9702

• UCREFRP Catalog Number: 9702
• Author: Petersen, J.H., and C.P. Paukert.
• Title: Development of a bioenergetics model for humpback chub and evaluation of water temperature changes in the Grand Canyon, Colorado River.
• USFW Year: 2005.
• USFW - Doc Type: Transactions of the American Fisheries Society
• Copyright Material: NO

250
humpback
ter values
nulate the
ne), which
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o example,
teria (ver-
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-y data are
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:TM) pa-
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umpback
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1 1997).
HUMPBACK CHUB BIOENERGETICS
Without inclusion of such a rule, it would be pos-
sible to get nonsensical parameter sets from Monte
Carlo sampling, such as optimum is greater than
maximum temperature because other random pa-
rameter combinations might "compensate" for
temperature parameters, allowing growth to fit the
test criteria.
Many parameter sets produced low or high
growth rates that did not fit test criteria, whereas
other parameter sets grew model fish that fit the
test criteria at either the intermediate or the final
time but not at both test times (Figure 113). Some
combinations of selected parameter values pro-
duced growth of humpback chub that matched size
in the 24°C laboratory growth experiment (Figure
113). Using the average parameter values from all
acceptable sets, modeled growth closely matched
laboratory growth (Figure 1A). Specific values of
model parameters are discussed in the Results sec-
tion.
Final parameter selection, model corroboration,
and sensitivity.-Fitting parameters with the Mon-
te Carlo model could be accomplished by assum-
ing that fish in the feeding experiment have fed at
either their maximum rate or some rate below the
maximum rate. Although humpback chub were of-
fered a 12% ration in the growth experiment (Gor-
man and VanHoosen 2000), fish might have fed
below their maximum consumption rate if tem-
perature was not optimum, there was interference
competition, or the food sources were not ideal.
For corroboration and final selection of parameter
values, we conducted Monte Carlo sampling of
parameters to fit the 24°C growth experiment under
two assumptions: (1) satiation, i.e., food avail-
ability was maximum and humpback chub were
feeding at their maximum consumption rate (p =
1.0), and (2) below satiation, i.e., humpback chub
in growth experiments were feeding at some level
below maximum consumption, so p was allowed
to vary during parameter fitting between 0.0 and
1.0. For this second assumption, the p value was
sampled as a random variable on each iteration of
the Monte Carlo model, similar to other parame-
ters.
To corroborate the humpback chub model and
select final parameter values, we used independent
growth rates of juvenile and subadult humpback
chub from various field and laboratory sources;
ran the model with appropriate diet, temperature,
and fish size; and evaluated the range and average
p values necessary to model observed growth.
Growth under a variety of conditions that produced
reasonable p values would corroborate that the
965
model was capable of producing a variety of
growth patterns under different temperatures and
conditions. An acceptable range of p values was
approximately 0.2-0.8 (J. Kitchell, University of
Wisconsin-Madison, personal communication).
Data were not available on specific consumption
rates and temperature, which might be used in a
different type of corroboration of the model (e.g.,
Petersen and Ward 1999).
Growth rates of humpback chub'in the field were
from several sources. Robinson and Childs (2001)
fit a von Bertalanffy growth model to juvenile
humpback chub captured during 1991-1994 in the
Little Colorado River (LCR), a spawning and rear-
ing tributary of the Colorado River. We used this
model to estimate size at monthly intervals and
estimated p values assuming growth during the
month and average LCR temperatures (taken from
their Figure 1). Valdez and Ryel (1995) reported
the average back-calculated size of humpback
chub aged 1-4 years collected from the main-stem
Colorado River, Grand Canyon, in 1992-1993. We
used these sizes and average water temperature in
the COR to estimate p values. Valdez and Ryel
(1995) examined scales for transition checks to
determine those fish that might have moved from
the warm LCR (>20°C) to the cold COR (-10°C)
and concluded that there was "little or no survival
of smaller fish descending from the LCR"; hence
we assumed that fish used in this analysis likely
grew under only the COR temperature regime. A
von Bertalanffy growth model fit to recaptured
humpback chub in the LCR (L. Coggins, GCMRC,
unpublished analyses) was used to predict start and
end size for three subadult size intervals (ages 1-
4). Average water temperature in the LCR was
used to model these fish. Where necessary, fork
lengths (mm) were converted to mass (g) using the
following regressions, which were derived from
field collections of humpback chub (GCMRC, un-
published analyses). The first equation applies to
main-stem Colorado River fish exceeding 150 mm
in length, the second equation to main-stem Col-
orado River fish 30-150 mm in length, and the third
equation to LCR fish 30-150 mm in length.
log ioweight = -5.597 + 3.194(log 10length),
r2 = 0.93;
log,weight = -4.838 + 2.873(log lolength),
r2 = 0.93; and
log ioweight = -4.975 + 2.904(log iolength),
rz = 0.90.