Anita. Behav., 1990,39, 338-345
Risk-sensitivity: ambient temperature affects foraging choice
T H O M A S C A R A C O , W O L F U. B L A N C K E N H O R N , G I N A M. G R E G O R Y ,
J O N A T H A N A. N E W M A N , G R E G G M. R E C E R & S U S A N M. Z W I C K E R
Behavioral Ecology Group, Department of Biological Sciences, State University of New York, Albany,
NY12222, U.S.A.
Abstract. Short-term physiological requirements strongly constrain some foragers. During the limited
time available for foraging, they must consume sufficient food to meet all energetic expenditures for 24 h.
Models for risk-sensitive decision-making predict that such a forager should be risk-averse toward reward
variance when the animal expects to meet its requirement, and should be risk-prone toward reward
variance when expecting an energetic deficit. Some previous demonstrations of this shift from risk-averse
to risk-prone behaviour relied on differences in both pre-experimental deprivation and inter-trial delays
within an experiment to vary the subjects' energy budgets, and these differences have allowed an alternate
interpretation of observed preferences. Therefore, earlier work on risk-sensitive foraging in small birds
was complemented by manipulating ambient temperature to induce positive and negative expected energy
budgets. For a given mean reward, the inter-trial delay was the same, constant length at both temperatures.
When subjects experienced a positive energy budget (warm temperature), risk-aversion exceeded preference for risk strikingly; the opposite occurred when the subjects could anticipate a negative energy
budget (cold temperature). Variation in inter-trial delays could not have influenced the change in
preference reported here.
Short-term energy requirements physiologically
constrain many birds and mammals, especially
those with relatively high metabolic rates (Barnard
& Brown 1985). When subject to such a physiological requirement, an animal should respond to the
inevitable stochastic variation in the energetic value
of the food rewards in a labile, risk-sensitive manner (e.g. Caraco 1980; Stephens 1981; McNamara
& Houston 1982). More specifically, the animal
should forage in a risk-averse manner when expecting an energy intake exceeding its physiological
requirement (a positive energy budget). But the animal should forage in a risk-prone manner when
expecting an energy intake less than its physiological requirement (a negative energy budget),
Stephens & Krebs (1986) call this the energy-budget
rule. The predictions are deduced from the assumption that an efficient forager's behaviour will reduce
the probability of failing to meet the animal's
energetic requirement (e.g. Caraco 1987).
The terms risk-averse and risk-prone refer to
preferences over probability distributions (see
Caraco & Chasin 1984). A risk-averse forager's
preference for a probability distribution increases
as the mean reward increases or the reward variance decreases. A risk-prone forager's preference
for a probability distribution increases as either the
0003-3472/90/020338 + 08503.00/0
mean reward or the reward variance increases.
Several studies have induced positive and then
negative energy budgets, and found that foragers
behaved in a risk-averse and then a risk-prone manner toward variation in reward-size, as predicted by
the energy-budget rule (reviewed by Real & Caraco
1986; Stephens & Krebs 1986; also see Moore &
Simm 1986; Ekman & Hake 1988). However, negative energy budgets do not induce risk-prone
behaviour in all animals (Battalio et al. 1985;
Wunderle et al. 1987; see Discussion).
Most ecological analyses of risk-sensitivity concern distributions of reward amounts. We may also
apply the concepts to distributions of time elapsing
until specified events occur. Some models allow the
length of the foraging day to vary randomly and
calculate the distribution of time a forager needs to
achieve a required energy intake (e.g. Caraco 1981,
1987; Pulliam & Caraco 1984; Clark & Mangel
1986). Other models fix the length of the foraging
period (or simply ignore it) and consider how
energy budgets might influence preference over
random delays between choice and consumption of
a particular food reward (e.g. Fantino & Abarca
1985; McNamara & Houston 1987; Zabludoffet al.
1988; Stephens, in press). A number of studies in
operant psychology report preference for variable
9 1990The Association for the Study of Animal Behaviour
338
Caraco et al.: Risk-sensitive foraging
over fixed delays; see review and interpretation by
Kagel et al (1986a), Fantino (1987) and Staddon &
Reid (1987). None of these studies estimates subjects' energy budgets, but clearly some animals
can prefer a variable delay with mean t over a
fixed delay of t time units between choice and
consumption of a given food reward.
Staddon & Reid's (1987) model of foraging
choice assumes a decision-maker will attempt to
regulate its feeding rate as close to some target as is
possible. A slightly oversimplified, but commonly
assumed, interpretation of their model predicts
that animals should be ri.sk-averse toward random
variation in reward size and risk-prone toward random variation in temporal delays. These predictions follow from the assumption that costs
increase with the squared deviation about the
hypothesized target rate of energy intake. Staddon
& Reid (1987) suggest that apparent empirical support for the energy-budget model might just as
strongly support their rate-regulation hypothesis.
To summarize their argument, consider the study
by Caraco et al. (1980).
Yellow-eyed juncos, Junco phaeonotus, chose
between simultaneously available constant and
variable rewards in a discrete trial procedure. They
fed ad libitum for the first 1-5 h in the morning, and
then experienced a period of food deprivation.
Caraco et al. (1980) induced positive energy budgets
by depriving the birds for 1 h prior to an experiment
and feeding them at an average rate of 1 seed/30 s
during an experiment. They induced negative
expected energy budgets by depriving the birds
for 4 h prior to an experiment and feeding them at
an average rate of 1 seed/60 s. Hence the time of
day and mean inter-trial interval differed between
treatments. Furthermore, the inter-trial interval
covaried positively with realized reward size to
avoid satiation effects during the positive energybudget treatment. That is, bigger rewards were followed by longer inter-trial intervals (this is not the
same as the delay between choice and consumption).
Staddon & Reid (1987; similarly Kagel et al.
1986b) suggested that risk-aversion at positive
energy budgets was a response to reward-size
stochasticity, and that risk-prone behaviour at
negative energy budgets was a response to delay
variation. Therefore, to complement the Caraco et
al. (1980) study, we need a procedure that still
avoids satiation during experiments and (1) controis for possible time-of-day effects, (2) uses constant inter-trial intervals and (3) uses the same
339
inter-trial interval for both positive and negative
energy budgets. To meet these criteria we conducted choice experiments that always began at the
start of the day (lights on). This controlled for possible time-of-day effects and averted satiation during preference tests. F o r a given mean reward, our
experiments used the same, constant inter-trial
interval throughout; we manipulated expected
energy budgets by varying ambient temperature
(i.e. by varying the costs of homeothermy). Our
results associate risk-aversion with positive energy
budgets and risk-proneness with negative energy
budgets, as the energy-budget rule predicts.
METHODS
We studied yellow-eyed juncos foraging in a laboratory environment. During the first year of the
study (September 1986 to August 1987), all subjects
were adults. During the second year (September
1987 to June 1988), we studied juveniles captured in
August just after leaving their parents' territory
(see Sullivan 1988). By the time we began experimenting with juveniles, they had attained adult
coloration and body mass. Hence our juveniles
were individuals facing their first winter.
We planned our experiments based on estimates
of food intake at three different ambient temperatures, Therefore, we present our analysis of energy
consumption in full and then detail the methods of
our choice experiments.
Energy Budgets
We maintained each junco in a separate cage
measuring 1 m long x 0-8 m wide x 0.7 m high. All
sides were opaque except for a hardware cloth bottom. One-way glass mounted in front of each cage
allowed us to observe the birds unobtrusively. We
determined temperatures by reading a thermometer mounted on the rear wall of each cage. In
each of two walk-in coolers equipped with reliable
temperature control, we placed two cages (each on
supporting legs). Automatic timers maintained a
10:14h light:dark cycle; a small bulb mounted in
the top of each cage provided the light. Grit and
water were always available. We provided mealworms as a dietary supplement, except when we
used a bird in an experiment.
We installed a feeding apparatus at the midpoint
of the front of each cage. To measure food consumption at a given temperature we presented a
known number of millet seeds, Panicum miliaceum,
340
Animal Behaviour, 39, 2
and counted the number remaining (in the apparatus or collected after falling through the hardware
cloth). We repeated this process periodically over
the course of a 10-h day and so obtained an observation of an individual's daily seed consumption
(see Caraco 1981, 1983). We used daily food intake
as a proxy for existence metabolism, since we
needed only to discriminate positive and negative
energy budgets.
We estimated seed consumption at three different temperatures: 1~ 10~ and 19~ When we
shifted a bird from one temperature to another, we
did so in 3~ per day differences and then waited 1
week before collecting any data at the new temperature. One week is more than enough time for a nonbreeding granivore to adjust its metabolism and
feeding behaviour to the demands of the new
temperature (Sprenkle & Blem 1984).
During the first year we twice sampled daily seed
consumption for each of five adult males and five
adult females at all three temperatures. We used a
logarithmic transform to homogenize variances
and subjected the data to an ANOVA. We took
temperature and gender as treatments, and noted
effects of individuals within gender. Neither the
interaction between temperature and gender
(F2.20= 1"58, Ns) nor the interaction between temperature and individuals within gender (Fi6,20 ~1.86, Ns) induced significant variation. We did not
detect a significant difference between males and
females (Fl,10=0.09), but variation in ambient
temperature induced significant variation in daily
seed consumption (F2,20=115-4, P < 10-4). We
additionally noted significant variation among
individuals within gender (F8,10=4.63, P<0.05).
A Tukey's test indicated that mean seed consumption at I~
averaged over the 10 individuals,
exceeded mean consumption at 10~ significantly,
and mean food consumption at 10~ exceeded the
mean at 19~ significantly.
Table I shows the mean levels of daily seed comsumption at each of the three temperatures. Since
males and females did not differ in this analysis, we
did not attempt to identify individuals by gender
during the rest of the study. The effect of temperature dominated these results; eaeh temperature
clearly imposed a different energetic requirement.
At a given ambient temperature average energy
requirements should not differ between independent juveniles and adult juncos (see Sullivan 1988).
In any case, during the second year we sampled
daily seed consumption of four juveniles until we
Table I. Mean daily seed consumption (__+s~) at different
ambient temperatures
Subjects
Adults*
Juveniles
I~
10~
19~
1219-2 (33.7) 940'7(28-4) 611'4(25.4)
1111.5(64.3) 994.5 (57.0) 605.5(26.7)
*Each entry for adult birds is a mean of 20 observations;
10 birds were each sampled twice at all three temperatures. Four juveniles were sampled. We collected 10
observations at I~ and 10~ and collected 19
observations at 19~
accumulated at least 10 observations at each temperature. Thirty of the 39 total observations were
split between two juvenile males. After a logarithmic transformation we subjected the data for these
two birds to a two-way ANOVA; the treatments
were individual and temperature. The interaction
was not significant (F2,24= 1-0, Ns), and we did not
find a significant difference between individuals
(F1,24= 1.33, rqs). Variation in ambient temperature
induced significant variation in daily seed consumption (F2.24= 25"2, P < 10- 3). Table I shows the
overall mean levels of daily food consumption;
adults and juveniles exhibit a similar pattern of
temperature-dependent food intake.
The preceding analyses indicated that both
adults' and juveniles' energy budgets vary significantly across temperature. In our choice experiments we let the birds feed at an expected rate equal
to the average consumption rate we observed at
10~ We conducted the experiments at I~ and
19~ Hence, the otherwise identical experiments
implied a significantly negative expected energy
budget at I~ and a significantly positive energy
budget at 19~
We regressed the mean cumulative seed consumption for adults at 10~ on hour of the foraging
day (i.e. the time elapsed since the lights came on
and the birds began feeding). With y representing
accumulated seed consumption and t representing
time of day (0 < t ~<10 h), we obtained y = 13.25 +
90.98t; r~0= 0.997, P<0.001. The slope has units of
seed/time; inverting we obtain time/seed. The result
is an expected energy intake of one millet seed every
40 s. We used this figure in designing our choice
experiments.
Choice Experiments
We used colour as the cue associated with levels
of reward variance. We attached a plastic track
Caraco et al.: Risk-sensitive foraging
measuring 7cm wide outside each cage at the
middle of the front panel; the track extended into
the cage through a small port. We mounted a feeding device with two removable, opaque plastic
covers on the track. At the back of the device were
three handles. An experimenter pushed the middle
handle to move the device along the track into the
cage. Pulling either of the other two handles
retracted the associated cover, so a bird could consume the seeds in a well measuring 2.5 cm 2 below
the cover. We placed a piece of coloured adhesive
tape on top of each cover. One of the two colours
indicated a constant (i.e. certain) reward during a
choice experiment. The other colour indicated a
variable reward with a mean equalling the constant
reward. During an experiment we assigned colours
randomly to the left and right sides of the feeding
apparatus, subject to the constraint that each
colour appeared on each side an equal number of
times each day. The juncos quickly learned to
approach the feeding device and peck the coloured
tape.
For a given subject, an experimental test of preference between a reward distribution and its mean
took 7 days. On day 1 we tested for colour bias.
Choice of either colour produced the same constant
reward in this test. We required that the subject
exhibit indifference to colour before proceeding to
the test of risk-sensitivity. We used a total of seven
colours throughout and never presented any colour
in consecutive experiments with a given bird.
Ifa subject proved indifferent to colour on day 1,
we gave it the next day off. We then performed the
same series of 40 trials on days 3, 4 and 5. The first
16 trials were forced-choice, where we presented
only one colour per trial. When the bird pecked the
coloured tape, it gained access to the reward. Each
colour appeared eight times, divided evenly
between the left and right sides of the feeding
device. Forced-choice trials allowed the subject to
associate reward characteristics with colour, and
gave the animal an estimate of the experimental
feeding rate. These 16 trials began at the onset of
the foraging day (t = 0).
Following the forced-choice training trials, we
presented 24 two-choice preference trials. The
juncos would approach the feeding device from the
rear of the cage and peck one of the coloured pieces
of tape. As soon as a bird pecked a colour, the
experimenter retracted the cover. When the bird
had eaten any seeds available and left the front of
the cage, the feeding device was withdrawn. All of
341
the juncos learned that pecking the remaining
colour, after finishing the seeds, would not yield a
reward. We provided supplemental food 1 h after
completion of a day's preference trials.
At each preference trial we recorded whether a
bird chose the constant reward or the variable
reward. We pooled an individual's 72 preference
trials from days 3, 4 and 5 and calculated that subject's p~, the proportional choice of the constant
reward. We used the normal approximation to the
binomial distribution to categorize each Pc value as
risk-averse, indifferent or risk-prone toward reward
variance. Similarly, we tested for position bias.
We did not test a subject on day 6 of an experiment. On day 7 we performed a colour-reversal
test. The certain and variable rewards were the
same as day 3 through 5, but the colour association
was reversed. The 16 training trials and 24 preference trials were conducted as above. Ifthepc estimate indicated a significant preference, we required
that the subject prefer the same variance (hence, the
other colour) or show indifference during the
colour-reversal test. If the Pc estimate indicated
indifference, we required that the subject not
exhibit a preference in the colour-reversal test. A
'failure' on the colour-reversal suggested greater
colour preference than risk preference, resulting in
rejection of the Pc estimate and repetition of the
experiment. Fortunately, only three of 65 experiments ended with a failure of the colour-reversal
test.
We used two-point distributions to generate
variable rewards. If the constant reward was x
seeds, the variable reward provided either ( x - a) or
(x + a) seeds with equal probability. Hence the variable reward had mean x and variance a 2. During
training and during preference trials, the larger and
smaller values of the variable reward occurred
equally often. Furthermore, we scheduled both
larger and smaller values an equal number of times
at the left and right sides of the feeding device.
Recall that the observed rate of seed consumption was essentially one seed every 40 s at 10~
Therefore, we set the constant inter-trial interval
within any experiment, in seconds, at 40x. That is,
the delay did not vary with temperature; so the
delay was a constant (for a given x) independent of
the forager's expected energy budget. We divided
the choice experiments into two sets, depending on~
the variance of the variable reward.
In the first set of choice experiments the variable
reward provided either ( x - 3 ) or (x+3) seeds on
Animal Behaviour, 39, 2
342
every preference trial. We used two levels of mean
reward, x = 3 and 4. We tested four adults and four
juveniles. The design was a three-way ANOVA
with treatments temperature (I~ and 19~
age
(adults and juveniles) and mean reward level.
We used a balanced, randomized-block design
with individuals as blocks. Two of the four individuals of a given group were assigned randomly to a
sequence of low and then high temperature; the
other two subjects in the same age group experienced high and then low temperature. Within each
pair of individuals experiencing the same sequence
of temperatures, we assigned one to a sequence of
lower and then higher mean reward; the other bird
experienced the opposite sequence.
In the second set of choice experiments the vari:
able reward provided either ( x - 2 ) or (x + 2) seeds
'at every choice trial. We used three levels of mean
reward, x = 2, 3 and 4. We tested two adults and
three juveniles. Each of these birds had previously
completed the first set (a2=9) before beginning
these experiments. Individuals chosen for the
second set were the birds that had first completed
all experiments at the higher reward-variance level.
We tested fewer individuals in the second set since
the clarity of the first set's results indicated that a
smaller sample would be sufficient. The design
was a three-way ANOVA adjusted for unequal
sample size. Treatments were temperature, age and
mean reward level. Again, we assigned individuals
across sequences of temperature and mean-reward
treatment combinations in a randomized-block
fashion.
RESULTS
We observed that a single experiment's choice
probabilities usually did not vary much among the
3 days of preference testing. However, in a few
cases, a bird would choose both levels of variance
nearly equally on the first test day (day 3 of
the experiment) and then exhibit a risk-sensitive
preference the next 2 days.
In 16 of 62 (25.8%) experiments, risk-indifference
resulted primarily because the bird exhibited a
position bias. Even though the two colour cues
were only 2 cm apart, all of the birds showed a preference for the left or right side of the feeding device
in at least one experiment. We conservatively leave
these indifferences in the data, since we predicted
significant preferences. We present the results of the
two sets of experiments separately.
Table II. Proportional choice of constant reward (Pc)
when variance of variable reward was 9
I~
Mean
reward (x)
Adults
A1
A2
A3
A4
Juveniles
Jl
J2
J3
J4
19~
3
4
3
4
0.44
0.42
0"10t
0"33t
0.40
0.47
0.40
0'33t
0.75*
0.60
0-64*
0.69*
0.72*
0.63*
0.71"
0.69*
0.33~
0'29t
0.43
0.34t
0.39
0"36t
0.39
0.72*
0.51
0.36t
0.51
0.94*
0.69*
0.59
0.68*
0.79*
*Significantrisk-aversion, P < 0.05.
tSignificant risk-proneness,P < 0.05.
High Variance
Table II shows the p~ values for all experiments
where the variance of the variable reward was 9.
For each entry the table identifies the result as indicating significant risk-aversion (standard normal
z>1-96), risk-proneness ( z < - 1 - 9 6 ) or indifference to reward variance. Temperature was
associated with a clear qualitative difference. The
distributions of the number of results in the three
categorical outcomes differed significantlybetween
temperatures (g2= 14.17, df=2, P<0-005). At I~
risk-aversion occurred only once and risk-prone
behaviour was common. At 19~ risk-proneness
occurred only once and 69% of the experiments
resulted in risk-aversion.
We transformed the Pc values according to arcsine x/Pc and assumed homogeneous variances.
Then we conducted a three-way ANOVA on the
transformed data. Neither the three-way interaction (mean reward-age-temperature: Fi,24= 0.61,
NS) nor any of the two-way interactions (mean
reward-age: F~,z4=0.01, NS; mean rewardtemperature: FI,24=0-01, Ns; age-temperature:
F1,24= 0.25, Ns) induced significant variation in the
choice probabilities. Among the main effects,
neither mean reward (Ft.24= 1-24, Ns) nor age
(Fl,24=0.06, NS) proved significant. However,
the temperature effect was highly significant (F~.24=
41.42, P < 10-4).
Both the qualitative and quantitative results
clearly indicate risk-sensitivity differed between
temperatures, that is, between negative and positive
Caraco et al.: Risk-sensitive foraging
343
Table Ill. Proportional choice of constant reward (Pc)when variance of variable
reward was 4
I~
Mean
reward (x)
Adults
A1
A3
Juveniles
J2
J3
J4
19~
2
3
4
2
3
4
0"51
0"217
0'47
0"33?
0'61
0.35?
0.51
0.75*
0.60
0.74*
0.67*
0.68*
0.43
0.58
0.29?
0.47
0.50
0.46
0.39
0.35?
0.29?
0.63*
0.40
0.85*
0.65*
0.39
0.88*
0.60
0.40
0.51
*Significantrisk-aversion, P < 0.05.
"['Significantrisk-proneness, P < 0.05.
expected energy budgets. The pattern in the incidence of preference for and aversion to variance in
reward size supports the energy-budget rule.
Low Variance
Table III shows the Pc values for all experiments
where the variance of the variable reward was 4.
The table identifies each result as indicating riskaversion, risk-proneness or risk-indifference. Riskaversion did not occur at I~ and preference for
risk did not occur at 19~ The distributions of
the number of results in the three categorical outcomes differed significantly between temperatures
(Z2= 14.25, dr= 2, P < 0"005).
We transformed the Pc values as above and conducted a three-way ANOVA. Neither the threeway interaction (mean reward-age-temperature:
F2,1s=0.02, MS) nor any of the two-way interactions (mean reward-age: F2,18= 1.14, NS)
mean reward-temperature: F2,~8=0.09, NS; agetemperature: F1,18=0"33, MS) induced significant
variation in preference behaviour. Among the main
effects, neither mean reward (F2,18=0.47, MS) nor
age (Fl,~8= 0'22, NS) proved significant. Temperature again induced a significant difference in choice
probabilities (FI,24=12.76, P<0-01), so that
preference behaviour again varied between energy
budgets.
DISCUSSION
Our results support the energy-budget rule and
exclude explanations involving response to delay.
When expected energy budgets were negative, we
noted only one case of preference for low variance
and recorded significant preference for high reward
variance in 42% of those experiments. When
expected energy budgets were positive, we noted
only one case of preference of high variance and
recorded significant preference for low variance in
61% of those experiments. This phenotypically
plastic shift between risk-prone and risk-averse
behaviour occurred in response to a temperature
change, hence a change in energy budgets; we held
every other aspect of a particular experiment constant. Neither mean reward level nor age (adult versus juvenile) influe/nced preference significantly.
Individual vari~fi.on in choice probabilities (Pc
values) was slightly greater among juveniles than
among adults, although adults showed significant
individual variation (within gender) in daily food
consumption. Even if variation in food consumption implied variation in required energy budgets,
the difference between our levels of ambient temperature assured positive energy budgets at 19~
and negative energy budgets at 1~
The energy-budget rule makes intuitive sense
when a non-breeding forager must meet a shortterm physiological requirement. When an animal's
expected rate of energy intake exceeds the minimally required level, a low intake variance assures
survival, but a high variance may increase the probability of starvation. When the expected rate of
energy intake falls below the required level, low
intake variance may assure starvation, but a high
variance provides a chance of survival (Caraco
1981, 1982).
344
Animal Behaviour, 39, 2
The energy-budget rule applies directly to variance in reward amount. However, preferences over
random delays appear more complex. Our results,
as intended by the experimental design, do not
address responses to variation in random delays
associated with foraging options. Ecological analogies to delay variance are more tenuous than analogies to variation in reward size (Kagel et al. 1986a)
but animals clearly respond consistently to delay
patterns (reviewed in Staddon 1983; Fantino &
Abarca 1985; Staddon & Reid 1987). Minimizing
the probability of failing to achieve a physiologically required food intake can predict aversion to,
or preference for, delay variance (McNamara &
Houston 1987; Zabludoff et al. 1988). Alternatively, if the future is always more uncertain than
the present, a larger reward in the future might be
less preferred than a smaller, more immediate
reward (Logue 1988). An economic model that discounts future rewards according to a 'variable-time
bias' formula does a good job of explaining
observed empirical results concerning preference
over delay variance (Kagel et al. 1986a), and
the reader may wish to consult McNamara &
Houston's (1987) model where both reward sizes
and delays vary randomly.
The energy-budget rule arises whether we treat
foraging as (1) a daily process leading to physiological success or failure (e.g. survival or starvation), or
(2) a process where fitness increases as a convexconcave function of energy intake during the foraging period. Several logical approaches lead to
these conclusions (Caraco et al. 1980; McNamara
& Houston 1982; Stephens & Charnov 1982;
Stephens & Krebs 1986; Gillespie & Caraco 1987).
In either case, fitness is a function of only total
energy intake, and does not depend on the pattern
of energy accumulation during the day. That is,
survival depends most on the forager's ability to
acquire enough energy to meet its overnight costs.
As body size increases, short-term energetic
requirements no longer impose a significant threat
to survival. For example, larger passerine birds
should survive longer than small birds when food is
not available. Metabolic costs per unit body mass
decline as body size increases, so a given percentage
of body mass devoted to energy storage lasts longer
in a larger bird (see Downhower 1976; Caraco
1982).
Once short-term requirements become unimportant, risk-prone foraging strategies will seldom
enhance survivorship. Houston & McNamara
(1986) discuss the 'continuous forager'; the model
animal has no short-term requirements and
attempts to maximize the expected time until its
energy reserves disappear and the animal starves.
In this model an efficient forager always responds
to reward-size variance in a risk-averse manner.
Some animals do exhibit consistent risk-aversion
toward reward variance independently of their
energetic status (Battalio et al. 1985; Wunderle et
al. 1987). Interesting empirical patterns may underlie the distinction between those organisms that
follow the energy-budget rule and those that do
not.
ACKNOWLEDGMENTS
We are particularly indebted to R. Holberton and
K. A. Sullivan, whose help made the study possible.
C. P. L. Barkan and F. Stollnitz provided valuable
advice on experimental design. M. D. Withiam
helped with the statistics, and B. V. White typed the
manuscript. We thank Kelly Kreiger for technical
assistance. We conducted the research in accordance with published guidelines on animal welfare,
U.S. Fish and Wildlife Service Scientific Collecting Permits PRT-674696 and PRT-702946, and
New York State Department of Environmental
Conservation license SCL88-188. This project was
supported by NSF grant BNS-8616736.
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(Received 17 January 1989; initial acceptance 29 March
1989;final acceptance 26 April 1989;
MS. number: A5465)