AMER. ZOOL., 27:337-346 (1987)
The Tradeoff Between Territorial Defense and
Foraging in the Great Tit (Parus major)1
RONALD C. YDENBERG
Department of Biological Sciences, Simon Fraser University,
Burnaby, B.C. V5A 1S6, Canada
AND
JOHN R. KREBS
Edward Grey Institute of Field Ornithology, South Parks Rd.,
Oxford 0X1 3PS, England
SYNOPSIS. We analyze territorial behavior in terms of decisions about time allocation.
Such decisions must be made whenever time invested in territorial defense cannot be
devoted to feeding, and vice versa. We describe the ecology and territorial behavior of the
great tit (Parus major) to show that a tradeoff exists, and then outline a series of laboratory
and field experiments in which the value of feeding or defense was experimentally manipulated. Territorial male great tits began to invest more heavily in territorial vigilance after
encountering intruders, but the increase in vigilance depended on the rate at which they
could feed, as well as their hunger level. We outline a dynamic analysis that takes account
of the fact that the optimal tradeoff will change as hunger is reduced. The results of an
experimental test of this dynamic model are also presented. We briefly review other
techniques whereby territorial tradeoffs have been investigated.
INTRODUCTION
defense mechanics on territory size (KnapMost recent research on territoriality has ton and Krebs, 1974; Dill et al, 1981; Maytaken one of three main approaches: (i) The nard Smith, 1982). (iii) Ecological implica-
economics of resource defense and exploitation tions of resource defense, especially studies of
the role of territoriality in inter- and intraspecific competition (Reed, 1982; Garcia,
1983; Dunbrack, 1984) and studies of the
relationship between territorial spacing and
population dynamics (Patterson, 1980).
In this paper we review some of our work
which considers a fourth approach to territorial behavior, one which has received
less attention than the other three. We will
discuss how a territorial individual allocates its time between resource defense and
resource exploitation. Our work is not concerned with simply describing the time
areas, (ii) Behavioral mechanisms of resource budgets of territory holders, but lays the
defense, including experimental (Smith, emphasis on trying to use experimental
1976; Krebs, 1977; Yasukawa, 1981) and manipulations to elucidate some of the factheoretical (Maynard Smith, 1982) work tors involved in time allocation. Our
on the use of different levels of defense account begins with a consideration of
such as ritualized displays and escalated causal factors but we will also discuss funcfighting, and work on the influence of tional aspects.
Central to this approach is the idea that
the defense and exploitation of resources
are conflicting activities. Behavior related
' From the Symposium on Territoriality: Conceptual
to preserving resources for future use (e.g.,
Advances in Field and Theoretical Studies presented at
the Annual Meeting of the American Society of Zool- territorial song or scent-marking) takes
ogists, 27-30 December 1984, at Denver, Colorado. place at the expense of feeding time. The
mainly of feeding territories {e.g., Gill and
Wolf, 1975; Carpenter and MacMillen,
1976; Pyke, 1979; Parker and Knowlton,
1980; Davies and Houston, 1981; Myers et
al, 1981; Schoener, 1983). This work,
which stems largely from Brown's (1964)
seminal paper on the economic defendability of resources, has dealt with questions such as the range of resource levels
for which defense gains exceed costs, the
optimum or evolutionally stable amount of
resource to defend, and patterns of
resource exploitation within exclusive
337
338
R. C. YDENBERG AND J. R. KREBS
long term benefit must be balanced against
the short term cost, and natural selection
will favor animals which do this efficiently.
This kind of conflict is a feature of many
territorial systems. For example, Jaeger et
al, (1981) describe the territorial scentmarking behavior of the salamander Plethodon cinereus. Under some circumstances
these animals frequently interrupt foraging to touch pheromone-producing glands
on the chin or cloaca to the substrate. Each
scent mark takes a few seconds and so
increases the interval between prey
encounters. The inference is that this short
term cost is compensated by a long term
benefit (sustained yield; see Jaeger et al.,
1981). Paton and Carpenter (1984) show
that rufous hummingbirds (Selasphorus
rufus) forage primarily in the edge areas of
their territories in the first few daylight
hours, and exploit the center later in the
day. The most efficient foraging pattern
would spread foraging effort evenly over
the territory, but since intruders are able
to rob most effectively along edges, the residents' foraging pattern appeared to be
aimed at minimizing nectar losses to
intruders. The hummingbirds were able to
more than make up the short term loss in
early morning feeding efficiency caused by
their defense policy, because the territory
center contained a rich nectar supply later
in the day.
We will describe how the ecology of our
study animal, the great tit (Parus major),
makes its defense and exploitation behavior incompatible. In his review of territorial behavior Schoener (1983) assumes that
defense always takes priority over feeding,
but we assume that great tits must balance
the two, and so feeding may sometimes have
priority.
TIME ALLOCATION IN TERRITORIAL
GREAT T I T S
General biology of the great tit
The great tit is a small (20 g) insect and
seed eating passerine resident throughout
England. Food is, at least in some years, a
limited resource at the time when great tits
establish and maintain territories (Gibb,
1960; van Balen, 1980). In Wytham Wood,
Oxford, spring territorial behavior starts
in January when paired males begin to sing
and chase. By mid-February boundaries are
clearly delineated. These boundaries
remain stable with minor changes through
the breeding season (April-June) until territories break up after the young become
independent. During the spring territorial
period great tits spend a large proportion
of their day feeding (up to 90%—Gibb,
1960) and forage mainly within 3 m of the
ground while territorial defense, especially
song, takes place in the canopy about 10
m from the ground (Hunter, 1978). Territorial and feeding activities are incompatible because they are done in different
microhabitats. Zach and Falls (1979) and
Rich (1985) describe similar situations in
the ovenbird Seiurus aurocapillus and sage
sparrow Amphispiza belli, respectively. Later
in the spring, great tits switch to feeding
in the canopy, where they glean tiny insects
from the swelling leaf buds. Males move
around their territories, pausing between
feeding stops to sing and call, or to watch
and listen. They quickly react to any other
great tits encountered within the territory
or at the boundary. Territorial interactions between established neighbors consist generally of song, but when new territories are set up physical contact and
visual displays are more frequent. The
degree of escalation required to evict
intruders increases as a function of the time
that the intruder is allowed to stay on the
territory (Krebs, 1982), and so we suppose
that it is advantageous to detect intruders
quickly.
This brief account of territorial behavior in the great tit suggests that the allocation of time to defense might be influenced by factors associated with both
feeding and intrusions: since the birds
spend most of their day foraging it is likely
that feeding requirements set an upper limit
on the time that can be invested in territorial defense, and because the cost of
evicting intruders increases if they are
allowed to persist on the territory, time
allocation should also be influenced by the
presence of intruders.
FEEDING VS. TERRITORIAL VIGILANCE
339
an experimental session. The intrusion site
was arranged so that it could not be seen
from either patch but could be viewed while
It will be useful first briefly to describe a bird travelled between patches. Kacelnik
some methodological details common to all et al. (1981) found that in control sessions
the laboratory experiments. In the exper- with no intruder, the birds tended to switch
iments we report here male great tits were between patches according to the pattern
housed in separate outdoor flight cages, that maximized intake rate, but that after
and could be admitted to an indoor arena the brief intruder presentation they shortwhere the experiments took place. The ened patch visits and thus switched more
males behaved very aggressively both in frequently. This resulted in the birds
and out-of-doors, evidently regarding the spending a higher proportion of time travflight cage and the indoor arena as "ter- elling and less time feeding: the birds
ritory." In the arena the birds fed from an appeared to sacrifice intake rate for the
operant patch consisting of a perch on chance to monitor the intrusion site.
which they hopped to obtain prey items
This interpretation was investigated fur(small fly pupae) from a dispensing device. ther by Ydenberg (1982) who added an
More complete descriptions of the aviaries, additional control. He compared the effect
the training procedure and the equipment of exposing the test birds to intrusions in
used can be found in Kacelnik et al. (1981) two conditions: (a) when the intrusion site
and Ydenberg (1984a). Intrusions were could be monitored from the feeding
arranged by briefly exposing a male great patches and (b) when it could not. This
tit held in a cage to the resident male, while manipulation was achieved by placing
simultaneously broadcasting song through either a clear (wire mesh) or an opaque
speakers placed next to the cage. A door (black plastic) screen between the feeding
could be raised and lowered remotely to patches and the intrusion site. If the change
control the exposure.
in foraging behavior following an intrusion
We first examine how the organization observed by Kacelnik et al. was specifically
of feeding behavior changes when vigi- related to territorial vigilance, and was not
lance becomes important. The experi- a general effect due to the procedure {e.g.,
ments we report here are an extension of disturbance), it should be seen only in the
those of Kacelnik et al. (1981), who trained opaque screen treatment when vigilance
captive male great tits to obtain food by and feeding were incompatible.
working in two operant patches. The
Table 1 shows that compared with the
patches delivered food items (pupae) on a no intruder treatment, the birds' overall
progressive ratio schedule, in which each feeding rate was significantly depressed in
successive food item required more the opaque screen intrusion treatment, but
responses (perch hops). Thus for example not in the clear screen intrusion treatment.
the first pupa in a patch might be delivered This supports the hypothesis that feeding
after the second hop, the second after the rate was sacrificed specifically to increase
sixth hop, the third after the twelfth and vigilance. Examining the effects of intruso on. At any point the bird could reset a sions on the birds' behavior in more detail
patch to its initial state by switching to the shows that, as in the experiments of Kacelalternate patch. This arrangement was nik et al., patch residence times shorten
designed to mimic the process of patch (Table 1). However, the largest change in
depletion: the birds maximized their intake behavior is in the allocation of time to
rate by switching between patches at a point travel. Travel time between the patches is
defined by the discrete analogue of the almost three times longer in the opaque
marginal value theorem (Charnov, 1976). screen treatment than in the control. Even
The effect of territorial intrusions on feed- in the clear screen treatment, in which the
ing was investigated by briefly exposing the resident could view the intrusion site from
test bird to an intruder before the start of the operant patch, travel time doubled. The
The influence of intrusions on
feeding behavior
340
R. C. YDENBERG AND J. R. KREBS
"hunger." The response to an intruder was
measured at two levels of food availability:
Feeding rate6
Travel time (sec)
"high," in which one food item was deliv(Pupae/min)
I reatment
between patches'1
ered every fourth hop on the perch in the
Control
2.31 ± 0.15 9.0 ± 0.5 8.14 ± 1.31
operant patch, and "low," in which a pupa
Clear
was delivered every 20th hop.
screen 2.25 ± 0.14 7.6 ± 0.3 13.52 ± 2.73
There was a bigger increase in singing
Opaque
rate in response to the intrusion when food
1.87 ± 0.10 7.9 ± 0.5 20.76 ± 5.46
screen
"Results of Ydenberg (1982). Mean ± standard availability was low than when it was high.
Paralleling this, the drop in feeding rate
error.
b
Heterogeneity between treatments (ANOVA), P <
during intrusions was greater in low than
0.025. A posteriori comparison between means: "clear" high availability trials on 15 out of 21 occaand "opaque" screen treatments differ, as do "con- sions and there tended to be more attacks
trol" and "opaque screen."
c
Heterogeneity between treatments (ANOVA), P < directed to the intruder in low availability
0.025. A posteriori comparison between means: both sessions (see Kacelnik and Krebs [1983] for
screened treatments differ from "control."
more details). One interpretation of these
d
Heterogeneity P < 0.025 between treatments results is that when incentive (food avail(ANOVA), only "control" vs. "opaque" significant ability) is low, feeding motivation (which is
on a posteriori test.
known to depend on both deficit and incentive—Sibly, 1975) is lowered relative to that
increase in travel time arose because the associated with attacking the intruder. In
great tit males no longer flew directly from functional terms the same idea could be
one patch to the other as in the control expressed by saying that when food availtreatment, but instead paused at a central ability is low, the cost in terms of lost feeding opportunity of giving up foraging is
perch, and sang or called.
It is important to note that the test males reduced.
gradually changed their behavior as they
In a related field experiment we invesfed to satiation in the course of each trial. tigated the effect of providing supplemenFor example, the time they took to travel tary food to wild territorial males on their
between the patches increased with each responsiveness to simulated intrusions
successive trip while the patch residence (Ydenberg, 1984ft). There were two catetime decreased (Ydenberg, 1982). These gories of provisioned males: "owners" had
progressive changes occurred in both the a feeding table placed within their terripresence and absence of intruders, but were tories, while "visitors" travelled to feeders
made more rapidly after exposure to the placed on neighboring territories. Control
intruder. We consider this point in more males did not visit any feeding tables. When
detail below.
both owners and visitors had been taking
food for at least five days, each male was
The influence of food availability and
exposed to a single simulated intrusion, in
deficit on territorial defense
which a stuffed male great tit on a 1 m high
stake
and one minute of song playback were
We now consider how food availability
presented
simultaneously. Figure 1 summay influence the response to intruders.
Kacelnik and Krebs (1983) report an marizes the results. Both groups of birds
experiment in which the response of cap- that had access to the supplementary food,
tive male great tits to a standard intrusion owners and visitors, responded more
was measured. The birds were deprived of strongly to the intrusion than did control
food in a carefully controlled way before birds. The experimental birds took less time
the start of each experimental session, in to make their closest approach, spent more
order to regulate as exactly as possible their time close to the dummy and were more
food deficit, defined as the difference likely to attack; in contrast, the control birds
between a bird's current cumulative intake used more song, a response which was given
and the target level (at the end of the day). from a distance in these experiments.
This definition corresponds roughly to
The similar behavior of visitors and ownTABLE 1.
Effects on feeding of presenting an intruder.'
Patch visit
length'
(Hops)
341
FEEDING VS. TERRITORIAL VIGILANCE
latency to closest
approach
500
time spent
•OOm
(s)
50
40
300
30
200
20
100
10
0
RICH TERRITORY (R)
UJ
DEFENSE (D)
FEEDING
0
FIG. 1. Territorial response to a simulated intrusion
(playback of song plus presentation of a dummy) by
three classes of wild male great tits. Table-owners (O)
and table-visitors (V), both receiving supplementary
food, respond more intensely than controls (C). Owners and visitors behave similarly: they take significantly less time to travel to the site of the intrusion
(latency to closest approach; P < 0.001; Mann-Whitney U-test) and spend more time near the dummy,
much of it out of the canopy, where all feeding takes
place (P < 0.025). In contrast control birds sing more,
a "cheaper" response, in that it is compatible with
feeding and is given from a distance.
ers argues against one possible interpretation of the results, namely that the provisioned birds were defending the rich
resource supply, and instead favors the idea
that supplementary food allowed the birds
to invest more time in territorial activity
by allowing them to meet their food
requirements more rapidly. The laboratory and field results, therefore, both suggest an effect of food availability on
territorial defense, but in apparently contradictory ways. In the laboratory, the birds
were more responsive to intrusions when
food availability was low, but in the field
responsiveness was higher when birds had
been given extra food.
One way to resolve these contradictory
results is suggested by considering details
of the experimental procedure, and their
effect on the test birds' food deficits. So
far we have not taken account of deficit,
except to note in the last section that the
birds gradually changed their behavior in
the course of each experimental trial. In
the laboratory the test bird's cumulative
intake was carefully regulated so that all
the birds were equally hungry. However in
the field experiment, the additional food
altered both food availability and food def-
B control males
low-
FOOD RESERVES
* provisioned males
high
FIG. 2. The benefit gained from feeding and defense
as a function of internal food reserves, on territories
with a rich (R) and poor (P) food supply. The benefit
of any activity is represented as the increase in fitness
that results, measured as a proportion of the fitness
gain possible from all activities. For example, when
food reserves are zero so that any increase in deficit
leads to starvation, all the benefit that could be gained
on both rich and poor territories comes from feeding,
so the curves converge. At any higher level of food
reserves, more benefit is gained from feeding on a
rich than on a poor territory. Defense benefits are
independent of internal food reserves and of food
supply on the territory because the loss of a territory
means the loss of allfitnesson both types of territories.
When an intruder is encountered, the resident must
decide to defend or to continue to feed, and we assume
it chooses the activity yielding the highest benefit. In
the laboratory experiment of Kacelnik and Krebs
(1983) the internal food reserves of the males with
poor and good food supplies were identical (labelled
A), and so the males with poor food supplies stood to
gain more from defense since (D — P) > (D — R). In
Ydenberg's (19846) field experiment, both internal
food reserves and food availability varied (labelled B),
and we hypothesize that (D — R) > (D — P) as shown
in the figure, so that males on rich territories stood
to gain more from switching to defense. Complete
details are given in Ydenberg 19846.
icit; the provisioned birds were very likely
less hungry than the control birds. The
possible importance of these procedural differences can be illustrated by a simple
model in which we consider the additional
benefit that birds on rich (=high food availability) and poor territories gain by switching from feeding to defense. The model is
outlined in Figure 2.
Summarizing the main points of this section, feeding behavior in the laboratory is
influenced by brief intrusions in ways which
are consistent with the interpretation that
342
R. C. YDENBERG AND J. R. KREBS
birds lower their food intake rate to monitor intrusion sites. The response of territorial great tits to simulated intrusions in
the laboratory and in the field is influenced
by both food availability and food deficit.
A DYNAMIC OPTIMIZATION APPROACH
TO THE FORAGING-DEFENSE TRADEOFF
We now turn from a consideration of
some causal factors influencing time allocation to an attempt to integrate causal and
functional approaches in a dynamic optimization model. From a functional standpoint, the male great tit's time allocation
problem can be viewed as one of minimizing the costs associated with territorial
defense. The nature of these costs and their
relationship to time allocation is intuitively
obvious, but the problem is to find a method
of combining the costs into a single function and derive some predictions about time
allocation. The problem is clearly a
dynamic one, because the best policy of
time allocation will change as a function of
the animal's deficit: a bird close to starvation should give most of its attention to
feeding, but as a result of feeding its deficit
will be reduced, thereby changing the best
policy for allocating behavior. Thus a complete functional account of the tradeoff
problem has to include some consideration
of how the animal's state changes in relation to behavior. One method of analyzing
this sort of problem is dynamic optimization (Sibly and McFarland, 1976; Milinski
and Heller, 1978; Mirmirani and Oster,
1978; McFarland and Houston, 1981). In
this section we describe a dynamic optimization analysis of great tit behavior and
its application to the experiments referred
to earlier in which males allocate time to
feeding and monitoring intrusion sites in
an aviary. The account is based on that of
Ydenberg and Houston (1986).
intrusion costs arise from the fact that time
and energy must be spent evicting intruders. These costs rise the longer intruders
are allowed to persist (Krebs, 1982).
First consider food deficit. The rate at
which deficit can be reduced (x) is related
to the rate of food intake in a patch and
to time allocation in the following way:
(1)
Bh + T
where B = number of hops in the feeding
patch during a vist (i.e., patch residence
time; h = time to make one hop; T = travel
time). This relationship depends on the
reward schedule set by the experimenter;
in this case B hops yield, on average, \ / B
rewards. This form of reward schedule was
chosen because it led easily to a tractable
solution, but in principle any reward schedule could have been used.
The cost function consists of two parts:
(1) intrusion and (2) deficit costs. A simple
way to treat intrusion cost is to assume that
it increases linearly with time spent in a
patch (when the bird is not vigilant), but is
inversely related to time spent travelling,
when the bird can monitor its territory, so
that longer travel is beneficial from a vigilance standpoint. Accordingly,
x = —
C, = k,B + 2k 2 /T
(2)
where kj and k2 are constants proportional
to the rate of intrusion (2k2 is used purely
for mathematical convenience). This is the
simplest form of the cost function which
we feel matches the biology of the great
tit. Essentially it means that longer visits to
the patches are more costly (less territorial
vigilance), while longer trips between
patches are less costly (more vigilance so
that intruders can be detected sooner). The
deficit costs can be written as
(3)
C2 = f(x)
In the experimental setup, the two kinds
of cost, internal food deficit and intrusion, The exact form of (3) is not important, so
depend on time spent in patches and on long as the cost function is separable into
time spent travelling between them: these terms in x and those in B, T (i.e., the intruare the variables that the animal can con- sion costs do not depend on the hunger
trol to regulate the costs. The deficit costs level; see Ydenberg and Houston, 1986).
are those associated with the hunger or The complete cost function is
food reserve level (e.g., risk of starvation,
McFarland and Houston, 1981). The
(4)
C = C, + C2
343
FEEDING VS. TERRITORIAL VIGILANCE
The dynamic optimization problem is to
reduce food deficit while minimizing the
time integral of (4). Solving this will specify
how the optimal relationship beweeen B
and T changes as deficit is reduced. Ydenberg and Houston (1986) apply Pontryagin's Maximization Principle (abbreviated
PMP; for detailed accounts of the biological applications of PMP see McFarland and
Houston, 1981; McNeill Alexander, 1982)
and show that the relationship between
patch residence time and travel time which
minimizes intruder costs is:
HUNGER.
declining food deficit
. SATIATION
uj
2
UJ
Q
CO
o
10
15
20
25
TRAVEL TIME (s)
B=
2
KT + h
(5)
where K = k,/k 2 (see Fig. 3).
We need to outline exactly what (5) says:
it specifies only the relationship between B
and T. The model does not predict explicitly how B and T change with time because
the co-state variable (X) whose function this
is cancelled out in the manipulations leading to (5). The equation specifies, for each
observed T, the residence time that minimizes intrusion costs. The knowledge that
the B-T time course should move from left
to right on Figure 3 comes from the observation (see above) that the travel time
increases as the birds feed.
The mathematical details of this procedure can be found in Ydenberg and
Houston (1986; see also Houston and
McNamara, 1985), but we can give an intuitive interpretation as follows. A hungry
bird waking up in the morning starts in the
bottom left hand corner of the trajectory
in Figure 3. As the animal reduces the deficit it gradually increases the time spent
travelling, and therefore in vigilance. The
relationship between B and T which maximizes intake rate is described by Charnov's marginal value model (Charnov,
1976), which predicts that as T increases,
so should B. When hungry, feeding is
important enough for the bird to increase
B in response to increases in T in a way
predicted by the marginal value model.
Eventually, however, internal food deficit
is sufficiently reduced so that patch residence time can be shortened for a further
gain in vigilance, and increases in T no
FIG. 3. The optimal tradeoff between patch residence time (measured in hops on the perch in the
operant patch) and travel time (in seconds) when there
are costs imposed by territorial intruders. All trajectories begin at low travel times (highest feeding rate)
and move to the right as food deficit is reduced. The
marginal value theorem (Charnov, 1976) shows that
in order to maximize energy intake, patch residence
time should increase in response to lengthening travel
times. (It should be noted that the marginal value
therorem explicitly does not consider cases where
intrusion is important.) The tradeoff model developed here incorporates costs arising from intruders
which increase while the male feeds in patches, but
fall while it travels between patches. The model shows
that patch residence time should show an initial rise
in response to increased travel time, but then should
begin to shrink as travel continues to lengthen. The
model predicts that at higher levels of intrusion risk
(increased K), patch residence time increases less in
response to increased travel time, and begins to decline
sooner, such that the entire trajectory is lowered.
longer effect increases in B. There is even
a decline in B as feeding diminishes still
further in importance. The extent to which
B increases to compensate for changes in
T depends on the way in which intrusion
risk is scaled relative to that of starvation
(the value of K): the bigger the risk of
intrusion, the smaller the change in B relative to changes in T (Fig. 3).
This model provides a way of combining
the costs of two different kinds of activity,
but the quantitative value of these costs is
not specified, only the form of their relationship to B and T. In principle the costs
could be measured in a common currency
such as fitness or survival but even without
this the model makes some testable and
non-obvious predictions. The most testable of these are that the relationship
344
R. C. YDENBERG AND J. R. KREBS
when the mean trajectories for the 6 birds
are plotted in B-T space.
11
10
OTHER STUDIES OF TRADEOFFS
S
9
WITH INTRUDER
1
2
3
4
5
6
7
8
9 10 1 1 1 2 13 14 15 16 17 18 19 20
TRAVEL TIME (S)
FIG. 4. The results of the experiment testing the
model shown in Figure 3. The graph depicts the
sequence of patch residence time-travel time combinations observed in trials when no intruder was presented (upper curve, open circles; numbers inside the
circles refer to successive equal portions of the experimental trials called quintiles) and trials when an
intruder was presented (lower curve, shaded circles).
The mean of the values observed in two replicate
trials was used to estimate the travel time and patch
residence time for each bird in each quintile in both
the intrusion and non-intrusion trials. The points
shown in the graph are the means of the quintile
estimates for each bird, and the vertical bars are standard errors. (For clarity, error bars are not shown for
travel times, but the co-efficient of variation of the
quintile estimates is about 35%.) An average of 51.7
patch visits was recorded in each quintile. Without
exception, all the birds show a consistent tendency to
increase travel times in the course of each trial (Friedman x2 method: non-intrusion treatment, x2 = 21.2,
4 df, P < 0.001; intrusion treatment, x2 = 18.3, 4 df,
P < 0.001). Residence times on the intrusion trajectory are significantly shorter in each quintile than on
the non-intrusion trajectory (3-way ANOVA considering only quintiles 2-5; df = 1,4; F = 11.17, P <
0.05), but the peak residence time at quintile 2 is not
quite significantly higher than quintile 1 or 3 on either
trajectory.
between B and T when plotted as a trajectory from a hungry state towards satiation
should be an inverted U with a long tail to
the right, and that the bow of the U should
be greater when intrusion risk is lower.
Ydenberg and Houston (1986) tested these
predictions during 15 minute sessions in
which male great tits foraged in an aviary
similar to that already described. The
results are summarized in Figure 4: the two
major qualitative predictions are borne out
Dynamic optimization is just one of a
number of techniques that have been used
to evaluate behavioral tradeoffs. Two other
methods may also be appropriate under
some circumstances. Whenever the costs
and benefits of incompatible activities can
be measured in the same currency, tradeoffs can be analyzed and the optimal tradeoff found. Davies and Houston (1981) used
this approach in their study of the pied
wagtail (Motacilla alba); based on calculations about the costs and benefits in terms
of food intake they could accurately predict when territory owners would tolerate
satellite males. Satellite wagtails cause the
foraging rate of the territory holder to
drop, but because satellites also assume half
of the defense duties, the owner is able to
spend more time feeding. Davies and
Houston's (1981) quantitative predictions
were possible only because other kinds of
costs associated with territorial defense did
not seem important. Their method would
not be valid if satellites brought with them
some additional cost, such as an increased
rate of predation, or if the owners ran a
risk of injury while evicting satellites.
Similarly, by assuming that small birds
in the non-reproductive season maximize
fitness simply by surviving, Pulliam and
Millikan (1982) were able to convert all
costs to units of survival. Again, this method
would not be valid if there were additional
fitness benefits to be gathered during the
winter such as the accumulation of fat or
protein reserves (Ydenberg and Prins,
1981), which could be carried over into the
reproductive season.
A second method of incorporating conflicting activities into models of optimal
behavior is illustrated by the work of Martindale (1981), who modelled a situation in
which gila woodpeckers (Melanerpes uropygialis) had to defend their nest sites while
raising their broods. In the desert suitable
nest cavities are in short supply and so there
is always a risk that the woodpeckers will
be evicted from their holes by other cavitynesters while they are away collecting food
FEEDING VS. TERRITORIAL VIGILANCE
for their nestlings. A central place foraging
model (Orians and Pearson, 1979) took the
risk of nest usurpation into account by
increasing the cost of time spent away from
the nest (though the shape of the function
relating risk to time away from the nest
could only be guessed). An experimental
test of the model showed that it successfully
predicted the behavior of the male (but not
female) woodpeckers.
Martindale's work can be considered an
example of the use of "utility theory," a
theoretical formulation with the explicit
aim of analyzing how choices are made. In
effect, a guess based on biological knowledge has been made as to how gila woodpeckers value the benefits of time spent
away from the nest (prey capture) against
the costs (nest usurpation). (Of course, we
assume that natural selection has
"designed" the evaluation system.) Other
biologists (e.g., Caraco et al., 1980) as well
as experimental psychologists (e.g., Rachlin
et al., 1981) have used experimental techniques to establish how animals evaluate
alternatives against one other. For example, Caraco and his colleagues have measured the preferences of several small passerines for constant vs. variable rewards.
The method involved offering dichotomous choices and finding "indifference
points," that is, combinations of the choices
between which the animals exhibited no
preference. This experimental approach
permits the description of preferences; in
the absence of any a priori predictions, it
is in theory possible to work backwards and
find a model that predicts the results
(McFarland, 1977). This inverse optimality
approach has been criticized as doing no
more than redescribing the results (Maynard Smith, 1978), but the descriptive
account of one set of results may become
a prediction for another set.
CONCLUSION
We have described an approach to the
study of territoriality that emphasizes time
allocation strategies. The crux of this
approach is that there is a tradeoff involved:
time devoted to feeding cannot be devoted
to defense (and vice versa) and the territorial animal must make decisions about how
345
to invest its time in these two alternative
activities. This approach differs from the
three areas in which most other research
on territoriality has fallen (see p. 337).
The analysis of behavioral tradeoffs is
rendered difficult by the fact that the optimum will often be dynamic, changing
through time as the environment or the
organism itself is altered. We used a technique based on PMP to analyze in a dynamic
way the feeding and vigilance problem,
though it is worth pointing out that we do
not yet know how individual great tits adjust
their behavior to produce the changes we
observed. We do not believe that the rules
governing these apparently complex
adjustments are necessarily complex themselves. One simple possibility based on hunger-linked changes in the giving-up time is
discussed by Ydenberg and Houston (1986).
ACKNOWLEDGMENTS
A large portion of the credit for this work
goes to Alisdair Houston and Alex Kacelnik. We also thank Tom Caraco and Peter
Taylor for their comments on the manuscript.
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