 and we
developed functional relationships to predict ocean survival
and returning spawners for age 2 (8% return), age 3 (88%
return), and age 4 (4% return), assuming that 100% of
individuals which survive to age 4 return for spawning.
Ocean survival to age 2 is given by:
A2¼Ai1M2
ðÞ1Mw
ðÞ1H2
ðÞ1Sr2
ðÞ&Wð13Þ
survival to age 3 is given by:
A3¼A21Mw
ðÞ1H3
ðÞ1Sr3
ðÞ ð14Þ
and survival to age 4 is given by:
A4¼A31Mw
ðÞ1H4
ðÞ ð15Þ
where, A
i
is abundance at ocean entry (from the Delta
Passage model stage), A
2,3,4
are abundances at ages 2–
4, H
2,3,4
are harvest percentages at ages 3–4 represented
by uniform distributions bounded by historical harvest
levels, M
2
is smolt-to-age-2 mortality, M
w
is winter mor-
tality for ages 2–4, and S
r2,r3
are returning spawner
percentages at ages 2 and 3. Age 2 survival is multiplied
by a scalar Wthat corresponds to the value of Wells’
Index of ocean productivity. This metric was shown to
significantly influence growth and maturation of age 2
fish [34]. The value of Wells’Index is a normally
distributed random variable that is resampled each year.
In our analysis, we used the following values from
Grover et al. [13]: H
2
00%, H
3
00–39%, H
4
00–74%,
M
2
094–98%, M
w
020%, S
r2
08%, and S
r3
096%.
The number of adult fish in the ocean that will return to
the spawning grounds is determined on day 334 of each year
according to the percentages described above. Returning
fish are assumed to be 65% female and are assigned a
prespawn mortality of 5% to determine the final number of
female returning spawners [30].
2.2 Environmental Input Data
Daily flows and temperatures experienced by salmon (Table 3)
are determined by selection of a water year type in the Sacra-
mento River as classified by the California Department of
Water Resources (critical, dry, below normal, above normal,
and wet). The probability of each type of water year being
selected is represented by a discrete distribution based on the
previous 100 years of data. With the exception of flow into the
State Water Project (SWP) and Central Valley Project (CVP)
pumping plants, flow is modeled using daily (tidally aver-
aged) flow output from the hydrology module of the Delta
Simulation Model II (DSM2-HYDRO; http://baydeltaoffice.
water.ca.gov/modeling/deltamodeling/). Export flow into the
CVP and SWP pumping plants is modeled using monthly
flow output from the hydrologic simulation tool CALSIM II
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that are “disaggregated”into mean daily flows based on historical
patterns. Mean flow and temperature wasaveraged each day over
the entire period of record for each of the five water year types to
create a single flow and temperature regime for each water year
type. Daily temperature in the Sacramento River at Bend Bridge
from 1989 to 2010 was obtained from the California Data Ex-
change Center (http://cdec.water.ca.gov/).
2.3 Sensitivity Analysis
Sobol’indices were used to evaluate the sensitivity of model
output to input parameters. Sobol’indices are a variance-
based global sensitivity method that produces main indices
(effects independent of other input parameters) and total
indices (effects accounting for first-order interactions with
Table 3 Environmental
variables used to inform func-
tional relationships in
the IOS model
Location Variable Model stage Source
Sacramento River at Bend Bridge Temperature Early Development CDEC
Sacramento River at Hood Flow Delta migration DSM2
Sutter-Steamboat Slough Flow Delta migration DSM2
Delta Cross Channel Flow Delta migration DSM2
Georgiana Slough Flow Delta migration DSM2
Sacramento River at Rio Vista Flow Delta migration DSM2
Interior Delta Exports Delta migration CALSIM2
Ocean Ocean productivity Ocean survival Wells et al. 2007
Table 2 Functional relationships
in the IOS model during each
model stage and environmental
variables associated with each
relationship
Model Stage Parameter Environmental variable Function
Spawning Daily proportion of total
spawners
None Equation 1
Early
development
Daily egg mortality Temperature Equation 7
Egg-to-fry development
time
Temperature Equation 5
Fry rearing Daily fry-to-smolt survival Temperature Equation 8
River
migration
Downstream survival None Normally distributed
random variable
Delta passage Reach-Sac1 survival None Normally distributed
random variable
Reach-Sutter/Steamboat Flow Equation 10
Reach-Sac2 None Normally distributed
random variable
Reach-Sac3 Flow Equation 10
Reach-Sac4 None Normally distributed
random variable
Reach-Geo-DCC None Normally distributed
random variable
Interior Delta Water exports Equation 12
Junction-Sac2-Sutter/
Steamboat
Flow Proportional to flow in each
reach
Junction-Sac3-Delta Cross
Channel
Flow Equation 9
Migration duration Flow Equation 11
Migration duration (Sac4) None Constant
Ocean
survival
Smolt-age 2 survival None Uniform random variable
Age 2 ocean survival Well’s Index of ocean
productivity
Equation 13
Age 3 ocean survival None Equation 14
Age 4 ocean survival None Equation 15
Age 3 harvest None Uniform random variable
Age 4 harvest None Uniform random variable
462 S.C. Zeug et al.
Author's personal copy

other input parameters). This method does not require a
linear relationship between model output and input param-
eters and thus is superior to other global methods, such as
multiple regression, when relationships are nonlinear or
nonmonotonic [5,8,29].
For the sensitivity analysis, 1,000 bootstrap resamples
were used to calculate 95% confidence intervals for Sobol’
main and total effects. The number of female spawners
returning (escapement) was used as the response variable
and model inputs included as independent variables for each
age class are listed in Table 4. Each group of returning
spawners is composed of three age classes (age 2, 3, and
4) that experiences a different set of environmental condi-
tions during their life. Thus, sensitivity analyses were con-
ducted separately for each year class. Certain parameters
were not included in all sensitivity analyses because they
did not apply to all year classes. For example, age 2 fish are
not exposed to harvest.
Latin Hypercube sampling was used to generate 1,000
Monte Carlo iterations of the IOS model for use in calculation
of the Sobol’indices. For each iteration, the first 4 years of the
model was seeded with 5,000 returning spawners and allowed
to run for 5 years. The fifth year of output data was used for
the sensitivity analysis because this is the first year that the
number of returning spawners is a function of model param-
eters. Fish returning to the spawning grounds are mix of 2-, 3-,
and 4-year-old fish that account for 8%, 88%, and 4% of the
total, respectively. Input parameters were considered sensitive
if their confidence interval did not include zero and were then
ranked based on their absolute values. Sobol’indices were
calculated using the package “sensitivity”within the R statis-
tical program [25].
To explore how uncertainty in parameter estimates influ-
enced model output, we conducted five additional sets of
1,000 Monte Carlo simulations where the variation around
the mean of selected parameters was increased by 10%,
20%, 30%, 40%, and 50%. The parameters we chose to
examine were those that could potentially be addressed by
management actions including: egg mortality, fry-to-smolt
survival, river migration survival, Delta survival, age 3
harvest, and age 4 harvest. Coefficients of variation were
calculated for each set of simulations to examine how the
sensitivity of model output changed with increased uncer-
tainty in input parameters estimates.
2.4 Influence of Environmental Parameters
To understand the influence of environmental parameters on
model output, we examined the response of escapement to
variation in the four environmental parameters: flow, exports,
temperature, and ocean productivity. For each parameter, we
performed three sets of 100 Monte Carlo simulations. All
simulations ran for four winter-run generations (16 years)
and included a baseline condition, a 10% increase in the
parameter and a 10% decrease in the parameter. A one-way
analysis of variance and a Tukey’s multiple comparisons test
was then used to determine which treatments resulted in
escapement estimates that were significantly different from
baseline conditions. All statistical tests were performed with
the R statistical program [25].
3 Results and Discussion
3.1 Sensitivity Analysis
Sobol’sensitivity indices suggested that escapement was sen-
sitive to different input parameters depending on the age class
examined (Table 4). For age 2 fish, main indices indicated
Table 4 Sobol’sensitivity indices (standard deviation in parentheses) for each age class of returning spawners based on 1,000 Monte Carlo
iterations
Input parameter Age 2 Age 3 Age 4
Main Total Main Total Main Total
Water year 0.300
a
(0.083) 0.306
a
(0.079) 0.181
a
(0.091) 0.150 (0.091) 0.073 (0.067) 0.012 (0.065)
Egg mortality 0.030 (0.016) −0.006 (0.016) 0.222
a
(0.081) −0.021 (0.081) 0.102
a
(0.044) −0.072 (0.044)
Fry-to-smolt survival 0.039 (0.020) −0.009 (0.020) 0.166 (0.090) 0.091 (0.092) 0.079
a
(0.017) −0.071 (0.017)
River migration survival 0.007 (0.034) 0.135
a
(0.034) 0.164 (0.084) 0.062 (0.085) 0.079 (0.018) −0.07 (0.018)
Delta survival 0.010
a
(0.002) −0.009 (0.002) 0.404
a
(0.180) 0.643
a
(0.177) 0.313
a
(0.134) −0.009 (0.132)
Smolt to age 2 survival 0.734
a
(0.118) 0.454
a
(0.113) 0.015 (0.016) −0.006 (0.016) 0.057
a
(0.017) −0.052 (0.017)
Ocean productivity 0.003 (0.009) 0.009 (0.009) 0.034
a
(0.015) −0.034 (0.015) 0.061
a
(0.030) −0.048 (0.029)
Age 3 harvest N/A N/A 0.029
a
(0.001) −0.028 (0.001) 1.48
a
(0.306) 0.188 (0.293)
Age 4 harvest N/A N/A N/A N/A 0.055
a
(0.003) −0.054 (0.003)
a
Index value was statistically significant at α00.05
Chinook Salmon Life Cycle Model 463
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escapement was sensitive to smolt-to-age-2 survival, water
year type, and Delta survival (Table 4). Main and total indices
were similar for water year whereas the main index value for
smolt-to-age-2 survival was considerably larger than the total
value (Table 4). Additionally, age 2 escapement was sensitive
to river migration survival when interactions were accounted
for in the total index. This suggests that there were strong
interactions between certain input parameters for fish return-
ing to the spawning grounds at age 2 and confirmed that
Sobol’sensitivity measures were the best choice for this
sensitivity analysis, as interactions are difficult to deal with
using other global analysis techniques [5]. The main index for
Delta survival was significant yet the total index value was
negative. Negative numbers are possible for Sobol’indices [2]
and we considered negative values to indicate zero sensitivity
[8]. Main indices for age 3 escapement suggested that model
output for this age class was sensitive to many of the input
parameters examined (Table 4). However, total index values
indicated there were strong interactions between inputs, and
age 3 escapement was only sensitive to Delta survival after
accounting for these interactions. Similarly, main indices for
age 4 escapement indicated that output was sensitive to many
parameters (Table 4) whereas after accounting for interactions
in the total index, none of the input parameters significantly
influenced model output.
Although there were differences among age classes in the
sensitivity of input parameters, each age is not represented
equally among returning spawners. Thus, sensitivity should
be viewed in terms of the contribution of each age class and
the relationship among age classes.Age3fishcomprisedthe
largest proportion of returning spawners (88%) thus, inputs
driving variability in this age class should have the largest effect
on total escapement. Delta survival, water year, and egg mor-
tality were significant drivers of variability in age 3 escapement,
however, water year and egg mortality were not significant after
accounting for interactions. The Delta passage portion of the
model has flow–survival relationships in two reaches, thus, it is
not surprising that there are interactions between water year
type and Delta survival. Similarly, temperatures were higher in
critical and dry water years and there was an exponential
relationship between temperature and egg mortality.
Age 2 and age 4 fish accounted for 8% and 4% of total
escapement, respectively. Age 4 escapement was most sensi-
tive to harvest of age 3 fish. This is an intuitive result as
harvest at age 3 has a direct influence on the number of fish
that survive to age 4. Age 2 escapement was most sensitive to
smolt-to-age-2 mortality and this relationship remained strong
after accounting for interactions with other inputs (Table 4).
This is a critical period of the salmon life cycle when fish are
transitioning from freshwater to saltwater habitats and a large
portion of total mortality occurs during this time [16]. Water
year also was an important driver of variability in age 2
escapement with significant main and total effects where as
Delta survival was not significant when interactions were
accounted for. This is likely a result of interactions with water
year as discussed above for age 3 fish.
As variability in input parameters was increased, escape-
ment ranged from 2,806±984 fish (mean and standard devi-
ation) in the baseline treatment to 2,337± 904 fish in the 50%
treatment suggesting that model output was robust to param-
eter uncertainty (Fig. 3). Coefficients of variation differed
among input variables yet, CVs for individual input parame-
ters did not vary much among treatments (Fig. 3). Ages 3 and
4 harvest had the greatest CVs of any variable (0.55–0.60) and
both of these parameters were represented by a uniform dis-
tribution due to limitations in the data available to inform the
relationship. The use of uniform distributions to represent
parameter uncertainty has been identified as a limitation in
other sensitivity analyses [11]. Harvest may have a profound
effect on salmon population dynamics [17,28]andtheIOS
model could be improved by further research on harvest of
winter run that would reduce uncertainty in the true levels of
harvest. All other input parameters were represented by nor-
mal distributions and CVs were less than 0.30 (Fig. 3).
There is a tendency to identify sensitive parameters as
most important to model output. However, Fullerton et al.
0
500
1000
1500
2000
2500
3000
3500
4000
Escapement
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Baseline 10% 20% 30% 40% 50%
Treatment
Coefficient of variation
Egg mortality
Fry-to-smolt survival
River migration survival
Delta survival
Age 3 harvest
Age 4 harvest
Fig. 3 Mean salmon escapement values (top panel) and coefficients of
variation for input parameters (bottom) when variability of each input
was increased by 10%, 20%, 30%, 40%, and 50%. All calculations are
based on 1,000 Monte Carlo iterations
464 S.C. Zeug et al.
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[11] recognized the importance of distinguishing between
sensitivity and ecological relevance. For example, several of
the relationships in the IOS model are based on limited data
that influence the estimate of input parameters and the form
of uncertainty distributions associated with those estimates.
For example, river migration survival has been hypothesized
to be influenced by flow [21], yet survival during the river
migration stage is not influenced by flow in our model
because the values we used to inform the relationship were
taken from a field study conducted over three low-flow
years [18]. Thus, the data available do not cover the range
of potential conditions that may be experienced by out
migrating salmon. A similar situation exists for other rela-
tionships such as smolt-to-age-2 mortality that is hypothe-
sized to be an important determinant of year class strength
but is difficult to estimate in the field and is thus represented
by a uniform distribution. This is in contrast to laboratory
studies of temperature–mortality relationships applied in the
early development and fry rearing model stages where one
of the goals was to examine biological responses over a
range of environmental conditions. One of the strengths of
the IOS model is that it can be used to identify where
knowledge gaps exist and the model is flexible enough to
allow the integration of new data and functional relation-
ships as they become available.
3.2 Influence of Environmental Variables
Escapement was significantly affected by both the 10%
increase and 10% decrease in temperature (F
2,297
0346, p<
0.001). However, the increase in temperature had a much
greater effect producing a 95.7% reduction in escapement
whereas the decrease in temperature yielded a 11% increase
in escapement (Fig. 4). Varying flow produced a 6.2%
increase and 4.7% decrease in escapement yet these differ-
ences were not statistically significant (F
2,297
02.19, p0
0.113). Similarly, variation in exports and ocean conditions
did not yield statistically significant differences in escape-
ment with pvalues of 0.656 and 0.114, respectively (Fig. 4).
The lack of significant changes in escapement with a
10% change in flow, exports and ocean conditions may
reflect the type of data used to parameterize these relation-
ships. The functions utilizing these inputs were constructed
from data obtained from observational studies that had large
error estimates associated with responses. Thus, large
changes in these variables are required to produce a signif-
icant response in escapement. Temperature functions were
parameterized with data from controlled experiments that
produced small error estimates. Additionally, temperatures
in the spawning and rearing area are close to the upper
tolerance limit of Chinook salmon and even small changes
have the potential to significantly affect the population.
Management of temperatures in the Sacramento River is
a priority for stabilizing or increasing Chinook salmon pop-
ulations. The Sacramento–San Joaquin Rivers represent the
southern limit of Chinook spawning and stream temper-
atures can often approach the thermal tolerances for certain
life stages [20]. Historically, Chinook salmon could avoid
sub-optimal temperatures by utilizing higher elevation hab-
itats [36]. However, these areas have been eliminated by the
Flow
0
1000
2000
3000
4000
5000
6000
7000
Number of spawners
Exports
0
1000
2000
3000
4000
5000
6000
7000
Number of spawners
Wells' Index
0
1000
2000
3000
4000
5000
6000
7000
Baseline Plus 10% Minus 10%
Number of spawners
Temperature
0
1000
2000
3000
4000
5000
6000
7000
Baseline Plus 10% Minus 10%
Number of spawners
Fig. 4 Box and whisker plots of winter run escapement under baseline conditions, a 10% increase, and a 10% decrease in the four environmental
inputs used in the IOS model
Chinook Salmon Life Cycle Model 465
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construction of impassable dams in the foothills of the
Cascade and Sierra Nevada mountains [35]. Thus, under-
standing how population dynamics of Chinook are influ-
enced by temperature-related mortality is essential for
understanding how populations may be impacted by man-
agement actions or natural climate variations that may result
in higher stream temperatures. The simulations conducted
here do not represent any potential management or climate
scenario, but instead demonstrate the utility of the IOS
model for understanding this important driver of Chinook
salmon population dynamics.
4 Summary and Conclusions
Our study developed and used a stochastic life cycle simu-
lation model of winter-run Chinook salmon. The model
brought together field monitoring data and laboratory studies
to create six model stages that represent distinct salmon
habitats and life stages. The model was created using
GoldSim software and a free player version is available that
will allow anyone to easily run and explore the IOS model.
The model can be used to simulate population dynamics and
mortality at each life stage for a period of years specified by
the user. Our emphasis in developing this model was to allow
managers a means to test and compare among alternative
water management or restoration scenarios. A persistent
problem in the management of anadromous salmonids has
been the use of professional opinion in place of quantitative
data to identify the life stages and/or habitats that will be
affected by management actions [28]. The development of
the IOS model provides a significant step such as recom-
mended by Good et al. [12] to provide managers with the
tools necessary for managers to make decisions based on the
best quantitative data available. This was demonstrated by
our simulation of variation in environmental parameters that
revealed significant differences in escapement in response to
higher and lower temperatures.
Sensitivity analysis revealed that uncertainty could be
reduced by improving estimation of the mean values and
uncertainty distributions of certain inputs and functional
relationships between environmental variables and biologi-
cal processes. This was particularly apparent for smolt-to-
age-2 survival and ocean harvest that were uniform random
variables. These variables had greater CVs than any other
input and Sobol’indices indicated they could significantly
influence model output. Additionally, river migration surviv-
al was not related to any environmental variables despite
hypothesized relationships with flow because the data used
was collected under a narrow range of conditions. Greater
certainty in these relationships would improve model perfor-
mance and reduce uncertainty in management and recovery
actions based on IOS simulations. Although this model was
specifically developed for winter run, the IOS model struc-
ture could easily be adapted for other salmon populations in
the Sacramento-San Joaquin River system and serve as an
example of how life cycle models can improve management
of anadromous salmonids throughout their range. The IOS
model will provide a much needed tool for resource manag-
ers and will continue to improve as more quantitative data
becomes available.
Acknowledgments The authors thank Robert Leaf, Sean Sou, Qinqin
Liu, and Aric Lester for their insightful comments on the model and
manuscript. Steve Cramer was responsible for early development of the
IOS model. Tommy Garrison provided valuable assistance with R code
for the sensitivity analysis and Jenny Melgo put together the map of the
Sacramento Basin. Funding for this project was provided by the Califor-
nia Department of Water Resources and The National Marine Fisheries
Service (requisition no. NFFR5300-9-18382).
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