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1832
Swim speeds and energy use of uprivermigrating sockeye salmon (Oncorhynchus
nerka): simulating metabolic power and
assessing risk of energy depletion
Peter S. Rand and Scott G. Hinch
Abstract: We simulated metabolic power consumed by Fraser River sockeye salmon (Oncorhynchus nerka) during
upriver migration based on direct measures of activity from physiological field telemetry. The most accurate prediction
of energy expenditure was obtained by expressing activity as a fine time scale (5 s) stochastic process. By imposing a
daily time step, predictions of energy use were considerably lower than observed energy use, suggesting that the
practice of modeling field energetics at a daily time scale, particularly for relatively active fish, may render dubious
results. Daily mean power consumption through the Fraser River Canyon by the average migrant was about 20 W,
about fourfold higher than for less constricted reaches. Power consumption predicted at fine time scales ranged from
<1 W (0.1 body length·s–1) during periods of reduced activity to 1700 W (8 body lengths·s–1) during bursts while
navigating through turbulent canyon reaches. Through Monte Carlo simulations representing environmental variability
observed during 1950–1994, we determined that 8% of the salmon runs during this time resulted in high risk of
exhaustion for the average migrant that could lead to elevated in-river mortality. Reducing harvest levels on sockeye
salmon that may be exposed to these unfavourable conditions may assist agencies in achieving a risk-averse
management strategy.
Résumé : Nous avons simulé l’énergie métabolique consommée par des saumons rouges (Oncorhynchus nerka) du
Fraser durant la montaison à partir de mesures directes de l’activité obtenues par télémétrie physiologique sur le
terrain. Nous avons obtenu la prévision la plus précise de la dépense énergétique en exprimant l’activité sous la forme
d’un processus stochastique à échelle temporelle fine (5 s). Avec l’utilisation d’un pas de temps d’une journée, la
dépense énergétique prévue était bien inférieure à la dépense énergétique observée, ce qui montre que la modélisation
bioénergétique dans des conditions naturelles qui utilise une échelle de temps d’une journée peut donner des résultats
douteux, particulièrement dans le cas de poissons relativement actifs. La consommation d’énergie moyenne journalière
chez le migrateur moyen dans le canyon du Fraser était d’environ 20 W, soit d’environ quatre fois la consommation
dans des tronçons moins étroits. La consommation d’énergie prévue à des petites échelles de temps variait de moins de
1 W (0,1 longueur de corps·s–1), durant les périodes d’activité réduite, à 1 700 W (8 longueurs de corps·s–1) durant les
périodes d’activité intense, quand les poissons progressent dans des canyons turbulents. Au moyen de simulations de
Monte Carlo représentant la variabilité environnementale observée de 1950 à 1994, nous avons déterminé que, dans
cette période, dans 8% des remontes de saumon, le migrateur moyen se trouvait exposé à des risques élevés
d’épuisement, d’où la possibilité d’une forte mortalité dans les cours d’eau. La réduction des taux de récolte du
saumon rouge qui peut être exposé à ces conditions défavorables pourrait aider les organismes de gestion à mettre en
oeuvre une stratégie réduisant les risques pour la survie des stocks.
[Traduit par la Rédaction]
Rand and Hinch
1841
The historical accounts of the rigors of migrating adult
salmon traveling up British Columbia’s Fraser River have
achieved near fabled status. The arduous journey from the
Pacific coast to spawning grounds in the interior of the Fra-
ser River watershed depletes a large proportion of the energy reserves that accumulate during their marine residency.
The catastrophic rock slide of 1913 at Hell’s Gate in the Fraser River Canyon impeded the progress of hundreds of thousands of salmon for several years and laid bare concerns
about the precarious nature of these commercially valuable
Received March 7, 1997. Accepted March 27, 1998.
J13905
P.S. Rand.1 Institute for Resources and Environment, University of British Columbia, Vancouver, BC V6T 1Z2, Canada.
S.G. Hinch. Institute for Resources and Environment and Department of Forest Sciences, University of British Columbia,
Vancouver, BC V6T 1Z2, Canada. e-mail: [email protected]
1
Present address: Department of Zoology, North Carolina State University, Raleigh, NC 27695-7617, U.S.A.
e-mail: [email protected]
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Rand and Hinch
stocks (Roos 1991). Although rock removal, bank reconfiguration, and fishway construction throughout the canyon have
been carried out as remediation, passage remains energetically demanding (Hinch et al. 1996; Hinch and Rand 1998).
While these engineering feats appeared to resolve some of
the problems of migration impedance, the risk of energy exhaustion associated with successful migration through this,
and other reaches along the migration route, remains a matter of conjecture.
Results from recent studies on Pacific salmon migrations
suggest that successful spawning in some stocks may be limited by energy reserves, and thus, individuals are faced with
strong selective pressures to minimize cost of transport to
the spawning grounds. Bernatchez and Dodson (1987)
claimed that selection for energy efficiency in migration is
likely to be very important for the longer distance migrants
like sockeye salmon (Oncorhynchus nerka). Levy and
Cadenhead (1995) reported on migratory behaviours of
sockeye salmon that suggested that these fish synchronize
their movements within the tidal cycle to minimize cost of
transport through the Fraser River estuary. Assuming that
energy reserves are a limiting factor to successful migration
and breeding in this species, it follows that selection may
operate strongly on behaviours that influence the rate at
which this stored energy is consumed.
Priede (1985) defined two types of selection pressure that
are likely to be important in defining an animal’s fitness.
Type 1 selection is driven by energy-conserving behaviours
that operate across relatively extended time scales (days to
weeks). These behaviours are important as a means to
achieve high energy efficiency, thus leading to more energy
diverted to metabolic processes that directly influence fitness. Type 2 selection is driven by fine time scale power
budgeting (seconds to minutes), where the organism is faced
with a defined metabolic scope that serves to limit power
consumption at critical points through the organism’s life
history. Departures from this defined scope in nature result
in increased risks of mortality. Adult Pacific salmon from
some stocks presumably are influenced by both types of selection as a result of their costly river migration.
Most efforts at describing adapted behaviours in these fish
have involved defining optimal swim speeds that minimize
cost of transport (Weihs 1973; Ware 1975). We contend that
these examples, along with the examples discussed earlier,
are appropriate for investigating type 1 selection but ignore
finer time scale power budgeting implicit in type 2 selection.
Swimming bursts measured at the scale of seconds occur
routinely in these fish in the field (Hinch and Rand 1998)
and, given that energy costs are a power function of swim
speed, these active periods can be inordinately expensive.
By coupling the use of electromyogram (EMG) telemetry
with simulation modeling, it is possible to generate more accurate measures of energetic costs in situ. In this paper, we
explore behavioural patterns measured across a broadly defined temporal scale (seconds to weeks) to compare the relative importance of both types of selection operating on
energy efficiency during river migration.
We have three primary objectives in this paper. The first
is to compare observations of energy use from empirical
studies with predictions made by a deterministic (coarse
time scale) and a stochastic (fine time scale) bioenergetics
1833
model. This comparison allows us to test whether averaging
over the variability observed in swim speeds introduces a
significant bias in predictions of true costs to migrating fish
in situ. The second objective is to describe the fates of
stored metabolic energy during the course of the river migration, including an evaluation of the importance of anaerobic costs from burst swimming and defining the full range of
power consumed for activity in the field. The final objective
is to conduct error and risk analyses on the model to rank
parameters with respect to their sensitivity and define risks
of increased mortality resulting from energy depletion for
the average migrant in any given year based on the natural
variability of environmental conditions in the river.
Below, we describe (i) how our model represents initial conditions and intra- and inter-annual variability in river conditions,
(ii) how we used data from telemetry to build and calibrate a
bioenergetics model, and (iii) how we conducted error and risk
analyses to explore parameter sensitivities and to conduct an assessment of risk of energy depletion to these migrating fish. A
complete list of the model parameters implemented in the simulation is given (with annotations) in Table 1. Model parameter names
that appear in the tables and text are expressed in uppercase letters.
A map of the Fraser River, with pertinent place-names and the
model segments referred to in the text, is presented as fig. 1 in
Hinch and Rand (1998). Although Hinch and Rand (1998) demonstrated differences between sexes and sizes in activity rates, we
chose here to simulate an average individual (sexes and sizes combined) in the migrating population. Exploring sex- and sizespecific migration behaviours is beyond the scope of this paper.
Description of initial conditions and river model
We assumed in the model that the mean migration start date of
the average individual at the mouth of the Fraser River was 7 July,
mean weight was 2880 g, and the mean energy density was
8370 J·g–1 (MNMIGST, INITWT, and ENRGYD; Table 1). We
quantified the variability in the former two parameters observed
over a 44-year period (1950–1994) (IPSFC 1990; Department of
Fisheries and Oceans (DFO), unpublished data; Table 1). Energy
density data came from IPSFC (1980) but were insufficient to assess interannual variability.
We developed a simple regression model to predict daily mean
temperatures in the Fraser River through the first four model segments during July and early August, the period during which the
early Stuart stock are resident in the river. We regressed water temperatures (measured in model segment 2 during 1950–1994, DFO
unpublished data) against day of month. The intercept (temperature
on 1 July), slope (rate of change of water temperature during July),
and parameter error terms for the relationship are presented in Table 1 (TEMPINT and TEMPSLP). We assumed river temperatures
to be 21 and 15°C in model segments 5 and 6, respectively. These
temperatures were used in the model to estimate standard (or
basal) metabolism of the fish (see Metabolic model below) and to
predict lower Fraser River discharge.
We estimated discharge using a regression relating discharge
measured at Hope, B.C., (100 km east of the Fraser River mouth)
to mean July river temperature during 1950–1986 (IPSFC 1990).
River discharge was inversely related to river temperature and appeared to become uncoupled from temperatures above about 17°C.
We defined a break point in the regression model and assumed a
discharge of 4273 m3·s–1 during years when mean July river temperature was >17°C. Parameter values and associated error terms
for the resulting regression can be found in Table 1 (DTMPINT,
DTMPSLP, and DTMPCUT).
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1834
Can. J. Fish. Aquat. Sci. Vol. 55, 1998
Table 1. List of model parameters implemented in the Fraser River sockeye salmon migration simulation.
No.
Parameter
Initial parameters
1
MNMIGST
2
INITWT
3
ENRGYD
River parameters
4
TEMPINT
Description
Nominal value
Units
Source
Migration start date, days from 1 July
Initial weight of salmon at Fraser River
mouth
Initial energy density of salmon
7 (3.0)
2 880 (221)
Day of July
g
IPSFC 1980
IPSFC 1980
8 370
J·g–1
Beauchamp et al. 1989
14.2 (1.4)
°C
–1 153 (160)
4 273 (338)
m3·day–1
IPSFC
data
IPSFC
data
IPSFC
data
IPSFC
data
IPSFC
data
1
1
2.219
Dimensionless
Dimensionless
log cm·s–1
5
TEMPSLP
6
DTMPINT
7
DTMPSLP
Intercept, temperature vs. day of July
regression
Slope, temperature vs. day of July
regression
Intercept, discharge vs. temperature
regression
Slope, discharge vs. temperature regression
8
DTMPCUT
Discharge at river temperatures >17°C
Swim speed parameters
9
SSMEAN
Multiplier of mean swim speed
10
SSVAR
Multiplier of variance of mean swim speed
11
SSNCINT
Intercept, swim speed vs. discharge
regression, nonconstricted reaches
12
SSNCSLP
Slope, swim speed vs. discharge regression,
nonconstricted reaches
13
SSCINT
Intercept, swim speed vs. discharge
regression, constricted reaches
14
SSCSLP
Slope, swim speed vs. discharge regression,
constricted reaches
15
SSVNCINT
Intercept, variance of swim speed vs. discharge regression, nonconstricted reaches
16
SSVNCSLP Slope, variance of swim speed vs. discharge regression, nonconstricted reaches
17
SSVCINT
Intercept, variance of swim speed vs.
discharge regression, constricted reaches
18
SSVCSLP
Slope, variance of swim speed vs.
discharge regression, constricted reaches
19
SSLIM1
Upper limit on swim speed, nonconstricted
reaches
19
SSLIM2
Upper limit on swim speed, constricted
reaches
Migration speed parameters
21
MS1INT
Intercept, migration speed vs. discharge
regression, river segments 1 and 4
22
MS1SLP
Slope, migration speed vs. discharge
regression, river segments 1 and 4
23
MS2INT
Intercept, migration speed vs. discharge
regression, river segment 2
24
MS2SLP
Slope, migration speed vs. discharge
regression, river segment 2
25
PTCANY
Proportion of time resident in canyon
within river segment 2
26
PTCFC
Proportion of time resident in constricted
reaches within the canyon
27
MSHG
Migration speed at Hell’s Gate (segment 3)
Metabolic parameters
28
RA
Intercept, respiration of 1-g fish at 0°C
29
RB
Coefficient, metabolism vs. body weight
regression
0.119 (0.05)
23 478 (2443)
m3·day–1
–0.0001
2.246
log cm·s–1
1990; DFO, unpublished
1990; DFO, unpublished
1990; DFO, unpublished
This study
This study
This study
This study
This study
log cm·s–1
1.55 × 10–5
–0.04828
1990; DFO, unpublished
This study
–6.6 × 10–5
0.08086
1990; DFO, unpublished
This study
This study
log cm·s–1
5.55 × 10–5
This study
This study
2.3
log cm·s–1
This study
2.6
log cm·s–1
This study
1.15
m·s–1
IPSFC 1990; DFO, unpublished
data
IPSFC 1990; DFO, unpublished
data
This study
–0.0001
0.74
m·s–1
–0.00012
This study
0.234
Dimensionless
This study
0.725
Dimensionless
This study
0.016
m·s–1
This study
0.00143
–0.209
g O2·day–1
Beauchamp et al. 1989
Beauchamp et al. 1989
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1835
Table 1 (concluded).
No.
Parameter
Description
Nominal value
30
RQ
0.086
Beauchamp et al. 1989
31
RTOTOTAL
0.0284
This study
32
RTOSLP
–0.00136
This study
33
UCRITI
34
UCRITS
35
ANSPEED
36
ANTAX
37
GONINT
38
GONSLP
Coefficient, metabolism vs. temperature
regression
Intercept, swim speed coefficient vs.
temperature regression
Slope, swim speed coefficient vs.
temperature regression
Intercept, critical swim speed vs. fish
length regression (at 15°C)
Slope, critical swim speed vs. fish length
regression (at 15°C)
Proportion of critical swim speed at which
anaerobic metabolic pathways are
invoked
Efficiency rating for anoxic energetic
pathways
Intercept, gonad energy requirements vs.
body energy per day regression
Slope, gonad energy requirements vs. body
energy per day regression
1.289
Units
log cm·s–1
0.6345
Source
Brett and Glass 1973
Brett and Glass 1973
0.8
Dimensionless
Webb 1971
0.85
Dimensionless
Gnaiger 1983
–0.00222
J gonad·
J body–1·day–1
IPSFC 1959
0.000452
IPSFC 1959
Note: Mean (SE) (N = 44) is given for those parameters varied in risk analysis. IPSFC, International Pacific Salmon Fisheries Commission; DFO,
Canadian Department of Fisheries and Oceans.
Swim speed
The details of the field program designed to measure tail beat
frequency and estimate swim speeds of sockeye salmon are described in Hinch and Rand (1998). It was necessary to describe the
swimming behaviour of an average individual in the migrating
population for each river segment of our model. Unless otherwise
stated, we pooled and log10 transformed the raw swim speed data
over individuals and computed means and standard errors (in log10
centimetres per second) by year and by reach. We pooled swim
speed data collected in the Fraser River Canyon (reaches 1–10 of
Hinch and Rand 1998) according to two broad bank classifications
(straight or bended banks and constricted banks), hereafter referred
to as nonconstricted and constricted reaches. For our purposes, we
considered reach 2 as a nonconstricted reach and reaches 4, 7, and
9 as constricted reaches (Fig. 1).
We developed two regression models to predict the mean and
variance of swim speed in constricted and nonconstricted reaches
by regressing the swim speed data against mean July river discharge during 1993 and 1995. We acknowledge a potential bias by
only having data from males during 1995. Unfortunately, there is
no straightforward method of correcting for this. The regression
parameters are included in Table 1 (SSNCINT, SSNCSLP,
SSCINT, SSCSLP, SSVNCINT, SSVNCSLP, SSVCINT, and
SSVCSLP). These parameters were applied to estimate swim
speeds in model segments 1, 2, and 4. We assumed no effect of
discharge on swim speeds for fish within model segments 3, 5, and
6 and applied a static swim speed distribution. For model segment
3, we pooled swim speed measurements made during 1993 and
1995 at Hell’s Gate to represent activity within this segment. We
pooled swim speed data across individuals, years, and reaches on
the Nechako River to represent swim speed within model segments
5 and 6.
We defined four additional parameters that governed the distribution of swim speeds applied in the model. Two parameters
(SSMEAN and SSVAR) served as multipliers of the mean and
variance defining the swim speed distribution applied in all river
segments. These parameters were assigned default values of unity.
The other parameters (SSLIM1 and SSLIM2) were used to define
an upper limit to the swim speed distributions applied in the model
Fig. 1. Measurements of swim speed from EMG physiological
telemetry during 1993 and 1995 in the lower Fraser River,
British Columbia. (a) Swim speeds (N = 2016) from individuals
observed within reach 2 described in Hinch and Rand (1998), an
example of a more typical, nonconstricted reach along the
migration route. (b) Swim speed data pooled from reaches 4, 7,
and 9 (N = 16 479), examples of reaches with severely restricted
banks that create complex hydrologic conditions. SSLIM1 and
SSLIM2 are parameters used in the model to serve as an upper
allowable limit for swim speeds applied in the simulation.
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1836
Fig. 2. Summary of data collected on migration speed (i.e.,
ground speed) for early Stuart sockeye salmon in the Fraser
River, British Columbia. Data from IPSFC (1990) (diamonds)
and least squares regression model fit (solid line) are based on
estimated rates of travel of the peak migration abundance from
Hell’s Gate to Prince George, B.C. Data from the Fraser River
Canyon (squares) and least squares regression model fit (broken
line) are based on rates of movement of fish carrying
transmitters between the release site downstream of the Fraser
River Canyon and Hell’s Gate (see Hinch et al. 1996 for details).
(Table 1; Fig. 1). These parameters were assigned values of 2.3
(log10 centimetres per second, or about 4 body lengths·s–1 for a 50cm salmon) and 2.6 (log10 centimetres per second, or about 8 body
lengths·s–1 for a 50-cm salmon) for nonconstricted and constricted
reaches, respectively.
Migration speed
Migration speed was computed as a function of predicted river
discharge in model segments 1, 2, and 4. We estimated migration
speed (metres per second) from timing of peak return abundance at
Hell’s Gate and Prince George, B.C. (our model segment 4, during
1951–1986, IPSFC 1990) and regressed the values against mean
July Fraser River discharge to derive a predictive model (Fig. 2).
As noted in IPSFC (1990), migration speed through model segment 4 is negatively correlated with river discharge (r2 = 0.37, P =
0.01). We applied the resulting intercept and slope parameters to
estimate migration speed through model segments 1 and 4
(MS1INT and MS1SLP; Table 1).
We used three data points for migration speed through the Fraser River Canyon during 1993–1995 to define the relationship between migration speed through model segment 2 and river
discharge (Fig. 2). We fit a least squares regression (r2 = 0.74, P =
0.33) to the three data points (MS2INT and MS2SLP; Table 1). Although the regression was not significant, the data did show a similar trend to that observed within model segment 4. We defined a
break point in the migration speed model applied to model segment 2 at a discharge of 5500 m3·s–1; at greater discharge, migration speed in the model was set at 0.1 m·s–1. We partitioned the
time resident in model segment 2 into canyon and noncanyon sections and further partitioned the time within the canyon between
constricted and nonconstricted reaches, as described above
(PTCANY and PTCFC; Table 1).
Data were insufficient to develop a similar migration speed
model for model segment 3, so we computed a mean from the estimates of migration speed through a 100-m reach below the Hell’s
Can. J. Fish. Aquat. Sci. Vol. 55, 1998
Gate fishways during 1993 and 1995 (MSHG; Table 1). Because
of the short residence time for sockeye salmon within model segments 5 and 6, and because river discharge is fairly even among
years in most of this area, we assumed migration speed to be independent of discharge in these segments (0.46 m·s –1 for segment 5,
0.69 m·s –1 for segment 6, Hinch and Rand 1998; IPSFC 1980).
Modeling metabolism
We account for dependence of weight, temperature, and swim
speed on metabolism in the river migration model. We used the
general energy balance approach of Beauchamp et al. (1989). We
adopted the intercept and weight- and temperature-dependent coefficients for standard metabolism of Beauchamp et al. (1989) (RA,
RB, and RQ; Table 1) and assumed an oxycalorific coefficient of
13 560 J·g O2–1. We estimated activity energy losses during the migration event using both a deterministic and a stochastic model
configuration. In the deterministic model, we simulated activity
costs on a daily time step using an observed mean swim speed. In
the stochastic model, we decreased the time step to conform to the
scale at which the EMG data were recorded (5-s interval) and applied activity levels by Monte Carlo sampling from a lognormal
distribution of swim speeds. Swimming costs are very expensive
during the upstream migration and there is evidence that anaerobiosis occurs during portions of the migration (see Hinch et al.
1996). Therefore, we developed a new energy model that accounts
for swim speed dependence on metabolism and partitions energy
use between aerobic and anaerobic metabolic pathways.
Brett (1964) and Stewart (1980) reported that the slope of the
regression relating metabolism to swim speed (RTO of Beauchamp
et al. 1989) was inversely related to temperature over the range 5–
25°C for 50-g sockeye salmon. We concur with these authors that
this interaction between RTO and water temperature is likely to be
a result of the increased importance of anaerobic metabolism at
warmer temperatures, where oxygen is more likely to become limiting. We thus partition energy expenditure resulting from activity
into two separate metabolic pathways based on occupied water
temperature and observed swim speed. We hereafter refer to these
laboratory-derived swim speed – metabolic coefficients as RTOaero.
We regressed values of this parameter for juvenile rainbow trout
(Oncorhynchus mykiss, Rao 1968), adult coho salmon
(Oncorhynchus kisutch, S.G. Hinch, unpublished data), and adult
sockeye salmon (Brett 1965; S.G. Hinch, unpublished data) against
water temperature. The resulting regression equation (RTOaero =
RTOtotal + RTOslp × temperature; RTOTOTAL and RTOSLP; Table 1) suggests an inverse relationship between RTOaero and temperature. The lack of data on the swim speed – metabolic
relationship for adult sockeye salmon necessitated borrowing data
from related species. We do note here that all these species are of
the same genus. We applied the value of the intercept (RTOtotal) in
the metabolic equation when swim speed predicted in the model
was below 80% of critical swim speed (Ucrit as defined by Webb
1971 and Brett and Glass 1973; ANSPEED; Table 1). The Ucrit was
computed in the model as a function of fish size (Brett and Glass
1973; UCRITI and UCRITS; Table 1).
In cases where swim speed was at or above 80% of Ucrit, we
partitioned the total energy expenditure between aerobic and anaerobic metabolic pathways. We first estimated total energy use using
the value of RTOtotal in the metabolic model. We then computed a
value for RTOaero using the regression equation above and then
solved for the value of RTOanaero by difference (RTOanaero =
RTOtotal – RTOaero). We multiplied total energy used for activity by
the ratios RTOaero:RTOtotal and RTOanero:RTOtotal to estimate contribution of power from aerobic and anaerobic metabolism, respectively. To account for the inefficiency of liberating energy through
anaerobic metabolic pathways, we applied a “tax” on the conversion of body energy to work of 15% (ANTAX; Table 1) during pe© 1998 NRC Canada
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riods of burst swimming based on a biochemical efficiency rating
computed by Gnaiger (1983). The power requirements from aerobic and anaerobic pathways were then summed to account for total
activity costs during each time step in the model.
We developed a simple model to account for energetic demands
of gonad development through the river migration. We computed
the rate of accretion of gonad energy between contiguous sampling
stations (joules in gonad per joule in eviscerated body per day,
IPSFC 1959). We regressed these data against total body energy to
arrive at a predictive equation to estimate daily rate of energy requirements for gonad development (GONINT and GONSLP; Table 1). Thus, we assumed that the flow of energy from body to
gonads was an increasing proportion of total body energy over the
migration and that conversion from body energy to gonads was
100% efficient. We invoked this gonad development model beginning on day 10 of the simulation (IPSFC 1959).
1837
Fig. 3. Results from the calibration run simulating energy use
for an average early Stuart migrant during 1956 in the Fraser
River, British Columbia. (a) The broken line represents the
simulated trend in energy content of the average migrant using a
mean swim speed and a time step of 1 day. The solid line
represents predictions from a fine time scale (5-s time step)
model that represents swimming behaviour as a stochastic
process. Empirical data used to calibrate the model were
obtained during 1956 from IPSFC (1959). (b) Time series of
simulated power consumption during the migration, partitioned
between swimming costs (aerobic and anaerobic), standard
metabolism, and energy required for gonad development.
Model calibration
We reproduced the fish characteristics and the environmental
conditions within the river during 1956 and simulated loss of body
energy through the migration from the Fraser River mouth to the
spawning grounds. These predictions were compared with observed eviscerated body energy for early Stuart sockeye collected
along the migration route during 1956 (IPSFC 1959). Model accuracy using the coarse (1 day) and fine (5 s) time step model configurations was measured by dividing the values for model
predictions by the values from field observations (corresponding to
the same day of migration) and multiplying by 100 to express the
difference as a percentage. The most accurate model configuration
based on this criterion was implemented in the subsequent error
and risk analyses described below.
Error and risk analysis
We conducted a comprehensive error analysis (Bartell et al.
1986) to help assess what variables were most sensitive in the
model. All 38 parameters in the model (Table 1) were varied by
2%, a value recommended by Gardner et al. (1981) for ecological
models. These parameter values were sampled using Monte Carlo
techniques at the beginning of each model iteration and held constant over the course of the migration simulation. The model was
iterated 1000 times. We assessed the impact of individual parameter values on the model estimate of final energy content on the
spawning grounds by computing relative partial sums of squares
(RPSS, as defined in Bartell et al. 1986).
We assessed the probability (or risk) of observing critically low
energy states for an average individual during 1000 simulated
years. Different model realizations were created by sampling from
the observed mean and variance in measures of the initialization
parameters (migration start date and initial weight of fish) and
river parameters (temperature and discharge) (Table 1) to represent
natural variation. The output was expressed as a distribution of
predicted energy content of average individuals arriving on the
spawning grounds. We defined the risk endpoint at a state of 80%
exhaustion of the initial energy reserve prior to entry into the
spawning grounds. This threshold was based on the lowest measured energy content of fish that successfully reached the spawning
grounds during the study reported in IPSFC (1959). Observations
included in IPSFC (1980) on late-run Adams River sockeye salmon in the Thompson River suggest that swimming ability can be
impaired when fish approach this threshold energy state. Therefore, risk was estimated as the probability that any given year resulted in an average individual with less than 20% of its initial
energy reserve intact. We conducted error analyses on the parameters varied in these Monte Carlo simulations.
Model calibration
We found good agreement between model predictions and
field observations by employing a time step in the model
that was consistent with the scale at which observations
were recorded in the field (about every 5 s) and expressing
the full range of fish activity through a stochastic modeling
approach (Fig. 3). The model, configured to reproduce river
migration conditions during 1956, provided predictions of
energy content within 15% of observed measures during a
field program conducted in the same year. Greatest deviations in model predictions from field data were observed
midway through the migration period. The pattern of error
indicated that the model underestimated true costs to the fish
within model segment 4 and overestimated costs in later
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Can. J. Fish. Aquat. Sci. Vol. 55, 1998
Table 2. Results from the model error analysis.
Rank
Parameter
Type III SS
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
SSLIM1
SSLIM2
SSMEAN
RTOTOTAL
SSNCINT
RQ
RB
MS1INT
RA
SSNCSLP
ENRGYD
TEMPINT
MS1SLP
SSVCSLP
ANTAX
MS2INT
UCRITI
PTCANY
SSCINT
TEMPSLP
SSVAR
SSVCINT
SSVNCINT
MS2SLP
UCRITS
DTMPSLP
INITWT
PTCFC
DTMPINT
SSVNCSLP
GONINT
DTMPCUT
SSCSLP
MSHG
GONSLP
MNMIGST
RTOSLP
ANSPEED
11.749
3.444
3.235
1.684
1.617
0.277
0.238
0.162
0.091
0.067
0.061
0.032
0.020
0.018
0.013
0.011
0.011
0.010
0.010
0.010
0.008
0.005
0.005
0.005
0.004
0.003
0.003
0.002
0.002
0.001
0.001
0.001
0.001
<0.001
<0.001
<0.001
<0.001
<0.001
F-value
3252.95
953.61
895.66
466.31
447.63
76.63
65.79
44.82
25.33
18.58
16.94
8.76
5.61
4.90
3.68
3.15
3.08
2.89
2.79
2.65
2.21
1.52
1.35
1.31
1.04
0.92
0.72
0.68
0.51
0.32
0.27
0.23
0.19
0.11
0.02
0.02
<0.01
<0.01
P
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0032
0.0180
0.0271
0.0554
0.0760
0.0796
0.0892
0.0951
0.1039
0.1374
0.2179
0.2450
0.2533
0.3082
0.3385
0.3966
0.4103
0.4758
0.5688
0.6057
0.6312
0.6660
0.7403
0.8891
0.8930
0.9548
0.9565
Note: Model parameters are ranked by sensitivity according to values of
type III sums of squares. The model was iterated 1000 times and values
of parameters were varied by 2% of their nominal values reported in
Table 1. Significance set at 0.05/38 = 0.001.
segments. The deterministic model configuration, with a
time step of 1 day, overestimated final energy content at the
spawning grounds by nearly 100% (Fig. 3).
Energy and power budget
Daily mean power requirements (measured in watts or
joules per second averaged over the day) for passage
through model segments 2, 3, and 5 (simulated days 4, 6,
and 18–21) were higher than for all other river segments
(Fig. 3). The greatest power consumption by individuals was
predicted to occur through the Fraser River Canyon segment
(segment 2 on simulated day 4). This was a result of elevated activity rates required to navigate through the constricted reaches in this segment. The estimate of power
consumption, 18.2 W, was over twofold higher than that
predicted on any other day of the migration. Although activity was elevated to pass through Hell’s Gate as well, the relatively short time for passage (about 3 h) through this model
segment resulted in only a marginal increase in total power
requirements (6.7 W) during that day of the migration. Passage through segment 5 during simulated days 18–21 was
energetically expensive due to the elevated temperatures
(21°C) characteristic of that part of the migration. After accounting for the added costs associated with the unique river
characteristics within model segments 2, 3, and 5, we also
detected a gradual linear increase in power consumption
through the migration caused by increasing river temperatures and the additional energy required to develop gonads
after simulated day 10 (Fig. 3).
A majority of the energy consumed by the fish over the
migration was used in swimming activity (84% of total energy). This percentage was much greater in the more difficult model segments. For example, during simulated day 4
while resident in the Fraser River Canyon, 98% of the power
consumption was used in activity. Of this amount expended
within the Fraser River Canyon, 36% originated from anaerobic metabolic pathways (Fig. 3). Mean daily activity costs,
expressed as a multiplier of standard metabolic rate, varied
from 10 during days resident in nonconstricted reaches to
over 40 during residence within the constricted reaches in
the Fraser River Canyon. Power requirements for gonad development represented about 8.4% of total power consumed
during the migration, while standard metabolism was responsible for 7%.
Metabolic power expended in activity, expressed in watts
at the time scale of the model, was highly variable. This
metric varied by as much as three orders of magnitude
within any given day of the migration and two orders of
magnitude between days. When relatively inactive, power
consumption for activity was less than 1 W, or 0.1 times
standard metabolic rate. Brief bursts resulted in sharp increases in power consumption. These bursts, modeled at
speeds of up to 8 body lengths·s–1, resulted in power consumption as high as 1700 W, or 3800 times standard metabolic rate. These bursts were more frequent and of greater
magnitude within the constricted reaches relative to the nonconstricted reaches in the river (see Fig. 1). More than half
of the power sustaining these bursts originated from anaerobic metabolic pathways.
Error analysis
Fourteen parameters, out of a total of 38, contributed substantially to variability in predicted energy content on the
spawning grounds (Table 2). We found the model sensitive
to assumptions related to the observed patterns in swim
speed. In particular, the model was extremely sensitive to
the defined upper limit of the swim speed distribution and
the mean observed swim speed (Fig. 1; Table 2). The coefficients that defined the activity–discharge compensatory
function (SSNCINT and SSNCSLP) were also found to be
important. The metabolic parameters, particularly the values
for RTOTOTAL (the swim speed – metabolic coefficient)
and RQ (the temperature-dependent coefficient) were also
sensitive model parameters. The only environmental param© 1998 NRC Canada
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Rand and Hinch
eter that was found to be important was initial river temperature. Of the initial parameters, only energy density was
found to be sensitive in the model.
Risk analysis
Results of the risk analysis indicate that there is an 8%
probability of observing critically low energy states in an average early Stuart sockeye, given the observed historical
variation in initial run characteristics and river conditions.
Energy stores, measured as a proportion of body energy remaining after reaching the spawning ground, ranged widely
from 0 to 55% (Fig. 4). The mean and median value of the
distribution was 33 and 35%, respectively. A total of 41 out
of 1000 simulations (or 4% of the simulated runs) resulted
in complete energy exhaustion prior to reaching the spawning grounds. The error analysis conducted on this model
configuration indicated that the predictions of risk are most
sensitive to changes in river discharge. The other two parameters found to be sensitive were mean migration start
date and the rate of change of river temperature during the
month of July.
Temporal scale dependence in fish bioenergetic models
We present results that have important implications for selecting appropriate temporal scales for accurately simulating
energetics and swimming behaviour of wild fish. Although
we modeled sockeye salmon during a period of relatively
high activity that may tend to exaggerate the potential error,
the results do point toward potentially significant errors in
previous bioenergetic modeling applications. We discovered
significant error in model predictions when activity was
modeled using a daily mean swim speed. Continued efforts
at quantifying energetic costs of fish engaged in other, less
active behaviours in the field will help determine the extent
of error in past bioenergetic model applications that have assumed an optimal swim speed. Briggs and Post (1997), using EMG telemetry with foraging rainbow trout, have begun
to address this issue; however, their approach of averaging
swim speeds over a 30-min period will underestimate true
costs in situ. It is important to note that even at the 5-s time
step we used in our study, we are still averaging over finer
scale behaviours that could contribute to estimation error.
We represented the dynamics of swimming in this study
as a fine time scale stochastic process. Although this model
configuration generated reasonable rates of energy use during migration, we suspect that these fish exhibit repeated
temporal patterns of swimming behaviour, possibly alternating between “resting” and “bursting” periods. The preponderance of swim speed data measured below 4 cm·s –1 (note
left tail of the distributions at <0.6 log centimetres per second in Fig. 1) in some reaches suggest that this behaviour
may be invoked during river migration. Observations we
have made using EMG telemetry at Hell’s Gate demonstrate
that the probability of successfully navigating through some
of the more difficult reaches may be strongly influenced by
behavioural strategies that include periods of stasis punctuated by swimming bursts.
1839
Fig. 4. Distribution of predicted energy contents of the average
sockeye salmon migrant across 1000 simulated years with
varying initial run characteristics (i.e., mean migration start date
and body size) and river conditions (i.e., temperature and
discharge). A total of 8% of the runs resulted in the average
migrant reaching critically low energy states that could lead to
elevated natural mortality in the population.
Fates of metabolic energy and scope for activity
Activity dominated the energy budget of these salmon migrants. For our calibration run, 84% of stored energy was
consumed by locomotor costs, while less than 20% was consumed by standard metabolism and gonad development.
Thus, if these fish are indeed faced with conserving energy
during their river migration, factors that control swimming
behaviour are likely to be of paramount importance in regulating the rate at which they consume their energy reserves.
We explicitly defined, for the first time, the range of
power consumed by activity for migratory salmon in a natural environment. We found swimming power, measured in
watts at a fine time scale (5 s), to vary by three orders of
magnitude within a given day and two orders of magnitude
between days during the migration. These rapid swimming
bursts appear to be made possible through power subsidies
in the form of increased anaerobic metabolism. It has been
long conjectured that these fish require power generated
through anaerobic metabolism to progress through some of
the more difficult river reaches. Brett (1996) could draw on
no reliable data to suggest whether or not anaerobiosis actually occurred in situ. High levels of nonesterified fatty acids
in blood (Ballantyne et al. 1996) and lactate in the white
muscle tissue (Hinch et al. 1996) from early Stuart sockeye
collected while migrating through Hell’s Gate provide further evidence that these fish are likely invoking anaerobiosis
during migration. Results from our study suggest that these
pathways can effectively double field activity scope (from
800 to 1700 W) and may be a critical determinant for successful passage through the more difficult river reaches.
Ecological and evolutionary significance of migration
energetics
Results from our error analyses helped reveal important
interactions between behaviour and energetics of sockeye
salmon that have relevance to life history and evolutionary
strategies for this species. Our results suggest that selective
pressures may operate strongly on the behaviours that influ© 1998 NRC Canada
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1840
ence fine time scale power budgeting while en route to the
spawning grounds. This is reflected in the sensitivity of
model predictions of energy use to the parameter values that
defined the upper limit to the swim speed distribution. These
selective pressures, referred to as type 2 by Priede (1985,
see our Introduction), would help define the frequency and
magnitude of bursts performed by these salmon as they
progress to the spawning grounds. While these bursts appear
to be necessary to successfully navigate through some of the
more difficult reaches, our results suggest that there must
exist strong selective pressures to minimize the frequency
and reduce the absolute magnitude of these bursts to avoid
risk of energy exhaustion. Fish do appear to restrict these
expensive bursts, particularly those that exceed 80% of Ucrit,
to difficult reaches within the Fraser River Canyon and
Hell’s Gate. If the fish exceed their metabolic scope, periods
of stress can ensue that lead to hyperactivity and, ultimately,
death (Black 1958; Wood et al. 1983). These results suggest
that these fish are operating close to a physiological threshold, which may necessitate strong selection that would serve
to fine-tune burst swimming behaviour.
Type 1 selection, as defined by Priede (1985) (see our Introduction), appears to also play a role in defining energy efficiency of migration in this species. In particular, the mean
swim speed defined in the model and the parameters that
governed the relationship between mean swim speed and
river discharge levels were all important based on the results
of our error analysis. This suggests that reducing mean swim
speeds in general, or reducing swim speeds under conditions
of high river discharge, can be adaptive and result in higher
energy efficiency during migration. Over an evolutionary
time scale, there must be some dynamic equilibrium between expanding field activity scope that allows for marginal increases in power to navigate through difficult
reaches (type 2 selection) and more conservative locomotor
behaviours that result in longer term savings in energy (type
1 selection).
Strategies that tend to conserve energy during migration
can ultimately result in increases in energy diverted to gonads that can directly contribute to fitness. Our error analysis indicated that predicted energy use was fairly insensitive
to the values of the coefficients that governed the rate at
which energy was consumed for gonad development. We
therefore conclude that power demands for gonad development are not likely to strongly compete for power for other
metabolic activities while en route to the spawning grounds.
We may be misled in this analysis, however, by modeling an
average individual. Costs for gonad development in females
are considerably higher than males, and thus may put females at a much higher risk of energy exhaustion. Further,
maintaining sufficient energy reserves to successfully mate
on the spawning grounds may be a critical factor in defining
fitness for both sexes. Energy expended during spawning
can amount to as much as 20% of initial energy reserves
(IPSFC 1980), and behaviours that conserve energy during
river migration may be critical in defining fitness on the
spawning grounds.
The migration start date in salmon (or, alternatively, return time from the ocean) has been suggested to be an important factor that affects the probability of a successful, and
Can. J. Fish. Aquat. Sci. Vol. 55, 1998
energetically efficient, migration to the spawning grounds
(Quinn and Adams 1996). Results of our error analysis suggest that start date is indeed a critical determinant of exhaustion risk in the river and help explain the relatively precise
homing behaviour exhibited by these fish. Indeed, the relatively narrow standard error of start dates for the early Stuart
stock (± 3 days, Table 1) suggests that precise timing may
be an important evolved trait among these stocks as a measure to help ensure an efficient river migration. There appears to be important energetic trade-offs associated with
timing and subsequent river conditions for this stock. The
interaction between temperature and discharge in the river
during a given year, the sensitivity of the temperature and
discharge parameters in the model, and the relatively precise
timing exhibited by this stock all suggest that there may be
strong selection for a precise time of river entry to minimize
the likelihood of experiencing difficult river passage. We
feel that these selective pressures are likely to be less important for later run summer and fall stocks of Fraser River
sockeye salmon given that these fish typically migrate
shorter distances and are exposed to lower discharge and often lower temperatures than those frequently encountered by
early summer migrants like the early Stuart stock.
Ecological risk assessment and management
implications
How can this model be incorporated into management?
The regulatory body charged with managing these stocks,
the Federal Department of Fisheries and Oceans (DFO), has
adopted a risk-averse strategy for managing British Columbia salmon (Blewett et al. 1996). Most of the regulatory effort by DFO is oriented toward managing harvest rates on
these stocks as a means to achieve target escapement goals.
We feel that it is critical for managers to realize that, while
harvest is likely to represent the dominant source of mortality on these stocks in most years, in some years, significant
“natural” mortality may occur resulting from difficulties encountered during migration. Although we looked only at the
early Stuart stock in our analysis, it is reasonable to assume
that these risks may also be important for other stocks as
well. Although much uncertainty still exists in translating
our risk index to an explicit mortality rate, we emphasize
that this mortality risk should be included as a factor in preand in-season management during years where difficult passage conditions are expected. For example, when model predictions suggest high natural mortality risk for the average
migrant in a particular year, harvest could be adjusted to reduce total fishing mortality, thus allowing more fish to successfully reach the spawning grounds.
It has been suggested that river temperatures and flow regime may change dramatically given our current understanding of global climate change (Moore 1991; Levy 1992). The
early Stuart stock may serve as the proverbial “canary in a
coal mine” given the importance of discharge, in particular,
and temperature on migration speed and risk of energy exhaustion en route to the spawning grounds. We hope that
this study encourages further efforts at understanding how
the river may change in the future and the degree of plasticity in salmon behaviour that may allow this species to cope
with these changes.
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We thank Mike Healey and Ingrid Burgetz for contributing to helpful discussions and Mike Henderson for continued support of this work. We are particularly grateful to
Tony Farrell for providing comments and suggestions on
modeling energetic costs. We also acknowledge the help of
Don Stewart, who provided results of unpublished analyses
from his Ph.D. dissertation. Funding was provided from the
Fraser River Action Plan through Canada’s Green Plan and
an NSERC research grant to S.G Hinch. P.S. Rand was also
supported through an NSERC strategic grant to M. Healey,
C. Walters, and P. LeBlond.
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