AMER. ZOOL., 23:261-272 (1983)
Models and Evidence for Feeding Control of Energy1
F. REED HAINSWORTH AND LARRY L. WOLF
Department of Biology, Syracuse Unwersity,
Syracuse, New York 13210
SYNOPSIS. The value of optimization theory is to provide falsifiable hypotheses and, when
appropriate, alternative models of resource regulation. A consideration of alternatives
suggests optimal energy regulation through feeding depends on time scale and supplies
of energy relative to demands. Maximization (on-off) control of energy reserves occurs
over short intervals involved in consumption, while proportional control occurs over
longer intervals (between meals) or as a consequence of trade-offs between energy regulation and nutrient or predation constraints. Maximization of rate of net energy gain
occurs most frequently when energy supplies are low relative to demands and when energy
and nutrients are not associated. This may be typical for small endothermic nectar feeders,
while proportional controls are characteristic of feeding behaviors for many other animals.
Controls for regulating energy content must also be affected by external environmental
variation which may require use of "rules of thumb" that approximate the maximum rate
of return.
reproductive success (Pyke et al., 1977;
A general theory has been proposed to Krebs, 1978; Hainsworth and Wolf, 1979;
explain feeding behavior of animals. It is Gass and Montgomerie, 1981; Wolf and
called "optimal foraging theory," and it Hainsworth, 1983). A large and growing
asserts that natural selection has resulted list of experimental studies emphasize the
in the non-random feeding patterns importance of rate of net energy gain maxobserved in animals. What is generally con- imization, including studies of patch use by
sidered to be optimized is some allocation chickadees (Krebs et al., 1974), ovenbirds
of time to feeding such that reproductive (Zach and Falls, 1976), great tits (Cowie,
1977), bees (Waddington and Holden,
output is maximized (Schoener, 1971).
In an early formulation of the theory of 1979), and fishers (Powell, 1979); explofeeding strategies Schoener (1971) speci- ration sampling by great tits (Krebs et al.,
fied two limiting cases of a general model 1978); swimming speed in fish (Ware,
where animals were classified as (1) time 1975); meal size in hummingbirds
minimizers, or (2) energy maximizers. Time (DeBenedictis et al., 1978; Hainsworth,
minimizers are animals whose fitness is 1978) and phantom midges (Giguere,
maximized when time spent feeding is min- 1981); feeding burrow construction in
imized, while energy maximizers are ani- pocket gophers (Vleck, 1981); proboscis
mals whose fitness is maximized when rate structure and function in butterflies (Kingof net energy gain is maximized. These solver and Daniel, 1979); size selection of
distinctions need not be exclusive if max- prey by great tits (Krebs et al., 1977), shore
imizing energy results in minimizing feed- crabs (Elner and Hughes, 1978), blue-gill
ing time; they are exclusive if minimizing sunfish (Werner and Hall, 1974), redshanks
(Goss-Custard, 1977), stoneflies (Malmtime compromises energy returns.
qvistandSjostrom, 1980), wagtails (Davies,
Most subsequent research on optimal 1977), and red-backed salamanders (Jaefeeding tactics has emphasized energy ger and Barnard, 1981), among others.
maximization as an "efficient"' way to cou- Although it is generally recognized that
ple energy resource use to survival and other constraints may influence feeding,
such as nutrient requirements other than
energy (Pulliam, 1975, 1980), develop1
From the Symposium on Optimization of Behavior mental changes (Quinney and Smith, 1980),
presented at the Annual Meeting of the American
and learning requirements (Heinrich el al.,
Society of Zoologists, 27-30 December 1981, at Dal- 1977: Waddington and Holden, 1979), rate
INTRODUCTION
las, Texas.
261
262
F. R. H A I N S W O R I I I AND L. L. WOLK
ON - OFF
PROPORTIONAL
R
Fie. 1. Schematic illustration of three different
models for control of a resource. R is a response, V
is a controlled variable, and \"M, is a set point.
of net energy gain maximization has
emerged as a principle component of feeding behavior optimization.
Maximizing rate of net energy gain during feeding may not apply to all situations.
It is the situations where it does not apply
that can be particularly instructive. As
Maynard Smith (1978) points out, "the role
of optimization theories in biology is not
to demonstrate that organisms optimize:"
rather, its role is to provide falsifiable
hypotheses. When a hypothesis is falsified,
an alternative must be proposed and tested
for \alidity. It is this process that results in
understanding and provides value to the
theories.
Most studies of rate of net energy gain
maximization are concerned with what animals do while thev are engaged in the shortterm search -> ingestion components of
individual feeding bouts. A relatively
neglected aspect of feeding behavior concerns how individual feeding episodes are
organized over longer times. Although
there is little information on the integration of feeding over long periods, studies
ofenergv regulation in hummingbirds suggest alternative models to energv maximization. The alternatives provide general
models for a number of other studies that
indicate the rate of net energy gain maximization hypothesis is falsified.
We will summarize the evidence for
hummingbird energy regulation over different time scales within the context of several alternative models for control of
energy resources, and we then will discuss
the general implications of some alternative models for understanding the organization of feeding behaviors where rate
of net energy gain maximization does not
apply. A conclusion is that alternative
models apply over different time scales with
their relative contributions influenced by
factors determining energy supplies relative to demands as well as nutrient and predation effects for feeding. Additionally,
energy controls apparent where energy
supplies are highly predictable must be
modified to account for variation in energy
availability from prey. We will discuss the
importance of variation after we examine
some evidence for controls obtained from
simplified laboratory experiments.
HUMMINGBIRD FEEDING AND MODELS
FOR ENERGY CONTROL
The hummingbird-flower nectar system
offers a number of advantages to study
feeding patterns. The birds are small endotherms with high per gram rates of energy
use(Lasiewski, 1963: Hainsworth and Wolf,
1970, 1979) producing high frequency
feeding with a dependence on energv for
efficient feeding (Wolf and Hainsworth,
1977). Feeding bouts are observed and
defined easilv: search is initiated when a
bird leaves a perch to visit flowers for nectar, while intervals for assimilation to initiation of a subsequent search are usuallv
spent awav from flowers, mainlv on a perch
(Wolf /'/ «/., 1976: Wolf and Hainsworth,
1977). Considerable information exists on
rates ofenergv expenditure for hummingbirds engaged in different activities (sleeping, perching, Hving) (Hainsworth rl al.,
1977: Fpting, 1980) and on nectar composition and flower characteristics influencing net gains of energv (Hainsworth,
1974: Baker, 1975: Hainsworth and Wolf,
1976: Stiles, 1971): Hainsworth and Wolf,
1979). I hus hummingbird feeding can be
FEEDING CONTROL OF ENERGY
studied under controlled conditions that
involve ecologically relevant features influencing rates of net energy gain.
There are several alternative models for
control of energy resources (Fig. 1). In the
language of systems engineering maximization is "on-ofF' control since the response
(R) of a system is always the same (maximum) when a regulated variable (V) is displaced from a set point (VseI). Two other
models for control of energy content are
proportional control and integral control.
For proportional control a response
depends linearly on the extent of displacement of a regulated variable from a set
point. For integral control the rate of a
response depends on the extent of displacement of a regulated variable from a
set point. When the time period for a
response is standardized, integral control
produces an exponentially increasing
response with an increase in displacement
from a set point (Fig. 1).
Set point is a useful descriptive term to
characterize when responses occur as a
controlled variable changes and does not
imply that a living system possesses a specific comparative mechanism as is the usual
meaning in systems engineering. Simple
homeostatic relationships between several
functions influencing the state of a controlled variable can produce the characteristics of a set point. We use the term as
a useful descriptive feature and do not
imply a specific type of internal comparison.
For the models of energy control the
variable (V) regulated by feeding is stored
energy, and a response (R) is any factor that
will restore stored energy over time to set
point values. Thus a response is anything
influencing rate of net energy gain. By
studying the nature of changes in rate of
net energy gain when stored energy varies
it should be possible to decide which models
characterize the nature of energy controls.
In the classification scheme of Schoener
(1971) on-off or maximization control is
equivalent to energy maximization. Proportional or integral control could be
equivalent to time minimization when
energy maximization is compromised with
263
TABLF 1. T^pes of short-term late of net ?iwig\ gam
maximization studies
1.
2.
3.
4.
5.
6.
Patch exploitation
Speed and pattern of movement
Meal size
Feeding apparatus functions
Item choice
Behavior modes for exploitation
a variable influencing time allocated to
feeding. However, proportional or integral control for energy could also occur
when feeding rate may appear to be maximized due to a variable such as diet
nutrient composition where a compromise
with energy maximization may not involve
feeding time (see below). Thus we view the
alternative control models as potentially
descriptive of a greater variety of possible
feeding responses than distinctions based
only on energy maximization and time
minimization.
Short-term maximization controls
Numerous studies suggest optimal foraging behavior can involve rate of net
energy gain maximization (see above),
although these studies seldom experimentally manipulate the regulated variable,
stored energy. In general, these studies of
on-off control involve short-term search -*
ingestion behaviors. The types of behavior
involved in studies of feeding energy maximization are summarized in Table 1.
The short-term variable most extensively studied in hummingbirds is meal size.
The birds consume average meal sizes less
than the maximum possible in the field and
laboratory (Hainsworth and Wolf, 1972:
Hainsworth, 1977: Wolf and Hainsworth,
1977), and a comparison of observed with
predicted meal sizes (based on several different models) indicated the meals resulted
in maximum rates of net energy gain due
to the effect of the weight of a meal on
energy expenditures (DeBenedictis el al.,
1978; Hainsworth, 1978).
Food choice for hummingbirds also may
involve short-term rate of net energy gain
maximization, although there is less experimental information on this. When hum-
264
F. R. HAINSWORTH AND L. L. WOLF
8
1°
-6
5
10
15
DISTANCE, m
20
Fie. 2. The difference between rate of net energy
gain for hovering and perching behaviors for foraging bouts over different distances. Calculations are
for an 8 g hummingbird assuming a flight speed of 2
m/sec at 85% of the cost of hovering; an ambient
temperature of 20°C and a body temperature of 41 °C
with heat production rates for perching from Hainsworth and Wolf (1972). Total energy intake is fixed
at 15 calories for both behavior modes. The solid line
assumes an intake rate of 15 cal/sec for hovering and
13.6 cal/sec for perching. The dashed line assumes
both these rates are halved.
and we can predict which behavior should
be used based on rate of net energy gain
maximization (Fig. 2). Perching involves
more time for extraction since birds must
land on a perch and orient to a flower
before probing it, but rate of energy
expenditure is lower than for hovering.
Preliminary tests with different artificial
flowers offered individually to hummingbirds equidistant from a perch suggest
hummingbird foraging behavior depends
on factors influencing rates of net energy
gain (Table 2). Hovering is always more
profitable in these experiments, but as the
profitability difference decreases the birds
begin to switch to perching, the less costly
foraging mode. This is contrary to predictions of maximization theory. In an analysis of the very high cost foraging behavior
of burrowing by pocket gophers, Vleck
(1981) has emphasized the importance of
foraging costs when these are high relative
to energy availability. Hummingbird feeding bout behavior appears to reflect the
impact of their foraging costs, and experiments such as these may define their sensitivity to various factors influencing the
total profitability of foraging bouts.
Proportional control between meals
mingbirds have a choice of food from two
feeders with large volumes they select the
more concentrated food even at the
expense of rate of net energy gain maximization (Hainsworth and Wolf, 1976), but
choice of flowers may represent a more
complicated trade-off between volumes and
concentrations. Rate of volume intake from
flowers with small volumes (<50 ^1)
depends on nectar volumes (Hainsworth
and Wolf, 1979), and nectar concentration
may influence volume rate of intake due
to viscosity effects for tongue loading
(Baker, 1975).
We have started to examine some other
short-term feeding bout characteristics of
hummingbirds to see if they fit the maximization model. Pyke (1980, 1981r/) suggested nectar eaters mav vary the mode of
behavior used to extract nectar, either
hovering or perching. Hummingbirds can
use either behavior if perches are available,
To study energy control over daily
periods, we measured rates of net energy
gain for hummingbirds (Eugenes fulgens and
Lampornis clemenciae) over 14 hr days while
we varied stored energy by depriving the
birds of food for 4-5 hr per day for several
days in succession. Rates of net energy gain
were measured each day after return of
food. Time and energy budgets were constructed to estimate expenditures which
were subtracted from energy intakes from
sugar water. Levels of stored energy were
measured from body masses in excess of
7.0 g at the start of days (see Hainsworth
etai, 1981 for further details of methods).
Figure 3 summarizes the results of these
experiments. In general, there was a proportional relationship between daily rate
of net energy gain and the extent of
decrease in stored energ\ from starting
values (right hand points for each line in
Fig. 3). The rate of net energy gain within
da\s is relatively constant for nectar feed-
265
FEEDING CONTROL OF ENERGY
TABLE 2. Measurements of net energy gam rales for hummingbirds exhibiting different behaviois to extract nectar from
individual flowers that differed in profitability within and across behavior modes and the distributions of behai'iors used
for extraction over several bouts offeeding *
Floral condition
Hovering
net cal/sec
Perching
net cal/sec
Bouts hovered
Bouts perched
Volume = 50 ti\
Concentration = 0 5 M
Corolla = 5 mm
Volume = 30 nl
Concentration = 0.5 M
Corolla = 35 mm
Volume = 30 tt\
Concentration = 0.23 M
Corolla = 3D mm
5.60
2.83
1.15
5.03
24
2
2.54
28
3
1.10
10
18
* For each condition travel time to the flower is 2.0 sec and flowers were presented singly with a perch
that could be used for extraction.
ing birds (Wolf and Hainsworth, 1977:
Collins and Morellini, 1979), and there is
some evidence that the daily rate is normally "set" by the extent of decrease in
stored energy overnight (Hainsworth,
1978).
Long-term proportional control has been
observed for energy regulation in other
species. Energy regulation by hibernating
ground squirrels has been described as proportionally controlled with a "sliding set
point" over the hibernating season (Mrosovsky and Fisher, 1970), and laboratory
rats hoard proportionally more food as
their body weight (energy reserves)
decreases (Fantino and Cabanac, 1980).
Also, measurements of time budgets for
Anna's hummingbirds indicate that feeding time decreases in the field as environmental temperature increases suggesting a
proportional adjustment in feeding bouts
as expenditures change (Stiles, 1971).
If energy regulation over relatively long
periods is proportionally controlled, the
slopes and intercepts of the function should
depend on demands for energy resources,
perhaps over a seasonal time scale. Within
the limits for rate of net energy gain either
an increase in slope or an increase in set
point would produce a higher rate of net
energy gain for a given displacement of
energy reserves. Set points and/or slopes
may vary on a seasonal basis as demands
for energy vary for processes such as molt,
migration, or reproduction, but at present
there is little experimental information on
this except for seasonal hibernators (Mrosovsky and Barnes, 1974).
Changes in set points may be expected
to occur in species that normally experience wide variations in levels of energy
reserves. Endotherms of small size have
high per gram demands for energy and
relatively low storage capacities compared
with demands (Calder, 1974: Hainsworth,
1981), and hummingbirds represent an
extreme example of these body size effects.
Also, hummingbirds employ a high energy
cost mode of foraging which can influence
variation in energy reserves depending on
concurrent benefits. Larger animals and/
or animals with less costly foraging behaviors relative to food benefits may be more
"buffered" with lower energy storage variations and may show less variation in energy
reserve set points. A similar effect occurs
in other physiological control systems. For
example, among mammals daily and seasonal torpor occurs only in relatively small
species, and their hypothalamic control
systems show wide variations in set points
compared with larger, non-hibernating
species (Heller el al., 1978).
WHY DIFFERENT CONTROLS?
Why do control types operate over different time scales, and how general should
this organization be among animals? An
animal that does not maximize on the shortterm cannot maximize over a longer period.
The question then becomes what leads to
a shift to proportional controls over longer
periods and what sets the periods?
A proportional control for energy regulation suggests some form of time minimization rather than energy maximiza-
266
F. R. HAINSWORTH AND L. L. WOLF
14
17
20
23
26
ENERGY RESERVES, Kcol
Fie 3. Average daily rates of net energy gain for
Eugenesfulgens (solid points), and Lamporms clemenaae
(open points) as a function of energy reserves. Rates
of net energy gain were measured from time and
energy budgets while energy reserves were measured
at the start of days from body masses in excess of 7.0
g assuming 9,500 cal/g (from Hainsworth et al, 1981).
tion. Over daily periods hummingbirds
adjust the frequency of their feeding and
rates of energy expenditure between meals
so energy maximization occurs only when
energy reserves have been severely
depleted (Fig. 3; Hainsworth et al., 1981).
The lack of energy maximization at times
other than during foraging bouts suggests
other factors compromise feeding time. For
example, if predation risk, was related to
feeding frequency, the latter may be
adjusted within the constraint of risk of
starvation. Also, rate of energy expenditure between meals for such functions as
territorial defense may be traded-off in such
a way that between meal activity changes
as energy reserves change. Under these
conditions feeding time would be minimized and time for other activities maximized when energy reserves were high
while energy maximization would be
observed when energy reserves were low.
Again, shifts between these would be more
likely to be observed in relatively small
species such as hummingbirds that experience greater variations in energy reserves
compared with demands.
GFNF.RALITV OF CONTROLS
The effects of body si/e and/or mode of
foraging on energ) reser\e fluctuations
may make hummingbirds a special case
compared with many larger species. Also,
the pattern of energy maximization for
nectar-feeding animals on the short-term
may not be typical of many consumer
organisms. The food source is a simple
sugar water solution usually without components influencing nutrient or toxin
intake. Also, nectar feeders generally are
considered not highly subject to risks from
predators while they forage. There is evidence that constraints both from nutrient
requirements and from predation can
change the control system for energy regulation on a short-term from energy maximization to proportional control (see
below).
The most direct evidence for a compromise with predation comes from experiments where energy reserves were varied
to yield different degrees of "hunger" in
predators. Sticklebacks varied the density
of Daphnin swarms they attacked as hunger
varied (Millinski and Heller, 1978).
Although they achieve a higher capture
rate by attacking high density swarms, they
prefer to do so only when energy reserves
are low. When they attack high density
swarms, time to attend to predator attacks
is reduced due to the "confusion" effect of
attending to prey capture. The changing
preference with hunger level indicates the
possibility for a trade-off between predation risk and starvation risk as reflected in
levels of energy reserves. Also, as distance
to cover increases for Yellow-eyed Juncos
(Junco phaeonotus) in feeding flocks, time
spent scanning for predators increases
(Caraco et al., 1980«). Seed eating finches
in winter must spend a large proportion of
a day feeding to meet energ) requirements
(Pulliam, 1980) so most of a day is spent
in search -» ingestion, perhaps increasing
risk from predation and necessitating a
proportional trade-off with behaviors to
reduce predation risks. In addition, exploitation of a resource requiring relatively
high commitments of time in activities
above resting metabolic rates could influence energy reserve variations. Maximization might be expected here but may have
to be compromised with other risks.
Consumers face the risk of starvation if
they cannot athiese a balanced daiK energ\
budget. Under this circumstance there is
FEEDING CONTROL OF ENERGY
evidence that some foragers may adjust
search -> ingestion behavior to respond to
the variance in food characteristics rather
thanjustmean values (Caraco etal., 19806).
Most models of optimal foraging are deterministic and depend only on means, but
models of feeding involving variation suggest predators should respond to the stochastic nature of resources in some cases.
This has been called "risk-sensitive" foraging. By favoring risk a forager would
accept the chance of doing poorly to capitalize on the chance of obtaining relatively
large rewards from higher variation. This
has been shown to occur in Juncos on a
negative daily energy budget (Caraco et ai,
19806). A risk-averse forager would avoid
food sources with high variation even when
the average reward was the same. Juncos
exhibited this behavior when they were not
starved and when feeding rates were high
(Caraco et nl., 19806). Recent experiments
with Dark-eyed Juncos (Junco hyemahs)
indicate preference for a variable reward
is strong with a negative daily energy budget, intermediate with a balanced daily
energy budget, and weak or absent with a
positive daily energy budget (Caraco,
1981). This indicates a proportional
adjustment in risk-sensitive foraging
behavior as energy reserves vary from set
points.
Finally, many foragers may exhibit feeding behaviors governed by nutrient constraints other than energy. Pulliam (1975)
indicated that non-energy nutrient
requirements could lead to proportional
trade-offs between energy and nutrient
values in diet selection, and field studies of
diet selection in Chipping Sparrows support the idea of an interaction between
energy and nutritional components for diet
selection (Pulliam, 1980). Analysis of the
food of wolf spiders relative to energy and
nutritional components suggests these
predators may optimize the composition of
dietary amino acids (Greenstone, 1979).
Many predators may operate under constraints requiring some trade-off between
energy and nutritional requirements, particularly those with diverse diets.
Where specific nutrients are involved
short-term behaviors may suggest maxi-
267
mization control with respect to the
nutrients. However, if nutrient and energy
content are correlated, behaviors could be
misinterpreted without independent information on the physiological requirements
of the predators. Although maximization
might appear to occur for either component based just on feeding rates, a proportional model for any one component could
be more appropriate. Problems of this sort
will be minimized when predators exhibit
selection of a wide variety of food items
where nutrients and energy are likely to
be dissociated.
The control of energy resources for any
animal is likely to involve both on-off and
proportional controls. On-off controls
occur over periods where interactions with
other systems either are not possible or are
not important for survival and reproductive success. For example, in Holling's
(1966) experiments with preying mantids,
certain very short-term behaviors were onoff in nature and showed no variation with
hunger levels. These included strike success and the time to consume one fly (Holling, 1966). The strike of a mantid is
thought to be so rapid that control during
the strike is not possible, although the aiming mechanism involves feedback between
visual and neck proprioceptive input (Mittelstaedt, 1962). Many components of
"reflexive" behaviors of feeding animals
may be modeled best in terms of rate of
net energy gain maximization. However,
the varied constraints that may influence
survival and reproduction that should be
integrated with feeding behaviors may lead
to a prevalence of proportional controls at
intervals beyond immediate consumption.
We summarize a number of variables that
may lead to a proportional trade-off in
energy regulation in Table 3. In general,
food resources, body size effects, and relative costs for feeding can influence the
number of feeding episodes required to
meet daily demands for energy. If an animal must feed continuously (a very small
endotherm, a costly foraging mode, and/
or low quality food) it should exhibit maximization control because energy supplies
are low relative to demands. If an animal
can achieve daily energy requirements with
268
F. R. HAINSWORTH AND L. L. WOLF
TABLE 3. Some major variables influencing maximiza- ity, and total flower production {e.g., Cortion versus proportional controls for energy regulation. bet el al., 1979). In addition to these genetic
1. Body size effects on energy reserve variations with
maximization more prevalent in small endotherms.
2. Foraging cost effects on energy reserve variations
with maximization more prevalent with high costs
relative to energy supplies.
3. Resource effects on energy reserve variations with
maximization more prevalent with low quality (or
variable) food.
4. Predatwn effects with maximization compromised
with risk of death.
5. Nutnent effects with energy maximization compromised with nutritional composition of diets.
less frequent and/or smaller feedings,
maximization control would represent a
lower proportion of total activity and proportional controls should become more
evident. Whether particular controls are
observed with respect to energy, however,
can depend on predation or nutrient effects
that may also influence survival and reproductive success.
CONTROLS WITH ENVIRONMENTAL
VARIATION
These control systems apparently used
by animals to regulate their internal energy
stores require accurate information about
the quality of the environment. The combination of "infinite-supply" feeders in a
laboratory as an energy source and precise
measures of energy reserves through internal sensing provides this information.
However, the reliability of information
available to animals about energy distribution and abundance is reduced in many
natural environments. The "noise" in the
information probably increases as we progress from the meal size and foraging efficiency decisions made in the context of the
internal environment to processing information from the external environment.
Uncertainty in information for nectarfeeders is partly a direct consequence of
genetic variation among and within plant
species in nectar production rates and sugar
concentrations (e.g.. Wolf et al., 1976).
These variables also depend on local, environmentalh determined differences among
plants based on factors such as temperature, relati\e humidiu, moisture availabil-
and environmental influences on the
energy supplies, foraging by nectarivores
creates an ever-changing pattern of energy
distribution. The location and boundaries
of patches of high and low quality change
as a direct result of the forager's behavior
(Zimmerman, 1981; Wolff/ al., in preparation). Relatively few point sources of
energy might decrease the uncertainty,
while multiple birds using one area generally will increase the uncertainty for an
individual.
The value of local information for making decisions about subsequent foraging
locations decreases as the uncertainty of
the pattern of nectar availability increases.
However, there is little published information on patterns of nectar availability in
natural situations. Focal plants of Delphinium nelsoni visited by bumblebees (Bombus
spp.) tended to have nearest neighbors of
a similar category of nectar availability (with
and without nectar) (Pleasants and Zimmerman, 1979). The pattern, however, can
change appreciably even within a day,
probably due to foraging by the bees (Zimmerman, 1981). Year-to-year differences
in nearest neighbor correlations of nectar
volumes have been reported for both beevisited and hummingbird-visited flowers
(Hodges, 1981: Wolf and Hainsworth,
1983). So far there is little information on
the spatial or temporal scale of these
between-inflorescence patterns.
The most detailed information about
patterns of nectar availability is within
inflorescences. Correlations among flowers have been reported for both bee- and
bird-visited flowers (Gill and Wolf, 1977;
Pyke, 19786: Hodges, 1981). The withinplant information seems to be consistent
through time in D. nelsoni. although the
absolute values of nectar availability change
(Hodges, 1981). Thus, nectarivores appear
to have some consistent information about
the quality of specific inflorescences once
visited, but information between inflorescences varies spatially and temporally.
Birds have at least two ways to improve
the information content of their foraging
habitat. First, individuals could reuse continualK the same subset of flowers and
269
FEEDING CONTROL OF ENERGY
remember the locations of recently visited
flowers. In this way, they could forage preferentially at flowers that have the most nectar. Additionally, territorial behavior could
reduce variations in patterns of nectar
availability that would be produced by other
foragers. Several studies have indicated that
territorial individuals can preferentially
visit least recently visited flowers (Gill and
Wolf, 1977; Kamil, 1978; Wolf and Hainsworth, 1983), but there is little information
on the mechanism for this. It may depend
on resource characteristics. A "memory"
mechanism may work when there are relatively few points to "remember."
A second way to improve the foraging
habitat is to adjust behavior within bouts.
From our work in Colorado it appears that
the hummingbirds generally have a very
simple rule that says "forage among adjacent clumps unless the inflorescence is bad,
then go farther away (Wolf and Hainsworth, 1983; see also Gass and Montgomerie, 1981). The nonrandom character of
the foraging bouts appears to be generated
by the location of starts of the foraging
bouts (Wolf and Hainsworth, 1983).
Similar, simple "rules of thumb" have
been proposed to explain the possible
responses of other foraging organisms to
variations in environmental information
(Pyke, 19786, 19816; Cowie and Krebs,
1979). These simple rules are unlikely to
be as accurate in their prediction of the
immediate outcome of a behavior as more
situation specific responses would be. So,
to use a rule of thumb, the organisms must
accept a tradeoff from the maximum possible predictability of future conditions. A
rule of thumb then becomes an optimization process itself (Iwasa et al., 1981).
Two types of errors are possible with a
rule of thumb—staying too long in a bad
location and missing a good location. The
type of rule that evolves should depend on
the relative importance of the two error
types. The importance will depend partly
on where on the value curve an organism
finds itself while foraging (Fig. 4). In general, for nectarivores the value curve for
single flowers negatively accelerates toward
an asymptotic net rate of return with
increasing nectar volumes. The position of
the curve will differ among plants and for-
Mocleanio globro
s
8
2
3
4
5
100
TIME FEEDING (sec)
Maclean ia
Fuchsia
0
94
302
510
719
92 7
2072
0
24
74
124
174
224
4974
INTAKE[)i\ /flower)
Fie. 4. Relationship between energetic benefits and
the nectar volume per flower on the time spent at a
flower. Data are for Panterpe insignis feeding at two
flower species. Benefits assume 100% assimilation and
costs only involve extracting energy from the flowers
(from Wolf, 1978).
ager species combinations (Fig. 4; Wolf et
al. 1976; Wolf, 1978; Gill and Wolf, 1979).
The response to the possible errors needs
to include rules for at least two possible
levels of action: (1) how to assess good and
bad locations; and (2) what to do after the
assessment is made. The rules generally will
take the form of how long to stay at a location (e.g., Charnov, 1976; Iwasa etai, 1981)
and the paths of foraging after leaving the
location (e.g., Cody, 1971; Pyke, 1978a).
Numerous, often complicated, calculations
have been proposed for these rules, mostly
in the context of perfect information or
infinite memory capabilities.
The importance of errors also depends
on the proportion of errors likely to occur.
Errors of omission of good inflorescences
can be avoided by making the rule of thumb
more stringent in high quality environments, but that must be balanced against
the cost of continuing to visit bad inflorescences. The relative costs and rewards of
shifts in the rule will depend on the within
versus between inflorescence variance, the
270
F. R. HAINSWORTH AND L. L. WOLF
pattern of that variation in space, and also
on the costs of moving between flowers
within and between inflorescences.
This suggests that a simple rule must shift
somewhat with changing reward structure
to maximize upside potential and to minimize downside risk at low reward levels.
At the same time, the rule must be able to
minimize downside risk with little attention to upside potential at high reward
levels. Sunbirds in East Africa foraging on
Leonotis nepetifolia show a shift from quick
assessment of multi-flowered inflorescences at high reward levels to nearly complete lack of assessment at low reward levels
(Gill and Wolf, 1977). The assessment
appeared to be based on encountering one
or more empty flowers in the initial feeding
attempts on the inflorescence.
Two major modifications would have to
be imposed on the value curve (Fig. 4) to
account for spatial variation in quality. If
the cost in time and energy of moving
between inflorescences is higher than the
cost of moving between flowers within an
inflorescence the value curves will shift with
foraging movements that are made. In
addition, the certainty of the position on
the curve of possible future foraging locations will differ. This suggests a possible
hierarchy of rules of thumb for the several
spatial scales encountered while foraging
(Gass and Montgomerie, 1981; Wolf and
Hainsworth, 1983). A rule used at one scale
might not apply to another. However, it
seems more likely the birds will use a general rule that will apply at more than one
spatial scale. For example, the simple rule
of thumb saying "visit nearby patches if
sufficiently rewarded" can be used within
inflorescences for flower visits, between
inflorescences within clumps, and between
clumps.
This means the birds must begin to integrate information about variance patterns
and average levels of nectar availability to
arrive at the appropriate expression of the
rule of thumb. The ability of the birds to
integrate this environmental information
will depend on their memon capacity and
the utility of the information that is
retained. This also is a tradeoff between
specificit) and generality (Wolf and Hainsworth, 1983). The more specific the infor-
mation the more predictive it is for a particular situation, but the more that must
be integrated in a complex environment.
The optimality problem will influence the
amount and type of information used to
assess inflorescence quality.
The occurrence of mistakes in foraging
using rules of thumb may be valuable in
acquiring information about changing patterns of nectar availability through time.
Thus, rules of thumb necessarily include
sampling that can be viewed as an integral
part of the overall foraging effort of the
organism in a variable environment (Krebs
el al. 1977, 1978: Hodges, 1981). The
occurrence and extent of sampling itself is
an optimality problem within the confines
of a long term foraging strategy associated
with resource variation in both space and
time (Krebs et al., 1978: Green, 1980).
Not surprisingly, we are forced to conclude that as the complexity and variation
in the environment increases with respect
to availability of prey, the ability of the
organism to maximize its rate of net energy
intake in the short term is compromised.
As we partition the influence on foragers
in terms of information processing it
becomes obvious that we are adding layers
of optimality problems each of which has
a decremental effect on maximizing the rate
of energy intake during a foraging bout.
The form and degree of these compromises reflect the underlying optimality
problems associated with specificity I'ersus
generality of rules for responding to local
conditions. Until we have good information on the position of the organism on its
value curve and the influence of the errors
on the good and bad side of the average
energy accumulation rate, it will be difficult to predict the relation between specificity of information, error rates, and net
benefits. The errors associated with staying
in a bad patch because of faulty early information also can be viewed as sampling by
the forager. The value of sampling should
vary with position on the value curve, the
long term patterns of autocorrelation
within patches, and the magnitude of variance in reward le\els. We conclude that
main foragers probabh are like mam subordinates in social systems in that the\ are
"making the best of a bad job."
FEEDING CONTROL OF ENERGY
ACKNOWLEDGMENTS
The authors thank Terre Mercier, Mark
Tardiff, Arthur Gurevitch, and David Drone) for their assistance. This research was
supported by the National Science Foundation and Syracuse University.
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