Behavioral Ecology Vol. 12 No. 2: 207-218
© 2001 International Society for Behavioral Ecology
A dynamic model of short-term energy management in small food-caching and non-caching birds
Department of Biological Sciences, Purdue University, West Lafayette, IN 47907, USA
Address correspondence to V.V. Pravosudov, who is now at Neurobiology, Physiology, and Behavior, University of California at Davis, One Shields Avenue, Davis, CA 95616-8519. E-mail: vpravosudov{at}ucdavis.edu .
Received 22 September 1999; revised 6 July 2000; accepted 31 August 2000.
 |
ABSTRACT |
|---|
 TOP ABSTRACT INTRODUCTIONMODELRESULTSDISCUSSIONREFERENCES |
|---|
The survival of small birds in winter is critically dependent on the birds' ability to accumulate and maintain safe levels of energy reserves. In some species, food caching facilitates energy regulation by providing an energy source complementary to body fat. We present a dynamic optimization model of short-term, diurnal energy management for both food-caching and non-caching birds in which only short-day, winter conditions are considered. We assumed that birds can either rest, forage and eat, forage and cache, or retrieve existing caches (the two latter options are available only to caching birds). The model predicted that when there is variability in foraging success (here modeled strictly as within-day variability), both caching and non-caching birds should increase their fat reserves almost linearly in the morning slowing down toward late afternoon, a result consistent with field data but different than the result of a previous dynamic program. Non-cachers were predicted to carry higher fat levels than cachers especially when the variability in foraging success is high. Probability of death for non-caching birds was predicted to be higher than that for cachers, especially at higher levels of variability in foraging success. Among caching birds, an increase in number of caches and fat reserves was also predicted if: (1) mean foraging success was decreased, (2) variability in foraging success was increased, and (3) energy expenditure at night was increased over our baseline conditions. Under the conditions simulated in our model, birds were predicted to cache only if cache half-life (i.e., time interval over which 50% of the caches are forgotten or lost to pilferage) exceeded 2.5 days, indicating that low pilferage rate and long memory favor more caching. Finally, we showed that such daily patterns of energy management do not necessarily require relaxing assumptions about mass-dependent predation risk.
Key words: caching, dynamic model, foraging, predation risk, pilferage.
|
INTRODUCTION |
|---|
|
TOPABSTRACTINTRODUCTIONMODELRESULTSDISCUSSIONREFERENCES |
|---|
During the non-breeding season, many small birds are faced with harsh conditions of short days, unpredictable food, and low ambient temperature. Under such demanding conditions, an animal should gain enough energy both to meet maintenance costs and to withstand possible high variability in food supply and/or other ecological conditions that can limit access to food (e.g., Bednekoff and Houston, 1994a
,b;
Lucas and Walter, 1991;
McNamara and Houston, 1990;
Pravosudov and Grubb,
1997a,b).
Theoretical analyses have indicated that high fat loads may also increase
the risk of predation either through a reduction in maneuverability or through
an increase in foraging time caused by increased metabolic demands
(Lima, 1986;
McNamara and Houston, 1990).
However, tests of predation risk tradeoffs associated with maneuverability
have proved equivocal. For example, some experiments demonstrated that heavier
birds have slower flight speed and lower ascent angle during take off compared
to leaner conspecifics (Metcalfe and Ure,
1995; Witter et al.,
1994), whereas other experiments failed to find a substantial
effect of body mass on flight characteristics
(Kullberg, 1998;
Veasey et al., 1998).
The question of how much energy a bird should maintain and how it should
accumulate energy during the day has attracted much attention (Bednekoff and
Houston,
1994a,b;
Grubb and Pravosudov, 1994;
Haftorn, 1989,
1992; Pravosudov and Grubb,
1997a,b,
1998;
Witter and Cuthill, 1993). In
general, both theoretical and empirical results suggest that birds should
increase their mass when food becomes less predictable, when nights become
longer, and when ambient temperature declines
(Bednekoff and Krebs, 1995;
Bednekoff and Houston,
1994a,b;
Ekman and Hake, 1990). Several
models predict that passerine birds should continue mass gain throughout the
day to reduce the risk of starvation during the day and to ensure that enough
reserves are stored to survive the night, a trend supported by empirical
evidence (Bednekoff and Houston,
1994b; Lehikoinen,
1987; McNamara et al.,
1994; see also reviews by
Pravosudov and Grubb, 1997a;
Witter and Cuthill, 1993).
Most of the literature addressing the issue of energy reserves has
considered birds that only store energy internally as body fat (e.g.,
Pravosudov and Grubb, 1997a;
Witter and Cuthill, 1993).
However, many animals store energy externally as caches in addition to their
storage of fat (Vander Wall,
1990); the joint regulation of these two energy stores has
important life-history consequences. Although many animals, including both
birds and mammals, must manage their fat and cache supplies during the winter,
the nature of tradeoffs of energy storage in birds, determined by flight
requirements, appear to be very different from that of mammals (see review by
Witter and Cuthill, 1993). The
first dynamic model of energy management in a caching passerine was published
by McNamara et al. (1990). The
main conclusion from that model was that in contrast to the predictions listed
above for non-caching birds, caching birds should lower their body mass during
the first part of the day in order to keep the risk of predation low and then
they should gain mass rapidly during the last part of the day. The prediction
rests on the assumption that caches represent a highly predictable food supply
which caching birds can draw on at the end of the day to build up necessary
energy reserves and the assumption that carrying fat reserves involves costs.
Unfortunately, there is scant evidence supporting the predicted daily routine
of mass gain in food-storing birds and some existing data argue against it
(Haftorn, 1989,
1992).
In another dynamic model of cache and fat regulation, Lucas and Walter
(1991) did not specifically
address daily patterns of energy regulation; instead they focused on expected
trends across days. In addition, they simulated fixed periods of access to
food that mimicked laboratory conditions
(Lucas and Walter, 1991). It
is not clear if these predictions apply to more natural patterns of access to
food.
Brodin (2000) recently
addressed the disparity between diurnal mass trajectories described from field
observations and those predicted by McNamara et al.
(1990). Brodin
(2000) suggested that the only
way to generate theoretically derived mass trajectories that are similar to
those observed in the field was to manipulate the mass-dependent component of
predation risk. Specifically, he suggested that a relaxation of the assumption
of a strictly monotonic relationship between mass and predation risk would
generate mass trajectories similar to those found in the field. However, this
conclusion is inconsistent with the results of Lucas and Walter
(1991) who showed that the
relative shape of the predation-risk function should have little effect on
energy regulation patterns (also see Lucas
and Howard, 1995). Since the sole focus of the Brodin
(2000) paper was factors
regulating diurnal mass trajectories, we feel that it is prudent to revisit
this conclusion.
We present a model that considers energy management of both caching and
non-caching birds. Our model includes a number of assumptions that appear to
be more realistic than those found in previous models. We ask whether our new
assumptions lead to a better match between predictions and data. We also
address the validity of conclusions drawn by Brodin
(2000) based on a similar
model. Finally, we investigated the effect on our predictions of changing a
number of parameters that characterize winter conditions. The conditions we
evaluated include food availability, variability in foraging success,
nocturnal temperature, mortality rates, and parameters that define caching
patterns of birds such as mean energetic gain from retrieval, variability in
retrieval gain, and cache pilferage rate. This exercise will also provide
general lessons on the factors that affect how organisms manage energy in
harsh and unpredictable environments.
|
MODEL |
|---|
|
TOPABSTRACTINTRODUCTIONMODELRESULTSDISCUSSIONREFERENCES |
|---|
We developed a stochastic, dynamic optimization model (Mangel and Clark, 1988
) with
two state variables: fat reserves and food-caches. The optimal state-dependent
decision matrix was calculated assuming that the birds maximize over-winter
survival, which depends on energy reserves and predation risk. Mean daily
patterns of body mass, eating, caching and retrieving intensities, and
probability of death were estimated from the optimal decision matrix using
forward simulation (as in McNamara et al.,
1990).
We modeled a small food-caching bird such as the Carolina chickadee,
black-capped chickadee (P. atricapillus) or willow tit. We assumed
that body mass may vary from 8.0 to 12.0 g
(Lucas 1994;
Lucas and Walter, 1991;
Pravosudov VV, and Lucas JR, personal observation) and that variation in mass
is caused by differences in fat stores
(Blem, 1990). We divided the
4.0 g of fat reserves into 100 increments. Increasing the number of increments
to 150 (retaining a range of 4.0 g of fat) had no effect on the results. We
assumed a maximum cache size of 300 food items divided into 300 increments.
The birds are assumed to scatterhoard food
(Vander Wall, 1990), and
therefore each cached item is stored independently of other cached items.
Increasing the upper limit to 400 items had no effect on the results of the
model. A linear interpolation was used to estimate survival consequences of
fractional increments of both fat reserves and cache size.
We divided an active day of seven h (which approximately corresponds to
December in, for example, Edmonton, Alberta, Canada [55° 42' N] or
Lund, Sweden [55° 33' N], into 21 20-min time intervals. During each
20-min time interval, a bird could perform one of four alternative behaviors:
forage and eat, forage and cache, retrieve existing caches, or rest. A
non-caching bird could only forage and eat, or rest. We decreased the time
interval to 10 min for several simulations and found no effect on the
predictions, and therefore assumed that the results from 20-min intervals are
robust. All real variables in the program were declared as double precision
(see Houston et al., 1997). In
all cases, both backward (i.e., the dynamic program) and forward simulations
equilibrated before 65 days. We therefore used this length as a conservative
duration for all simulations. We used a single set of parameters for our
baseline model, and tested the effect on the predictions of altering a number
of these parameters. Each component of the model is listed below, and baseline
parameters are specified in each section (also see Tables
1,2,3,4,5).
|
|
|
|
|
Starvation risk
Following Lucas and Walter
(1991), we assumed that above
some critical mass (minimal body mass [8 g] plus 10% of the maximum body mass
range [4 g] or 8.4 g) the risk of starvation was zero. We used an incomplete
beta function to calculate the probability of starvation below that mass.
Parameter values for the incomplete beta function were taken from Lucas and
Walter (1991).
Predation risk
We modeled predation risk as a two-stage process, the probability of a
predator attack and the probability of depredation if an attack occurred (as
in Lima, 1986;
Lucas and Walter, 1991). When
a bird was resting, its probability of being killed by a predator was zero.
When a bird was active, the attack probability per 20-min time interval
(
= 6.67 x 10-4, recalculated from
Lima, 1986) was constant. If
attacked, the bird's probability of capture (pcapture) was
mass-dependent. Lima (1986)
assumed an accelerating quadratic function, although the relationship he used
is nearly linear over the range of mass we used in our model
(Figure 1A). Current empirical
data (Kullberg, 1998) suggest
that linear relationship between mass and predation risk is highly unlikely.
Therefore for our baseline model, we chose an arbitrary function with
predation-risk values similar to Lima's
(1986) at extreme mass levels
(pcapture =.078 at mass = 8 g;
pcapture =.173 at mass = 12 g), but also included
accelerating risk with an increase in mass
(Figure 1A):
 | (1) |
|
The probability of being killed by a predator per 20 min was:
 | (2) |
We also tested whether the near-linear relationship from Lima
(1986) generated results
different from our baseline model.
Energetic gain
We used prey encounter rates and food-item caloric values from field data
on small parids (Brodin, 1994;
Pravosudov, 1983,
1985) to calculate the
probability of encountering a food item and the mean foraging success (food
found during foraging can be either eaten or cached) from a foraging bout.
Variability in prey encounter rate was simulated using a truncated normal
distribution. When a bird decided either to feed or to cache during any given
20-min time interval when it is foraging, it could find from zero to six food
items with a mean of three items. Each item was equal to 0.064 g of fat that a
bird could gain from eating the item, thus three items generated 0.192 g of
fat gained/20 min (based on Brodin,
1994; Pravosudov,
1983,
1985) and some specified
variance between zero and 0.02 with the baseline variance of 0.01. We varied
the value of each item from 0.047 to 0.080 g of fat (generating a mean
foraging return of 0.14 to 0.24 g of fat per 20 min) to test how changing mean
energetic gain affects the result of our model.
We assumed that mean energy gain from cache retrieval is a function of
number of existing caches: the more existing caches the higher the return. The
logic behind this is as follows: parids have fairly large territories (up to
50 ha for Siberian tit; Pravosudov,
1987; 4-5 ha for Carolina chickadees, personal observation) and
these birds are scatterhoarders. If a bird has only a small number of caches
when it decides to retrieve them, it might be far away from these caches and
it would take more time and energy to retrieve them thus making the mean
return smaller. At higher cache densities, cache retrieval should be more
rapid and the mean energetic reward from retrieval should correspondingly
increase. The function we used to calculate the mean energetic gain from
retrieval per 20 min time unit is (see
Figure 1B):
 | (3) |
Where 
R = mean retrieval gain measured in g of fat/20
min, Nret = 5 = zero intercept of retrieval function (measured in
number of items retrieved), Mret = 0.064 = value of one retrieved
food item (g of fat), and CS = number of individual caches.
The bird can retrieve an average from five to six (= 1.2 x
Nret) items per 20 min (Mret converts this into g of fat
gained from eating this food) if it has more than five food items cached. If
fewer than five items are cached, the bird simply retrieves all of them (i.e.,
CS x Mret). The shape of the curve is determined by the
function (1 - e-0.025xCS). Thus, we assumed that energetic
gain from cache retrieval is 1.7 to two times larger than the mean energetic
gain from foraging (0.192 g of fat/20 min). Some other models used either
smaller (Brodin, 2000;
Brodin and Clark, 1997) or
larger (McNamara et al., 1990)
ratios of retrieved gain to foraging gain.
Under the baseline conditions, we assume a zero variance in energetic gain from retrieval. We also varied the variance in energetic gain from retrieval to test the sensitivity of the model to this parameter. Variance in retrieval gain was incorporated in the model using a truncated normal distribution of Nret with a mean equal to 5 and a variance ranging from 0 to 0.02.
Cache loss
For the baseline conditions, we assumed that pilferage rates were constant
during the entire 24-h of each day and that the combination of pilferage and
forgetting cache locations resulted in a 50% loss ("half-life") of
the cache in 20 days. There is some debate about the true pilferage levels in
the field (Lucas and Zielinski,
1998). Some authors argue that caches last only a few days
(Sherry et al., 1982;
Stevens and Krebs, 1986). In
contrast, Brodin (1994)
suggested that these high pilferage rates measured in the field result from a
bias caused by providing food at feeders. The 20-day half-life is a figure
Brodin (1994) measured in a
Swedish population of willow tits. We tested the effect of cache loss rates on
the results of our model by varying the cache's half-life from 20 to 2.5
days.
Note that we assume that animals that forget or lose their caches do not
increase food encounter rate (in contrast to
Brodin and Clark, 1997;
Smulders, 1998).
Metabolic costs
Mass-dependent basal metabolic costs were taken from Lucas and Walter
(1991) and scaled for 20-min
time intervals:
 | (4) |
BMR = basal metabolic rate measured in g of fat lost per 20 min (for
conversion of metabolic rate into g of fat we assumed that a gram of fat is
equivalent to 37716 J [Chaplin,
1974; Lucas and Walter,
1991]), Mass = body mass of a bird in g, and
 | (5) |
All justifications for the BMR equation are presented in Lucas and Walter
(1991). Note that equation 4
incorporates the effect of higher fat loads (higher body mass) and that this
mass-dependent basal metabolic rate is one of the two modeled fat maintenance
costs (the second cost is mass-dependent predation risk described above).
To calculate the metabolic cost of different activities, we used multiples
of the BMR:
 | (6) |
 | (7) |
 | (8) |
 | (9) |
 | (10) |
Using doubly-labeled water, Carlson and Moreno
(1992) showed that the cost of
short flights, routinely used by parids during foraging, can be as high as 12
times night-time BMR. Thus, we think that our estimation of MR of any activity
that usually involves short flights including foraging, caching and retrieving
food caches is reasonable. The figure for resting metabolic rate (1.95BMR) is
from Weathers et al. (1984)
and Buttemer et al. (1986).
Figure 1C presents values of
metabolic rates for the range of energy reserves considered in the model.
For the baseline calculations, ambient temperature was constant at -5°C both day and night. Since nocturnal temperature is often lower than diurnal temperature, we tested the effect of varying night temperature from -5 to -15°C.
|
RESULTS |
|---|
|
TOPABSTRACTINTRODUCTIONMODELRESULTSDISCUSSIONREFERENCES |
|---|
Effect of variability in foraging success: comparison of food-caching and non-caching birds
Almost no caching is expected when there is no variability in foraging success (Table 1). As a result, daily patterns in the size of fat reserves for caching birds are identical to those of non-cachers: both groups were predicted to maintain their morning body mass until midday followed by a steady increase until dusk (Figure 2). Thus when foraging success is certain, the birds minimize the cost of acquiring and maintaining energy reserves early in the day. In the afternoon, the birds gain energy needed for overnight survival by eating virtually all encountered food.
|
2 = 0, squares:
At any appreciable level of variance in foraging success, the daily
patterns of fat reserves change significantly compared to the hypothetical
no-variance condition. When foraging success is stochastic, the birds are
expected to gain mass more rapidly in the first part of the day slowing down
toward late afternoon (Figure
2). The most striking result here is that, contrary to previously
published predictions (McNamara et al.,
1990), caching and non-caching birds are predicted to maintain
qualitatively similar daily patterns in the regulation of fat reserves
(Figure 2). Indeed, both groups
of birds are predicted to gain similar amounts of fat over the course of the
day (Table 2). With an increase
in variance in foraging success, both caching and non-caching birds are
predicted to increase the absolute size of their fat reserves as a hedging
strategy against increased risk of starvation. The increase in absolute mass,
however, is much higher in non-caching birds since they have only one option
(increasing their fat reserves) to hedge against unpredictable foraging
conditions. In caching birds, the relatively lower size of fat reserves is
compensated for by an increase in cache size when foraging success becomes
more variable (Table 1).
With zero variance in foraging success, feeding rates are predicted to be low early in the day, then peak in mid afternoon (Figure 3), a pattern reflecting the optimal daily mass trajectory (Figure 2). In contrast, at the higher levels of variance in foraging success, birds are predicted to eat most actively during the first part of the day (Figure 3). Activity is minimal just before roosting (Figure 3) causing mass to level off and even decrease slightly at that time (Figure 2). These daily patterns in feeding gains are similar for both caching and non-caching birds (Figure 3).
|
At all levels of variance in foraging success, food-caching birds are predicted to cache food primarily in the morning and retrieve caches primarily in the evening. There is also a small peak in morning retrieval (Figure 4). These patterns derive from the trade-off between risk of starvation and risk of predation. Birds should cache early in the day when time is not limited, and when this activity can be performed at low mass levels (and therefore at lower predation risk). Mass levels must increase by dusk in order to meet nocturnal metabolic expenditures. Retrieval could be crucial when foraging has failed to provide enough energy to meet energetic costs. This is particularly true late in the day when foraging time is limited. However, food-caching birds get most of their energy from foraging and food caches constitute only a small part of their daily diet, even at the highest level of variability in foraging success (Figures 3 and 4). Nonetheless, probability of death of cachers at high levels of variance in foraging success is considerably lower than probability of death of non-cachers (Table 2). This result suggests that under the baseline conditions, caches are used only when feeding is not successful, and the strategic use of cached food can substantially decrease mortality rates.
|
Effect of food availability on energy reserves of food-caching
birds
Increasing mean foraging success by 12.5% over the baseline condition (0.22
g of fat/20 min) generates almost no changes in predicted fat reserves
(Table 3). However, the
increase in foraging success generates a reduction in cache size and a
reduction in probability of death (Table
3). A further increase to 25% over the baseline (0.24 g of fat/20
min) has a similar effect (Table
3). Higher foraging success reduces starvation risk and thus
decreases the value of cached food. When the mean foraging success was
decreased by 12.5% below the baseline value (0.17 g of fat/20 min), birds were
predicted to increase their fat reserves only slightly while greatly
increasing their number of caches (Table
3). The most interesting result here was that the optimal daily
pattern of caching activity changed dramatically when mean foraging success
was reduced below the baseline: birds were predicted to cache almost all day
with a peak in the evening (Figure
5) as opposed to the peak in the morning predicted for all other
conditions tested. The shift in daily caching pattern results from a shift in
time budget, especially a decrease in resting. In general, resting reduces
predation risk at the cost of the lack of energetic intake. This tradeoff is
not adaptive when birds must expose themselves to predation risk more in order
to avoid starvation, a condition that is met in our model with a reduction in
mean foraging success by 12.5% below baseline. Under these conditions, a bird
is most likely to eat early in the day, and show increased caching, resting
and retrieval late in the day (Figure
5). Late in the day, a bird will retrieve at the low body mass,
eat at intermediate mass and cache if it is relatively heavy (data not
shown).
|
Optimal daily retrieval patterns were similar for a wide range of foraging conditions (i.e., with both increased and decreased gain compared to baseline conditions) with a large peak in the evening and a small peak in the morning (Figure 5). Under reduced foraging success, retrieved caches represented a larger part of the diet during the evening compared to the baseline conditions (Figure 5). Finally, a reduction of foraging success to 25% below baseline (0.14 g of fat/20 min) results in an extremely high probability of death (Table 3).
Effect of lower temperature at night
For simplicity, in our baseline model we considered ambient temperature to
be constant at -5°C. Since air temperature during the night is usually
lower than during the day, we tested the model with a nocturnal temperature of
either -10°C or -15°C. We did not address the issue of hypothermia
(e.g., Reinertsen and Haftorn,
1986), because we have shown previously that use of nocturnal
hypothermia should not affect the daily mass patterns
(Pravosudov and Lucas, 2000).
In food-caching birds, lower temperature at night results in higher fat
reserves before roosting but there was almost no change in morning mass
(Figure 6). The birds are
predicted to gain just enough mass to compensate for higher losses during the
night. The optimal daily mass patterns were not predicted to change
qualitatively, but birds were predicted to gain more mass in the first part of
the day when ambient temperature at night was lower
(Figure 6). Optimal number of
maintained caches was predicted to increase with the higher nighttime energy
demands (Table 4). Non-caching
birds, on the other hand, were predicted to increase both morning and evening
fat reserves (Figure 6).
Reducing nighttime temperature affects probability of death more in
non-caching birds (Table 4; 38%
increase from -5 to -15°C) than in caching birds (21% increase).
|
Effect of higher metabolic cost of resting
For the baseline model, we assumed (following
Lucas and Walter, 1991) that
the metabolic cost of any activity is almost four times higher than the
metabolic cost of resting (Figure
1). However, McNamara et al.
(1990) assumed no difference
in metabolic costs between activity and inactivity for their baseline model,
so we tested whether these assumptions affected the results of our model. If
we increased the metabolic cost of resting from 1.95 BMR to 8.0 BMR (MR of any
activity), there is no qualitative change in the predictions and only a small
change in predicted levels of energy reserves: fat reserves decreased by 2%,
number of caches increased by 14%, and probability of death increased by 22%
compared to the baseline.
Effect of cache half-life
A reduction in the half-life of the cache had a profound effect on energy
management in caching birds. Number of caches was smaller at 10 days half-life
and caching ceased almost completely at 2.5 days cache half-life
(Table 5). The predicted level
of fat reserves and probability of death also increased with a decrease in
cache half-life (Table 5).
Effect of mean energetic gain from cache retrieval
If we double potential retrieval rates by increasing the value of
Nret (unconstrained minimal number of retrieved items per 20 min)
from five to 10, almost no changes were predicted in the levels of fat
reserves compared to the baseline conditions
(Figure 7A). However, at this
value of Nret number of caches was predicted to decrease by 22%.
When we increased Nret to 39.0 (making retrieval gain 13 times
larger than mean feeding gain as in
McNamara et al., 1990), the
optimal daily energy management patterns also were not predicted to change
appreciably. At Nret = 39, fat reserves were predicted to increase
by 1.9% (compared to the baseline) and the optimal daily trajectory of body
mass also remained unchanged (Figure
7A). Number of caches was predicted to be 28% smaller than that at
the baseline conditions. Optimal daily caching routines were not predicted to
change qualitatively (data not presented) and retrieval had a small peak in
the morning and a large peak at the end of the day at all modeled conditions
(Figure 7B). Thus, increasing
only the mean energetic gain from retrieval has almost no effect on any of the
patterns of interest.
|
Effect of variability in mean energetic gain from cache
retrieval
For the baseline model, we used zero variance in mean energetic gain from
cache retrieval (Figure 1B).
Increasing the variance of retrieval gain to about half of the variance in
foraging gain (baseline) had almost no effect on the predictions. When the
variance was increased further to that similar to the baseline variance in
foraging success, number of caches was predicted to decrease and fat reserves
to increase (data not presented). Since the variance in retrieval gain
indicates an uncertainty in getting such a reward, this result suggests that
when retrieval becomes more variable, it pays to invest more in fat reserves
and less in caches.
Effect of the almost linear relationship between predation risk and
body mass on model's predictions
For all of our calculations we assumed an exponential relationship between
risk of predation and body mass. When we simulated almost linear relationship
between risk of predation and body mass (as in
Lima, 1986:
Figure 1A) there were no
predicted changes in all daily patterns of energy management (for daily mass
trajectories see Figure 8A).
The only predicted differences were in absolute levels of fat and number of
caches: fat levels were predicted to decline by about 1% while number of
caches was predicted to increase by about 12% at the baseline conditions with
almost linear mass-dependent predation risk function.
|
|
DISCUSSION |
|---|
|
TOPABSTRACTINTRODUCTIONMODELRESULTSDISCUSSIONREFERENCES |
|---|
Our model supported some of the basic predictions of the previous dynamic models (Lucas and Walter, 1991
; McNamara et al.,
1990): birds should cache more food when: (1) foraging success
becomes more variable, (2) mean foraging success becomes lower, and (3)
overnight energy expenditures are increased. Our model also predicted that
caching birds should carry less fat than non-caching birds. However, contrary
to the results from McNamara et al.
(1990), our model under
baseline conditions predicted: (1) both caching and non-caching birds should
increase their fat reserves more rapidly during the first part of the day
slowing down toward late afternoon, and under a wide range of conditions there
is no qualitative difference between cachers and non-cachers in their optimal
daily mass trajectories (Figure
2), (2) caching occurs primarily in the morning (however, when
mean foraging gain was small, birds were predicted to cache more in the
evening), and (3) cache retrieval occurs mostly in the evening but there is
also a small peak in the morning. These predictions fit the patterns observed
in the field quite closely (Haftorn,
1989,
1992;
Lilliendahl, 1997).
All of the predicted energy management strategies are a direct result of
stochasticity of foraging built into the model. At any non-zero level of
variance in foraging success, birds should hedge against resource shortfall by
increasing their energy reserves. However, hedging strategies involve costs
(Lima, 1986;
McNamara and Houston, 1990):
mass-dependent metabolic rate, mass-dependent predation risk, and higher
predation risk when birds are foraging, caching or retrieving caches compared
to birds that are resting. One well-known consequence of these costs is a
foraging gain-predation risk trade-off that should cause the bird to regulate
its energy reserves at lower levels when variance in resource abundance is low
compared to conditions when variance is high
(Bednekoff and Krebs, 1995;
Ekman and Hake, 1990;
Lima, 1986;
Lucas and Walter, 1991;
McNamara and Houston, 1990).
In this respect, caching birds can maintain lower fat reserves than
non-caching birds because food caches provide a high-return, low variance food
source that can be built up when conditions are favorable (also see
Hurly, 1992 and
Hitchcock and Houston,
1994).
Optimal daily fat trajectories
Several different types of daily mass trajectory have been described in
birds monitored in the field. For example, in willow tits, a food-caching
parid, noon mass is significantly higher than morning mass (Haftorn,
1989,
1992), a result in line with
both our predictions and those of Brodin
(2000), but contrary to the
predictions of McNamara et al.
(1990). Haftorn
(1992) also showed that
diurnal mass patterns of caching parids were similar to those of non-caching
parids; this is also predicted by our model. Hurly
(1992) published daily mass
trajectories of marsh tits (Parus palustris) under laboratory
conditions. He suggested that the trajectories showed a delay in mass gain in
the middle of the day similar to that predicted in McNamara et al.
(1990). However, a closer
analysis of the trajectories he published indicate that two birds (of four
birds tested) exhibited a nearly linear increase in mass, and only one bird
showed a decrease in mass at midday. Thus, these results are more in accord
with the empirical data published by Haftorn
(1989,
1992) than with the
theoretical predictions from the McNamara et al.
(1990) model. Lilliendahl
(1997) published daily mass
patterns of willow tits (a caching bird) and great tits (a non-caching bird);
willow tits gained weight more rapidly in the morning, whereas great tits
showed a more linear mass gain over the course of the day. Finally, in
black-capped chickadees (Poecile atricapillus), a bimodal mass
increase (morning and afternoon) but no midday decline has been observed
(Graedel and Loveland,
1995).
Optimal daily eating routines
Under most parameter levels we simulated, our model predicted similar daily
eating routines for caching and non-caching birds. When foraging success is
variable, both groups of birds are predicted to eat most intensively in the
morning and least intensively in the evening. For non-caching birds, similar
feeding routines have been predicted by several previous models (e.g.,
Bednekoff and Houston, 1994a,
b;
McNamara et al., 1994). Such a
pattern in feeding rates is caused, in part, by no foraging interruptions and
high energetic requirements (McNamara et
al., 1994), conditions that we have simulated here.
Optimal daily patterns of caching and retrieval
Under most parameter levels we simulated, our model predicted that birds
should cache in the first part of a day and retrieve caches during the last
part of a day. This result agrees with previous models
(Lucas and Walter, 1991;
McNamara et al., 1990). Our
results disagree with the predictions by Brodin
(2000), who suggested that when
birds gain mass faster in the morning, they should cache in the middle of the
day. This discrepancy between Brodin's
(2000) model and our own are
discussed further below.
When mean foraging success was low, our model predicted more intensive
caching during the evening and less caching during the first part of a day
(Figure 6C). This result
suggests that the optimal daily routine of caching should be flexible and, in
some instances, change with altered environmental conditions. Indeed, while
many experimental studies showed a morning peak in caching (e.g.,
Lucas and Walter, 1991;
McNamara et al., 1990), Hurly
(1992) showed no consistent
diurnal pattern and Pravosudov and Grubb
(1997b) showed that birds
tended to cache more during the later part of the day. Results from our model
suggest that when foraging success is unpredictable and low, birds should not
risk their future survival by spending time on caching during the morning.
Instead, caching should be exhibited only after some insurance fat reserves
have been accumulated.
Most of the retrieval falls in the later part of the day under the
conditions we simulated. It seems that birds should retrieve caches only when
it could be critical for them to obtain sufficient reserves in a short time.
However, our model also predicted a small peak of retrieval in the morning
when fat reserves are at their minimum. Morning retrieval has generally not
been predicted by other models and it has not been observed frequently in the
field. However, morning retrieval has been observed in some experimental
studies (Pravosudov and Grubb,
1997b; but see Lucas and
Walter, 1991) supporting our predictions. It seems that birds
should use cached food only at critical times during the day: in the morning,
when the fat reserves are lowest and risk of immediate starvation is high, and
in the evening when it is crucial to reach some safe level of fat reserves to
survive the night.
It is important to note that McNamara et al.
(1990), Lucas and Walter
(1991), and Brodin
(2000) considered only
shortterm caching. Here we define short-term caches as those that are usually
retrieved within 30 days of storage. However, shortterm caching is not
universal (Vander Wall, 1990).
Boreal parids, such as Siberian (Parus cinctus) and willow tits
(P. montanus) can cache tens of thousands of food items in autumn and
retrieve these cached items several months later
(Brodin, 1994;
Haftorn, 1956;
Pravosudov, 1985). This
pattern is defined as a long-term caching behavior. Usually, when birds cache
food intensively during autumn, almost no short-term retrieval occurs since
food is plentiful (e.g., Haftorn,
1956; Pravosudov,
1985). Long-term caching strategies have been modeled by Brodin
and Clark (1997) and Smulders
(1998). However, even though
boreal parids use long-term caching tactics in the fall, their caching
patterns in the winter can be characterized as short-term (Pravosudov,
1983,
1985). In parids that occupy
milder climates, for example Carolina chick-adees (Poecile
carolinensis), intensive autumnal caching during short periods has not
been observed and they likely only cache food on a short-term basis (e.g.,
Lucas, 1994;
Lucas and Walter, 1991).
Indeed, short-term caching is characteristic of a variety of taxa occupying
milder climates (VanderWall,
1990). Thus the caching patterns that we have modeled are a
realistic description of energy management tactics of a fairly broad range of
species.
The value of cached food
It is important to note that no field data have been published on the rate
of energetic gain obtained from cache retrieval compared to the rate of gain
from ordinary foraging. We assumed that such a value is about two times more
than the mean gain from foraging. Brodin
(2000) considered a range of
values from 0.2 to 2.0. In their model of long-term caching, Brodin and Clark
(1997) used a smaller ratio of
retrieved versus encountered food energetic return. McNamara et al.
(1990) assumed that birds
could retrieve about 13 times more than the mean foraging gain. It is
difficult to justify any of these assumptions other than to note that stomach
capacity must limit how much a bird can physically consume
(Bednekoff and Houston, 1994a).
We can indirectly evaluate these assumptions by asking whether the model's
predictions correspond to observed trends. One such prediction concerns the
daily routine of body mass. Our predicted daily patterns of body mass match
field observations (see Haftorn,
1989,
1992) better than previous
models.
Our model predicted that birds should cache and retrieve a small amount of
food compared to the food consumed during foraging. In agreement with this
prediction, available field data on some boreal parids show that in the middle
of winter these birds may cache about 10% of food they find (Pravosudov,
1983,
1985). However, even limited
cache use is predicted to increase survivorship of caching birds
(Table 2). Field data on the
Eurasian nuthatch (Sitta europaea) showed that these birds retrieved
caches mostly when conditions were bad and not under favorable conditions
(Nilsson et al., 1993). This
suggests that if caches are long-lasting, birds might only use them during
critical periods, so even a small number of caches can enhance survival rates.
Similar conclusions about the importance of limited cache use have been
reached by Hitchcock and Houston
(1994), who modeled cache use
in acorn woodpeckers (Melanerpes formicivorus).
Longevity of caches
Another area for which we have inadequate field data is how long caches
last (Lucas and Zielinski
1998). Cache loss can include natural loss due to pilferage,
spoilage, and so on, and forgetting cache locations
(Lucas and Walter, 1991). In
our model, we assumed that if the location of an item is forgotten then the
cached item does not add to the pool of food available for foraging. If we
assumed that created caches increase overall food encounter rates, then caches
created by one individual would be available to another individual which does
not appear to be true (review Pravosudov
and Grubb, 1997b). Our model predicted that unless cache half-life
is more than 2.5 days, no caching should occur. Above this threshold, cache
size should increase with an increase in cache longevity. Mortality rates also
drop considerably with increased cache longevity. This result suggests that:
(1) birds should not cache if caches are pilfered intensively, and (2) longer
memory for caches promotes increased survivorship and increased reliance on
cached food. When caches disappear at a high rate, birds should abandon
caching and use fat reserves to hedge against stochastic foraging. Field and
experimental data indeed suggest some parids retrieve their caches up to 48
days after storing them (Brodin,
1994), and that they can remember their caches for 28 days in
experimental conditions (Hitchcock and
Sherry, 1990).
Few experimental studies have evaluated the effect of pilferage on caching
behavior. Hampton and Sherry
(1992) showed that pilferage
concentrated in one part of an aviary caused black-capped chickadees to alter
their use of the high-pilferage area, but no data were presented on the effect
of pilferage on caching rates. Kamil et al.
(1993) showed that Clark's
nutcracker (Nucifraga columbiana) similary avoid pilfered sites.
However, that study also did not ask whether pilferage affects caching rates.
Clearly more work needs to be done on this issue.
The conclusions from our model differ from conclusions based on models
developed by Brodin and Clark
(1997) and Smulders
(1998). Both previous models
indicated that memory constraints would have little influence on the fitness
of a caching animal. However, these models differ from ours in how they treat
forgotten caches. In our model, forgotten caches are lost. In the Brodin and
Clark (1997) and Smulders
(1998) models, forgotten
caches are still available to the bird and, more importantly, they increase
future food encounter rate. The difference between the models makes the
difference in predictions about the selective advantage of memory fairly
transparent. Ecological conditions should dictate which set of assumptions is
more realistic.
Energy expenditure
A previous model by Houston and McNamara
(1993) predicted that for
non-caching birds, increased energy expenditure should result in increased fat
reserves as a result of hedging against higher metabolic costs. In caching
birds, it was predicted that increased energy spent at night should result in
larger fat reserves and larger number of caches
(McNamara et al., 1990). Our
model similarly predicted that in both caching and non-caching birds, a
decrease in temperature overnight should result in fat levels elevated in the
evening and caching birds were predicted to increase their number of caches.
While non-caching birds were predicted to increase both morning and evening
mass, as predicted by Houston and McNamara
(1993), caching birds were
predicted to increase their evening fat reserves only
(Figure 6). It appears that
while non-caching birds increase their morning fat reserves to insure that
they can achieve a safe level of fat by the evening, caching birds should
increase morning cache rate instead of increasing fat reserves. The relative
fitness consequences of their use of caches in lieu of fat reserves is
illustrated in the lower mortality rates of caching birds compared no
non-cachers.
Haftorn (1992) argued that
birds do not store food in the winter when energy expenditures at night are
extremely high, because there is not enough food available to the birds.
However, some parids do cache some of their food even in the middle of the
winter (Pravosudov 1983,
1985), and the amount of
caching observed (approximately 10% of all items found) is in general
agreement with the amount of caching predicted by our model. Given that our
model predicts no caching under very limited food access, the field results
reported by Pravosudov (1983,
1985) imply that some parids
may have sufficient resources to support caching behavior.
Finally, our model predicts that increased nocturnal energetic expenditures should actually cause an increase in caching rates, assuming that enough food is available. It would be interesting to know if food-caching birds living in less extreme conditions would cache more under such conditions.
The McNamara et al.
(1990) model
Our model produced some results that are consistent with the results of the
McNamara et al. (1990) model.
Both models predict that variability in foraging success should result in
increased number of caches and that non-cachers should carry higher levels of
fat reserves than cachers (also see Lucas
and Walter, 1991). However, the optimal daily patterns of fat
reserves differ substantially between these two models. Why is there such a
difference? We have already shown above that increasing the gain from
retrieval of caches to 13 times larger than the mean gain from foraging (the
value used in McNamara et al.,
1990) does not change the optimal daily routines. If we add two
additional assumptions used in the McNamara et al.
(1990) model, complete loss of
caches overnight and no disappearance of caches during the day, we get results
similar to those of the McNamara et al.
(1990) model
(Figure 7). Now, fat reserves
are predicted to decline from the morning until the last time interval during
which the birds should increase mass by retrieving cached food. If we make
gain from cache retrieval only two times larger than mean foraging gain, but
assume overnight cache disappearance and no cache loss during the day, no
caching was predicted. Thus, the daily patterns of body mass of caching birds
described in McNamara et al.
(1990) appear to result from a
combination of assumptions which do not have strong empirical support: very
high gain from cache retrieval, loss of caches overnight and no loss of caches
during the day.
Brodin (2000)
model
Brodin (2000) suggested that
only a relaxation of the effect of mass-dependent predation risk (coupled with
other assumptions discussed below) will produce a daily pattern of body mass
in which hoarders gain more mass in the first part of the day (the
"field-like" pattern), as opposed to the morning reduction in mass
predicted by McNamara et al.
(1990). Lucas and Walter
(1991) came to the opposite
conclusion: that the mass-dependent component of predation risk does not have
a substantial effect on energy regulation. The discrepancy between these
models appears to result from several assumptions.
Our results suggest that Brodin's
(2000) conclusions are valid
only if the maximum number of caches a bird can store and maintain is quite
small. In his model, Brodin assumed a maximal number of caches of only 20
items (here scaled to our estimate of the value of each food item). In
addition, our results suggest that the set of conditions that Brodin
(2000) identified represent
only a small subset of possible conditions causing a `field-like' daily mass
pattern. For example, we found no substantial difference in diurnal mass
patterns predicted by our model at baseline conditions using exponential
mass-dependent predation risk function compared with an almost linear
mass-dependent predation risk function: in both simulation birds were
predicted to gain most mass in the first half of the day, a pattern
qualitatively similar to the "field-like" mass pattern
(Figure 8A). If, like Brodin
(2000), we reduced the maximum
number of caches to 20 caches, our model predicted mass patterns very similar
to ones predicted in Brodin
(2000) with highest mass
increase in the morning (Figure
8B). However, this pattern persisted whether we used a quadratic
mass-dependent predation risk function or an exponential function similar to
the function used by Brodin
(2000)
(Figure 8). In addition, Brodin
(2000) suggested that this
field-like pattern also results from cache retrieval being lower than the
energetic gain from foraging. This assumption does not seem to be particularly
robust: our model generates "field-like" daily mass patterns under
baseline conditions where retrieval rates exceed foraging rates. The only
conditions we could identify for which the shape of mass-dependent predation
risk changed predicted daily mass patterns was an increased mean foraging gain
coupled with a reduction in maximum number of caches
(Figure 8B). We also obtained
highest mass gain in the morning without limiting maximum number of caches to
20 caches, but by increasing mean energetic gain from feeding by 25% over the
baseline. Thus, while we can verify Brodin's
(2000) conclusions about the
influence of the effect of mass-dependent predation risk on diurnal mass
trajectories, our analysis adds two caveats to the conclusion. First, the
result appears to rely on a fairly restrictive assumption about maximum number
of caches. Second, in contrast to Brodin's
(2000) conclusions, there is a
broad range of additional conditions that generate the same predicted pattern
irrespective of the shape of mass-dependent predation risk.
Thus, unless there is some extreme constraint in the maximum amount of food
the birds can store, our analyses indicate that the different mass
trajectories referred to by Brodin
(2000), that is,
"field-like" versus those from McNamara et al.
(1990), do not derive from
differences in the mass-dependent component of predation risk (see
Lucas and Walter, 1991).
Indeed, there is no single factor that dictates the relative shape of the
diurnal mass trajectory. Mean levels of predation risk (as opposed to strictly
mass-dependent risk) will clearly affect this pattern. The rate at which food
is encountered and the variance in that rate also will affect the pattern.
Even day length is an important component in the expression of diurnal mass
trajectories (McNamara et al.,
1994), although this has not been addressed in any of the models
of caching behavior.
Finally, note that we assume that predation risk is the same for foraging
birds and for birds retrieving cached food. Brodin
(2000) assumed no predation
risk while retrieving food. If we relax our assumption by reducing predation
risk while retrieving to zero, our qualitative results are unchanged (data not
shown). Thus, this prediction about the predation cost of cache retrieval is
not the basis for the differences between our model and Brodin's
(2000) model.
In conclusion, our model provides a general understanding of the factors that affect energy management strategies of organisms living in unpredictable environments. Factors that we considered in our model such as variability and availability of food supply, risk of predation, metabolic expenditure, and ambient temperature are critical elements of the optimization of energy management tactics for virtually all animals. While the details of ecological tradeoffs may vary from one species to the next (e.g., cost of carrying fat in flying and non-flying organisms could be different), we have continued the development of an integrated, multidimensional approach that will provide a general framework for the study of complex decision-making under realistic ecological conditions.
|
ACKNOWLEDGEMENTS |
|---|
V.V.P. was supported by a NSF Research Postdoctoral Fellowship in Biosciences Related to the Environment awarded in 1997. Part of the research described here was supported by NSF grant IBN-9222313 (to J.R.L.). We thank Denise Zielinski, Todd Freeberg, Jim Kellam, Karen Munroe, Joy Lewis, Colin Clark, Peter Waser, David Westneat, and two anonymous reviewers for criticism of the manuscript.
|
REFERENCES |
|---|
|
TOPABSTRACTINTRODUCTIONMODELRESULTSDISCUSSIONREFERENCES |
|---|
Bednekoff PA, 1996. Translating mass dependent flight performance into predation risk: an extension of Metcalfe and Ure. Proc Royal Soc Lond B, Biol Sciences 263: 887-889.
Bednekoff PA, Houston AI, 1994a. Avian daily foraging patterns: effects of digestive constraints and variability. Evol Ecol 8: 36-52.[Web of Science]
Bednekoff PA, Houston AI, 1994b. Optimizing fat reserves over the entire winter: a dynamic model. Oikos 71: 408-415.
Bednekoff PA, Krebs JR, 1995. Great tit fat reserves: effects of changing and unpredictable feeding day length. Functional Ecol 9: 457-462.
Blem CR, 1990. Avian energy storage. Curr Ornithol 7: 59-113.
Brodin A, 1994. Time aspects of food hoarding
in the willow tit (PhD Dissertation). Stockholm, Sweden: Stockholm
University.
Brodin A, 2000. Why do hoarding birds gain fat in
winter the wrong way? Suggestions from a dynamic model. Behav
Ecol 11
27-39.
Brodin A, Clark CW, 1997. Long-term hoarding in the Paridae: a dynamic model. Behav Ecol 8: 178-185.[Web of Science]
Buttemer WA, Hayworth AM, Weathers WW, Nagy KA, 1986. Timebudget estimates of avian energy expenditure: physiological and meteorological considerations. Physiol Zool 59: 131-149.[Web of Science]
Carlson A, Moreno J, 1992. Cost of short flights in the willow tit measured with doubly-labeled water. Auk 109: 389-393.
Chaplin SB, 1974. Daily energetics of the black-capped
chickadee, Parus atricapillus, in winter. J Comp
Physiol 89:
321-330.
Ekman JB, Hake MK, 1990. Monitoring starvation risk: adjustments of body reserves in greenfinches (Carduelis chloris L.) during periods of unpredictable foraging success. Behav Ecol 1: 62-67.
Graedel SK, Loveland RE, 1995. Seasonal and diurnal mass variation in black-capped chickadees and white-throated sparrows. Wilson Bull 107: 723-727.
Grubb TC Jr, Pravosudov VV, 1994. Toward a general theory of energy management in wintering birds. J Avian Biol 26: 255-260.
Haftorn S, 1989. Seasonal and diurnal body weight variations in titmice, based on analyses of individual birds. Wilson Bull 101: 217-235.
Haftorn S, 1992. The diurnal body weight cycle in titmice Parus spp. Ornis Scand 23: 435-443.
Haftorn S, 1956. Contribution to the food biology of tits, especially storing of surplus food. Part IV. A comparative analysis of Parus atricapillus L., P. cristatus L., and P. ater L. K Norske Vidensk Selsk Skr 4: 1-54.
Hampton RR, Sherry DF, 1992. The effect of cache loss
on choice of cache sites in black-capped chickadees. Behav Ecol
5: 44-50.
Hitchcock CL, Houston AI, 1994. The value of a hoard: not just energy. Behav Ecol 5: 202-205.
Hitchcock CL, Sherry DF, 1990. Long-term memory for cache sites in the black-capped chickadee. Anim Behav 40: 701-712.
Houston AI, McNamara JM, 1993. A theoretical investigation of the fat reserves and mortality levels of small birds in winter. Ornis Scand 24: 205-219.[Web of Science]
Houston AI, Welton NJ, McNamara JM, 1997. Acquisition
and maintenance costs in the long-term regulation of avian fat reserves.
Oikos 78:
331-340.
Hurly TA, 1992. Energetic reserves of marsh tits (Parus palustris): food and fat storage in response to variable food supply. Behav Ecol 3: 181-188.
Kamil AC, Balda RP, Olson DJ, Good S, 1993. Returns to emptied cache sites by Clark's nutcrackers, Nucifraga columbiana: a puzzle revisited. Anim Behav 45: 241-252.[Web of Science][Medline]
Kullberg C, 1998. Does diurnal variation in body mass affect take-off ability in wintering willow tits? Anim Behav 56: 227-233.
Lehikoinen E, 1987. Seasonality of the daily weight cycle in wintering passerines and its consequences. Ornis Scand 18: 216-226.
Lilliendahl K, 1997. Daily patterns of body mass gain in four species of small wintering birds. In: fattening strategies in wintering passerines (PhD dissertation). Stockholm: Stockholm University.[Web of Science]
Lima SL, 1986. Predation risk and unpredictable
feeding conditions: determinants of body mass in birds. Ecology
67: 377-385.
Lucas JR, 1994. Regulation of cache stores and body mass in Carolina chickadees (Parus carolinensis). Behav Ecol 5: 171-181.[Web of Science]
Lucas JR, Howard RD, 1995. On alternative reproductive tactics in anurans: dynamic games with density and frequency dependence. Am Nat 146: 365-397.
Lucas JR, Walter LR, 1991. When should chickadees
hoard food? Theory and experimental results. Anim Behav
41: 579-601.
Lucas JR, Zielinski DL, 1998. Seasonal variation in the effect of cache pilferage on cache and body mass regulation in Carolina chickadees: what are the trade-offs? Behav Ecol 9: 193-200.
Mangel M, Clark CW, 1988. Dynamic modeling in behavioral ecology. Princeton, New Jersey: Princeton University Press.[Web of Science][Medline]
McNamara JR, Houston AI, 1990. The value of fat
reserves and the trade-off between starvation and predation. Acta
Biotheor 38:
37-61.
McNamara JR, Houston AI, Krebs JR, 1990. Why hoard? The economics of food storing in tits, Parus spp. Behav Ecol 1: 12-23.
McNamara JR, Houston AI, Lima SL, 1994. Foraging
routines of small birds in winter: a theoretical investigation. J Avian
Biol 25:
287-302.
Metcalfe NB, Ure SE, 1995. Diurnal variation in flight
performance and hence potential predation risk in small birds. Proc R
Soc Lond B Biol Sci 261:
395-400.
Nilsson J-A, Kallander H, Persson O, 1993. A prudent hoarder: effects of long-term hoarding in the European nuthatch, Sitta europaea. Behav Ecol 4: 369-373.
Pravosudov VV, 1983. Tits' feeding rate during winter in northern taiga (in Russian). Vestn Leningr Univ 21: 16-22.
Pravosudov VV, 1985. Search for and storage of food by Parus cinctus lapponicus and P. montanus borealis (Paridae) (in Russian). Zool Zh 64: 1036-1043.
Pravosudov VV, 1987. Ecology of two closely related species of tits (Parus cinctus and P. montanus) in the north western part of the USSR (in Russian). Ornitologia (Moscow) 22: 68-75.
Pravosudov VV, Grubb TC Jr, 1997a. Energy management
in passerine birds during the nonbreeding season: a review. Curr
Ornith 14:
189-234.
Pravosudov VV, Grubb TC Jr, 1997b. Management of fat reserves and food-caches in tufted titmice (Parus bicolor) in relation to unpredictable food. Behav Ecol 8: 332-339.[Web of Science]
Pravosudov VV, Grubb TC Jr, 1998. Management of fat reserves in tufted titmice (Parus bicolor): evidence against a trade-off with food hoards. Behav Ecol Sociobiol 42: 57-62.
Pravosudov VV, Lucas JR, 2000. The costs of being cool: a dynamic model of nocturnal hypothermia by small food-caching birds in winter. J Avian Biol 31: 463-472.
Reinertsen RE, Haftorn S, 1986. Different metabolic strategies of northern birds for nocturnal survival. J Comp Physiol 156: 655-663.[Web of Science]
Sherry DF, Avery M, Stevens A, 1982. The spacing of stored food by marsh tits. Z Tierpsychol 58: 153-162.[Web of Science][Medline]
Smulders TV, 1998. A game theoretical model of the evolution of food hoarding: applications to the Paridae. Am Nat 151: 356-366.[Web of Science]
Stevens TA, Krebs JR, 1986. Retrieval of stored seeds by marsh tits Parus palustris in the field. Ibis 128: 513-525.[Web of Science]
Weathers WW, Buttemer WA, Hayworth AM, Nagy KA, 1984. An evaluation of time-budget estimates of daily energy expenditure in birds. Auk 101: 459-472.[Web of Science][Medline]
Witter MS, Cuthill IC, 1993. The ecological costs of avian fat storage. Phil Trans R Soc Lond B 340: 73-92.
Witter MS, Cuthill IC, Bonser RH, 1994. Experimental investigations of mass-dependent predation risk in the European starling, Sturnus vulgaris. Anim Behav 48: 201-222.
Vander Wall SB, 1990. Food hoarding in animals. Chicago: University of Chicago Press.[Web of Science][Medline]
Veasey JS, Metcalfe NB, Houston DC, 1998. A reassessment of the effect of body mass upon flight speed and predation risk in birds. Anim Behav 56: 883-889.
CiteULike 
Connotea 
Del.icio.us What's this?
This article has been cited by other articles:
|
|
 |
|
  T. C Roth II and V. V Pravosudov Hippocampal volumes and neuron numbers increase along a gradient of environmental harshness: a large-scale comparison Proc R Soc B, February 7, 2009; 276(1656): 401 - 405. [Abstract] [Full Text] [PDF]
|
|
|
|
 |
|
 J. M McNamara and A. I Houston Optimal annual routines: behaviour in the context of physiology and ecology Phil Trans R Soc B, January 27, 2008; 363(1490): 301 - 319. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
A. Brodin Theoretical models of adaptive energy management in small wintering birds Phil Trans R Soc B, October 29, 2007; 362(1486): 1857 - 1871. [Abstract] [Full Text] [PDF]
|
|
|
|
 |
|
 J. P. Kelly and W. W. Weathers Effects of feeding time constraints on body mass regulation and energy expenditure in wintering dunlin (Calidris alpina) Behav. Ecol., November 1, 2002; 13(6): 766 - 775. [Abstract] [Full Text] [PDF]
|
|
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||