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Behavioral Ecology Vol. 13 No. 4: 571-574
© 2002 International Society for Behavioral Ecology
Efficiency as a foraging currency in animals attaining a gain below the energetic ceiling
Department of Plant-Animal Interactions, Netherlands Institute of Ecology (NIOO-KNAW), PO Box 1299, NL-3600 BG Maarssen, Netherlands
Address correspondence to B.A. Nolet. E-mail: nolet{at}cl.nioo.knaw.nl .
Received 27 April 2001; revised 28 November 2001; accepted 18 December 2001.
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONDISCUSSIONAPPENDIXREFERENCES |
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Previous research has found that efficiency, or, more precisely, the foraging gain ratio (FGR), is a valid currency in foraging theory when (1) there is a limit to the energy that can be assimilated by the forager and (2) a forager is trying to meet an energy requirement. The FGR is b/ (c — cr), where b is the rate of metabolizable energy intake, and c and cr are the rates of energy expenditure while foraging and resting, respectively. Here I show that, when energy expenditure has a cost besides energy, animals should also choose the option with the highest FGR when they are aiming at a given positive daily gain. The next question is which gain they should aim for? Researchers have shown that observed intake levels of growing ruminants are close to the levels predicted by maximization of the efficiency of oxygen utilization. This currency can be approximated by (B — C + Cr) / C, where B is the daily metabolizable energy intake, and C and Cr are the total and basal daily energy expenditures, respectively. By simulating growth at different intake levels, I found that mass-specific oxygen consumption rate is indeed minimal at the observed intake levels. This is the first study in which these efficiency measures (FGR and the efficiency of oxygen utilization) are combined.
Key words: energy balance, feed intake regulation, foraging gain ratio, growth, optimal foraging theory, oxygen utilization.
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONDISCUSSIONAPPENDIXREFERENCES |
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In classical optimal foraging models, foragers are assumed to maximize their long-term rate of net energy intake (or gain). Gain maximization was taken to correlate with fitness. Early in the development of optimal foraging theory, efficiency (i.e., the ratio of benefits to costs) was rejected as a general currency because it fails to distinguish between trivial benefits obtained at small cost and more substantial benefits obtained at larger cost (Stephens and Krebs, 1986
).
More recently, however, a number of empirical studies have recorded behavior
that is consistent with the predictions of efficiency maximization and that is
divergent from the predictions of rate maximization
(Houston, 1995;
Schmid-Hempel et al., 1985;
Ydenberg, 1998;
Ydenberg and Hurd, 1998;
Ydenberg et al., 1994). These
findings renewed the interest in efficiency as a valid optimal foraging
currency. Now there is a synthetic body of theory predicting under what
conditions a form of efficiency rather than rate should be maximized. It
proved to be useful to distinguish two foraging situations, feeding and
provisioning, the latter consisting of food delivery (most often to offspring)
and self-feeding. The empirical evidence for efficiency maximization is
largely restricted to provisioning situations
(Ydenberg, 1998).
I restricted the present study to feeding situations. Also in this case,
efficiency maximization is predicted under certain conditions. First, when
there is a limit to the energy that can be assimilated, foragers should choose
the foraging option that maximizes a form of efficiency because, by doing so,
they maximize their daily energy gain. This efficiency currency is the
foraging gain ratio (FGR), defined as b/ (c —
cr), where b is the rate of
metabolizable energy intake, and c and
cr are the rates of energy expenditure while
foraging and resting, respectively
(Hedenström and Alerstam,
1995; McNamara and Houston,
1997). Second, when metabolic rate has a cost besides energy, the
option with the highest FGR should also be chosen if the forager is merely
trying to meet an energy requirement
(Hedenström and Alerstam,
1995).
In this study I concentrated on the conditions under which efficiency
maximization is predicted for growing animals (i.e., animals that attain, on
average, a positive gain), but whose daily intake is not restricted by an
energetic ceiling such as digestive capacity. I tackled this problem in two
steps: first I investigated which foraging tactic is optimal, and then I
investigated the optimal gain, given the foraging tactic. Tolkamp and
Ketelaars (1992) argued that
growing ruminants opt for a gain that maximizes a form of efficiency. Their
currency, the efficiency of oxygen utilization, has percolated in the
handbooks of animal production science (e.g.,
National Research Council,
2000), but it has gone hitherto virtually unnoticed in the
ecological literature. To my knowledge, this is the first attempt to link the
foraging gain ratio and this alternative efficiency currency.
Meeting an energy requirement
When energy intake is limited, animals are predicted to shift from rate
maximization to FGR maximization
(Hedenström and Alerstam,
1995; Ydenberg et al.,
1994). Energy limits primarily apply to conditions that are
energetically demanding, and reaching these limits—if ever
(Winter, 1998)—may be
confined to the particular phases of the year, such as the reproductive season
(Drent and Daan, 1980;
Kirkwood, 1983;
Weiner, 1992). Because of a
possible conflict with raising offspring at better times of the year, animals
may not operate near their energetic limits at other times of the year. At
those times, the optimal behavior may be to balance the energy budget.
Many life history features are hard to explain without invoking a trade-off
between energy expenditure and condition
(McNamara and Houston, 1996).
A decrease in immune responsiveness at high working loads has been shown
experimentally (Deerenberg et al.,
1997). There is also empirical support for the idea that animals
should expend energy parsimoniously to avoid compromising their survival
(Daan et al., 1996;
Schmid-Hempel and Wolf,
1988).
The argument that animals that are spending energy parsimoniously and are
merely trying to meet their energy requirements should also maximize the FGR
goes as follows (see also Hedenström
and Alerstam, 1995). Let the daily gain, G, be:
 |
;
Kruuk, 1995):
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 | (1) |
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A good example of foragers minimizing their energy expenditure while
maintaining their energy balance are kestrels (Falco tinnunculus) in
winter (Masman et al., 1988).
These birds have two modes of foraging: hunting while in flight or sallying
forth from a perch. Flight-hunting is costly, whereas perch-hunting is
inexpensive. Birds could satisfy their daily energy needs by 2.0 h/day of
flight-hunting. In reality, kestrels flight-hunt only 1.1 h/day and spend 4.6
h/day perch-hunting. Because of a restricted day length (10.4 h/day), the
birds cannot maintain energy balance by exclusively perch-hunting, and they
would be required to flight-hunt for at least 0.7 h/day. The observed behavior
is thus close to the energy minimization option. The FGR of perch-hunting
(+
, since Masman et al.
[1988] assumed that the energy
costs for resting and perch-hunting were the same) is indeed greater than that
of flight-hunting (2.9). The efficiency (b/c) is 2.0 and 2.5 for
perch-hunting and flight-hunting, respectively, so if the birds had based
their decision on efficiency, they would never have perch-hunted.
Growth
For growing animals, meeting their energy requirement does not suffice
because they have to attain a positive energy balance. If an animal selects a
given positive gain, this can be expressed as a multiple, g, of the
daily resting costs, Tcr. The daily gain,
G, is thus:
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The next question is which daily gain to choose. Many authors have taken
the mechanistic view that voluntary daily intake is maximized within the
limits set by physical constraints, especially in ruminants
(Bergman et al., 2001;
Ingvartsen, 1994, and
references therein). Analyzing a huge database, Ketelaars and Tolkamp
(1992) found no evidence for
the predicted ceiling in digestible organic matter intake at the high end of
organic matter digestibilities and hence questioned this view. Instead,
Tolkamp and Ketelaars (1992)
introduced the concept of efficiency of oxygen utilization to explain the
voluntary daily intake of growing ruminants. They argued for the primacy of
efficiency of oxygen utilization because oxygen consumption damages cells
through the release of free radicals, having a cumulative effect.
Tolkamp and Ketelaars' model is based on the well-known differences in
efficiencies of utilization of metabolizable energy below and above
maintenance intake levels, both of which are in turn related to the
metabolizability of the food (see Appendix). The differences in these
efficiencies are presumably caused by differences in the biological
efficiencies of catabolism and anabolism. Because it is unlikely that the
animal shifts abruptly from catabolism below maintenance to anabolism above
maintenance, the efficiency of utilization of metabolizable energy can be
envisaged as gradually changing with daily metabolizable energy intake
(B) (Agricultural Research
Council, 1980). As a result, the heat increment of feeding (i.e.,
the heat produced in excess of the basal level after the ingestion of food) is
modeled to increase gradually with B. Hence, in this model the total
daily energy expenditure, C, is a function of B
(Figure 1a).
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I have derived various optima from this function
(Figure 1b). In laboratory
ruminants, the heat increment of feeding constitutes all foraging costs and
can thus be written as C — Cr.
Tolkamp and Ketelaars (1992)
showed that the observed voluntary daily metabolizable energy intake of
ruminants is near the point Ohif, where the net energy intake per
energy expended is highest; in other words, where (B —
C + Cr) / C is maximal
(Figure 1b). This ratio is a
close approximation of their efficiency of oxygen utilization (the net energy
intake per oxygen consumed). As acknowledged by Tolkamp and Ketelaars
(1992), a distinction between
predictions based on efficiency of the utilization of energy or oxygen is in
practice not possible.
Tolkamp and Ketelaars
(1992) did not, however,
provide theoretical evidence whether maximization of this form of efficiency
is indeed optimal in the sense that it would result in minimal oxygen exposure
in the cells. I checked this by simulating the growth of sheep with an initial
mass, M0, of 30 kg to a mature mass of 130 kg and
calculating the average mass-specific oxygen consumption rate,
VO2, over a certain time period using the same
assumptions and parameter values as Tolkamp and Ketelaars
(1992). The sheep chose a
daily voluntary intake during the growing phase, and the growth rate was
directly proportional to the corresponding G. Thus,
Mt = M0 + pGt (if
Mt < 130) or Mt =
130 (Figure 2a), where
t is time and p is a conversion factor to transform retained
energy into body mass. I implicitly included the constant p in
t by using an arbitrary time scale. Once the animals reached their
mature mass, their daily voluntary intake was modeled to drop to the
maintenance level.
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At high intake levels (Onet and Oeff), the mass-specific VO2 was calculated to be high initially but to fall abruptly as the mature weight was reached (Figure 2b). At low intake levels (Ohif and Obal+), the mass-specific VO2 was never very high, but it remained at relatively high levels because of the extended period of growth (Figure 2b). So, when the mass-specific VO2 was averaged over the period of growth (varying from t = 0 to 100 for Onet to t = 0 to 1694 for Obal+), it was, on average, the lowest at intake levels just above maintenance level (Figure 3a). The picture was rather different when the mass-specific VO2 was averaged over the whole time period (until t = 1694 when all sheep had reached mature mass). In this case, it was lowest near the observed intake levels (Figure 3b).
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONDISCUSSIONAPPENDIXREFERENCES |
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In Tolkamp and Ketelaars' model, the rate b is constant, whereas c is monotonically decreasing with the amount eaten. Hence, FGR is maximal at zero intake, which obviously cannot be optimal (Figure 1b). The efficiency of oxygen utilization, on the other hand, seems to predict the observed intake levels well. I evaluated the effect of the maximization of the efficiency of oxygen utilization by calculating mass-specific oxygen consumption rates because the damage by oxygen is relevant at the scale of the cell. As I have shown here, maximization of the efficiency of oxygen utilization indeed minimizes the long-term, mass-specific Vo2. The approximation of this efficiency can be considered another type of foraging gain ratio: (benefits—foraging costs) / total costs. It should be noted that these efficiency currencies are different by nature because the FGR deals with instantaneous rates, whereas the efficiency of oxygen utilization deals with daily rates.
Tolkamp and Ketelaars' concept has been critized on several grounds
(Emmans and Kyriazakis, 1995).
The two most important objections are (1) an intake level greater than the
voluntary daily intake should never be observed, and (2) the optimal voluntary
daily intake expressed as a multiple of basal metabolic rate is not modeled to
change with maturity, which is not in agreement with the observation that
ruminants do not grow throughout their life spans. A more thorough analysis
should take into account that the optimal daily voluntary intake scaled to
basal metabolic rate decreases gradually rather than abruptly during growth
(Ketelaars and Tolkamp, 1996).
However, this is at odds with the observation that the efficiencies of
utilization of metabolizable energy do not seem to change with maturity level
(Emmans and Kyriazakis, 1995).
This inconsistency is not easily solved. Furthermore, the sheep used in the
work of Tolkamp and Ketelaars
(1992) were fed ad libitum but
did not have a free diet choice, and they were kept in isolation in a
hazard-free environment. The sheep therefore did not experience conditions
that may affect the foraging behavior of wild ruminants. The tactic used by
wild ruminants (and other animals) is probably partly determined by factors
other than energy, such as predation risk, social interactions, and insect
harassment (Bergman et al.,
2001). Despite these limitations, the model clearly deserves
further testing, particularly in nonruminants in which foraging costs are not
largely represented by the heat increment of feeding.
A promising recent approach in animal ecology is the use of state-dependent
dynamic optimization models that take into account that energy expenditure is
incurring a cost to the animal by, for example, decreasing its condition
(Houston and McNamara, 1999).
In such a modeling framework, variables more directly related to fitness (such
as lifetime reproductive success) can be used as the currency, and the optimal
daily energy gain can then be derived under various scenarios.
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APPENDIX |
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TOPABSTRACTINTRODUCTIONDISCUSSIONAPPENDIXREFERENCES |
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The efficiency of metabolizable energy utilization is higher at or below maintenance (km) than above maintenance (kg), and is further dependent on the metabolizability, q, of the feed as km = 0.56 + 0.207 q, and kg = 1.32 q - 0.318 (Agricultural Research Council, 1980
). The net energy intake (NEI) is the metabolizable energy
intake, B, minus the heat increment of feeding, and can be calculated
as (Tolkamp and Ketelaars,
1992)
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), where M is body mass in kilograms. The
efficiency of oxygen utilization is defined as NEI divided by the total oxygen
consumption. Total oxygen consumption can be calculated from total energy
expenditure (C' = 1 + B' — NEI')
using a linear decrease from 50.76 to 46.51 l O2/MJ when NEI'
increases from 0 (i.e., a fasting animal) to 2.0 (i.e., an animal that
deposits large amounts of fat). |
ACKNOWLEDGEMENTS |
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I thank Maaike de Heij, John Fryxell, Marcel Klaassen, Miguel Rodríguez-Gironés, Bert Tolkamp, and two anonymous referees for valuable discussions on this subject and for comments on the paper. Special thanks go to John Fryxell for hosting my sabbatical at the Unversity of Guelph. This is publication 2885 of the Netherlands Institute of Ecology.
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