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<br />HUMPBACK CHUB BIOENERGETICS
<br />Alternatives to minimize or remove threats to
<br />humpback chub recovery have been discussed and
<br />planned for over a decade (USFWS 1990). Re-
<br />moval of potential predators, competitors, or both
<br />is a management action that is currently underway.
<br />Rainbow trout prey on juvenile and subadult
<br />humpback chub (Valdez and Ryel 1995) and may
<br />be an important source of mortality. In 2003, over
<br />6,000 rainbow trout were removed from the Col-
<br />orado River in the reaches above and below the
<br />confluence of the Little Colorado River, a major
<br />spawning site and nursery habitat for this popu-
<br />lation of humpback chub. This removal program
<br />reduced the local trout population by about 90%
<br />(Grand Canyon Monitoring and Research Center,
<br />U.S. Geological Survey [GCMRC], unpublished).
<br />Installation of a temperature control device
<br />(TCD) at Glen Canyon Dam is another manage-
<br />ment action being discussed. Hypolimnetic water
<br />from Glen Canyon Dam is released into the lower
<br />Colorado River causing temperatures to be 9-12°C
<br />year-round; the historic temperature range is about
<br />2-26°C (Kaeding and Zimmerman 1983; Stevens
<br />et al. 1997). Modifications to Glen Canyon Dam
<br />being considered would enable water managers to
<br />release warmer surface water into the lower Col-
<br />orado River during part of the year (USDI 1999).
<br />Warmwater releases would partially simulate the
<br />historic temperature patterns and would presum-
<br />ably improve the growth rates of humpback chub.
<br />Warmer water would also minimize temperature
<br />shock for juvenile humpback chub entering the
<br />Colorado River from warmwater tributaries, thus
<br />increasing their rate of survival. However, there
<br />has also been speculation that warmer water could
<br />increase competition, predation mortality, or both
<br />for humpback chub by altering the feeding patterns
<br />or increasing the growth rates of rainbow or brown
<br />trout (USDI 1999; Robinson and Childs 2001).
<br />Predictive tools are needed to assist managers
<br />and researchers in evaluating the potential out-
<br />comes of actions such as predator removal and
<br />temperature modifications in large river systems.
<br />Models that integrate physical factors such as tem-
<br />perature and biological processes such as feeding
<br />rates should be especially useful, allowing man-
<br />agers to run divergent scenarios and eliminate ac-
<br />tions with little chance of success. We developed
<br />a bioenergetics model for humpback chub and ap-
<br />plied the model to simulate how water temperature
<br />changes may influence the growth rate and food
<br />requirements of humpback chub. Results are dis-
<br />cussed in the context of management options,
<br />961
<br />needs for specific data to improve the model, and
<br />data needed to test hypotheses in the field.
<br />Methods
<br />Humpback chub model development and parameter
<br />estimation.-The general bioenergetics model is
<br />G = C - (R + SDA + F + E),
<br />where G is growth, C is consumption, R is res-
<br />piration, SDA is specific dynamic action, F is ex-
<br />cretion, and E is egestion (Jobling 1994; Hanson
<br />et al. 1997). Consumption was modeled as
<br />C = Cm.-p'.l7),
<br />where Cmax is the maximum rate of food intake for
<br />an individual of a given size, p is a proportionality
<br />constant that scales consumption according to food
<br />availability, and f(T) is a temperature dependence
<br />function. The maximum rate of food intake, C., is
<br />an allometric function of fish mass W (g), namely,
<br />Cm. = CA • WcB,
<br />where CA and CB are fit parameters. Respiration
<br />is modeled as
<br />R = (RA • W-) • f(T) • ACT,
<br />where ACT is a multiplier for fish activity and RA
<br />and RB are allometrically fit parameters. We used
<br />the warmwater form for the temperature (T) de-
<br />pendence of C and R (Kitchell et al. 1977; equation
<br />(2) in Hanson et al. 1997), which allows specifi-
<br />cation of optimal (CTO, RTO) and maximal (CTM,
<br />RTM) temperatures and includes a measure similar
<br />to Q10, the factor by which a physiological rate
<br />increases with a 10°C increase, that approximates
<br />the rate at which the function increases over rel-
<br />atively low water temperatures (CQ, RQ). For C,
<br />the temperature function is
<br />f(T) = VX.e[x•0-hl
<br />where
<br />V = (CTM - T)/(CTM - CTO);
<br />X = {Z2•[1 + (1 + 40/x)0.5]21/400,
<br />Z = log e(CQ) • (CTM - CTO), and
<br />Y = log,(CQ) • (CTM - CTO + 2).
<br />The respiration temperature function has the
<br />same form, but CTM, CTO, and CQ are replaced
<br />by RTM, RTO, and RQ, respectively. These tem-
<br />perature-dependence equations have been used to
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