Optimal Foraging and the Size Selection of Prey by the Bluegill

Optimal Foraging and the Size Selection of Prey by the Bluegill Sunfish (Lepomis Macrochirus)
Author(s): Earl E. Werner and Donald J. Hall
Source: Ecology, Vol. 55, No. 5 (Late Summer, 1974), pp. 1042-1052
Published by: Ecological Society of America
Stable URL: http://www.jstor.org/stable/1940354
Accessed: 09-11-2015 09:36 UTC
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Ecology (1974) 55: pp. 1042-1052
OPTIMAL FORAGING AND THE SIZE SELECTION OF PREY
BY THE BLUEGILL SUNFISH (LEPOMIS MACROCHIRUS)1
EARL E. WERNER2AND DONALD J. HALL
Zoology Department, Michigan State University,East Lansing 48824
Abstract.The bluegillsunfish,
is knownto selectpreyon thebasis of
Lepomismacrochirus,
size.We presentevidencethatthissize selectionis relatedto theoptimalallocationof timespent
searchingfor,and handlingprey.A modelrelatingsearchand handlingtimeto energyreturnis
to determine
constructed
the optimalbreadthof diet. Prey are permitted
to differin size and
relativeabundance.All elementsof themodelare estimatedfromexperiments
withthebluegill
feedingon populationsconstructed
fromsize classes of Daphnia magna. Relativevisibility
of
the different
prey sizes markedlyaffectsrelativeencounterrates or "effective"proportions.
Effectiveproportionsare determinedempiricallyfromfeedingexperiments
and theoretically
fromreactiondistancein orderto correctfor this bias. Search time is thenmanipulatedby
varyingabsoluteabundanceof prey.
At low absolute abundance,prey of different
size are eaten as encountered.As prey
abundanceis increased,size classes are droppedsequentiallyfromthe diet in accordancewith
the theory.Search and handlingtimesare estimatedfor these experiments
and quantitative
comparisonswiththe model indicatethese changesin diet maximizereturnwith respectto
timespentforaging.
Key words: Diet breadth; fish; model; optimal foraging; predator; size selection; time
allocation.
INTRODUCTION
It has often been hypothesizedthat natural selection will elect those foraging patterns in a species
that are most economical. Thus, a careful scrutiny
of existingbehaviors should indicate some tendency
to optimal strategiesin the foragingprocedure. Intuitively,this is an appealing working hypothesis;
its usefulness,however, depends on how good the
ecologist's guesses are regardingthe nature of costs,
benefits,and constraintsin a given situation. When
the latter are judiciously conceived, rather simple
theoretical relations concerning the breadth of the
diet can be constructed (MacArthur and Pianka
1966, Emlen 1966, Schoener 1969). To date, models
of this sort have been employed primarilyin qualitative ways regarding the economics of a species'
behavior. Here we look at some predictionsof such
a model in quantitativeterms.
We are concerned with prey selection by fishes,
primarilythe bluegill sunfish(Lepomis macrochirus).
The bluegill is very general in both the array of
invertebratespecies it consumes and the habitats
where it forages (Keast 1970). It can be demonstrated,however, that considerable selection occurs
in regard to the particle size of food taken. We
have noted this both in the field (Hall et al. 1970)
and in laboratory experimentsshowing an inverse
relationship between prey size and mortalityrate.
A similar pattern has been described for several
otherfishes (e.g., Ivlev 1961, Galbraith 1967, Brooks
1968).
The importance of food size also appears repeatedlyin the literatureon growthin fishes. Growth
rate differenceshave been correlatedwith food size
in field (e.g., Parker and Larkin 1959, LeCren 1958)
and laboratorystudies (Paloheimo and Dickie 1966).
In bluegill populations we found that three-folddifferences in individual growth rates were related to
the abundance of food particleslarger than 0.01 mg
dry weight(Hall et al. 1970). Most authors attribute
these differences to relative foraging efficiencies,
but the data rarelyprovide any insighton this aspect
of the problem.
Size selection of prey and foragingefficiencyconcern the same basic questions and bear importantly
on fitnessin fish. In our examination of the bluegill, we develop a simple model demonstratingoptimal prey choice and laboratory experimentsdesigned to test predictionsof the model.
THEORY
A broad review of the large literatureexploring
foraging patterns from the perspective of optimal
behavior can be found in Schoener (1971). Here
we use the optimalityprinciplein settingup a model
1
ManuscriptreceivedMay 4, 1973; acceptedJanuary for the size selection of prey. We essentiallyfollow
23, 1974. Contribution
No. 250 of the W. K. Kellogg the developmentof MacArthur
and Pianka (1966)
Biological Station.
2 Presentaddress: W. K. Kellogg Biological Station, except for minor differencesin how prey are presumed to differ. A more detailed discussion and
MichiganState University,
HickoryCorners,49060.
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Late Summer 1974
TABLE 1.
x
f(x)
b
x
k
T.
N
B
SIZE SELECTION
1043
BY THE BLUEGILL
Symbolsused in the text
Prey size (weight)
of prey by size
Frequencydistribution
Largestitem takenby the predator
Lower bound on the optimaldiet
Handlingtime per item
Time spent searchingto encounter[f (x) dx]
items
f, f(o() do-,numberof itemsin a diet of breadth
[x,b]encounteredin T,
fgaf(o() do-,biomass representedby a diet of
breadth[x,b] encounteredin T.
b
a
Prey Size (x)
of preywithan
distribution
FIG. 1. A size-frequency
arbitrarydiet [xb] cross-hatched.The largestsize prey
available is designatedb. The curve f(x) is assumed
developmentof the model can be found in Werner definedover the interval[ab].
(1972).
The problem is to choose an optimal breadth of
T, + k Sbt(a) du
diet when prey of differentsizes are available in
X
R=
(3)
f(a) du
differentrelative densities. The bluegill feeds by
The optimal breadth of diet is given by the value
patrollingthe environmentand handling each prey
individually. Most of these prey are not pursued of x which minimizes R. This is obtained by difand being small relative to the predator are simply ferentiating(3) with respect to x and setting the
swallowed intact. Thus, over a considerable range derivativeequal to 0. Since f(x) is assumed defined
of prey sizes (e.g., the zooplankton to which we will over [a,b] the derivativeis 0 only when
restrictour attentionhere) the handling time per
- kfitf(cr)du=O.
(4)
xTs+xkSt(c)da
particle is constant which we designate k.
Further, we assume that the environmentis unSeveral relationsof interestcan be seen from this
limited and treated in a fine-grainedfashion by the formulation. SubstitutingN and B in (4) for simpredator. Search time, T,, is defined as the time plicity (recognizing that the lower limit varies with
required to encountera given frequencydistribution x) and rearranginggives
(f[x]) of differentsized prey,where x is prey weight
B
or biomass f(x) is not a probabilitydensityfunction;
(
N
+ Tl/k
symbols are defined in Table 1. Thus, for instance,
and
weed
bed
a
search
to
is
required
the
time
T.
where x is the lower bound on the optimal diet.
encounter [f 1(x) dx] items if the predator does
Thus, increases in search time broaden the diet as
not stop and handle any of the prey encountered. seen in Fig. 2. An increase in handling time diThe upper bound on the size of items in the diet minishes the effect of T8 and thereforeresults in
(i.e., that available) is denoted by b. Since handling a decrease in diet breadth.
time per item is constant,the fish should never pass
As expected, the optimum diet depends in part
up a large item, and should include smaller items upon the way prey are distributed,i.e., the relative
only if overall efficiencyis therebyincreased.
rates at which biomass and numbers accumulate as
More precisely,if f(x) is definedover the interval x recedes from b. For instance, particular values
[a,b] as in Fig. 1, the biomass (B) gained from an of T. and k will have a greatereffecton the curves
arbitrary diet chosen from the distribution en- in Fig. 2 when large items are rare since B and N
countered is
will be small initially (i.e., x near b). If B and N
are relatively large initially, as in the case where
(1 )
B=Sb
r=
()do,
prey of all sizes are equally abundant, T8/k will be
where a is the dummy variable of integration. The swamped out relativelymuch quicker. In Fig. 3, x
cost, in time, for obtaining this diet will be the is plotted against T, for distributionsof different
search time (T,) plus the handling time incurred. form.
Handling time will be k times the number (N) of
Further,we see from (5) that
items handled, where
B
x
(6)
N =SD (a) du.
(2)
k
kN
T, +
The ratio of time to biomass consumed (i.e., a
cost/benefitratio) is then
The ratio on the left is actually the reciprocal of
the time to biomass ratio set up in (3). According
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EARL E. WERNER
1044
AND DONALD
Ecology, Vol. 55, No. 5
J. HALL
l/z
z
Sebarch
TIime(TIs)
FIG. 3. Lower limitof the diet (i.e., diet breadth)
as a functionof search time for preydistributions
that
are uniform,
follow 1/x,or whereN.+, = 0.9 N. (similarlyN.+, = 0.7 N,).
x
Prey Size(x)
b
FIG. 2. Curves of the ratio B/(N + Tilk) for a
negativeexponentialdistribution
f(x) as search time is
increased,TJ(1) < T.(2), etc. The straightline representspointsof equal value on thetwo axes. The lower
bound on the optimal diet (x) is given by x B/(N + Ti/k), i.e., wherethe lines cross.
over very short time intervals. In this way it is
possible to use small pools and specifically count
the prey distributionsto be used. Thus, the experiment must be ended before the prey distributionis
grossly distorted or the pattern of size selection
exhibitedby the fishchanges. Comparisons are then
made between the prey sizes consumed by the fish
and those encounteredin the environment.
We are interested in the relation between diet
breadth and search time demonstratedin the theory.
Search time is easily manipulated in this systemby
varying the overall abundance of prey (e.g., while
holding proportionsconstant). In order to compare
results of these experimentswith predictionsof the
model, however, we must firstbe able to determine
x, f(x), T8 and k in our system. Prey size (x) is
simplymeasured as dry weightbiomass. A series of
experiments enables us to determine the relative
visibilityof the differentsizes of prey used and
hence their effectiveproportions. This is necessary
to obtain f(x). We next indicate how the costs, T8
and k, are measured and finallypresentexperiments
where search time is varied. The patterns of size
selection obtained in the latter experimentsare then
compared to the predictionsof the model.
to (6) the return (biomass) per time unit under
optimal diet is equal to the biomass of the smallest
prey taken divided by the handlingtime per particle.
For a given x, the return/timewill fall on a line
with slope 1/k and interceptat the origin. Clearly,
a change in breadth of diet is energeticallymore
significantto a predator consuming prey which require little handling time.
Generalizationslike these can be obtained in some
form from most all optimal foraging models. In
this case, however, the model is in a form that
immediatelylends itselfto testingon a real system.
Because the preferenceranking of prey by the fish
seems to follow the simple criterionexpressed in the
model, a more abstract formulation of preference
is not needed. Ultimately,our ability to test relaMaterials and methods
tions like these would seem to depend on retaining
The
bluegills were seined from lakes in souththe simplicityin such models when confrontingthe
western
Michigan or obtained from the Michigan
real system. We can now look criticallyat the sizeof Natural Resources. They were held
Department
in
of
an
light
opselection of prey by the bluegill
in large indoor pools until used and fed zooplankton
timal diet hypothesis.
from local lakes when available and lean ground
EXPERIMENTATION
beef otherwise.
Because it is easily cultured and attains a relarelies
where
The theory
on a static analysis
the
prey environmentis assumed to be unlimited and tively large size, Daphnia magna was used as
unchanging. This simplifies the construction of prey in all experiments. Size classes were obtained
theory but unfortunatelyto set up parallel experi- by gentlywashing the Daphnia through a series of
mental conditionswould require a large commitment four standard brass sieves with screen openings of
of time and space. We have approximatedthe theo- 2, 1, 0.84 and 0.5 mm. Since Daphnia grow in disretical conditionsby performingfeedingexperiments crete size intervalsor instars,the sieving procedure
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SIZE SELECTION
Late Summer 1974
TABLE
BY THE BLUEGILL
1045
2. Size of Daphnia magna (with SE)
I
Class
Mean length(mm)
n
Meanweight(lg)
n (pans @ animals/pan)
3.6 ? 0.05
20
371?--44
5 @ 25
provided four size classes which were easily distinguishable by eye. The sieving did not appear
to harm or impair the animals in any way. The size
classes were then washed from the screens into
beakers. By drawing a sample into a large pipette,
the individuals could be counted and prey populations constructedof the proportions desired for a
given experiment.
A sample of each size class was taken to obtain
lengthand dry weightcharacters. Length was taken
as the distance from the tip of the head to base of
the caudal spine. Weightswere obtained on a Cahn
electrobalance after drying25 to 200 specimens on
a weighingpan at 60'C for 5 to 7 days. These data
are presentedin Table 2.
The experimentswere performedin circular pools.
commercially available as children's wading pools.
1.3-1.7 m in diameter and 15-28 cm deep. Ten
fish of approximatelythe same size were placed in
the pools at least 24 h in advance of an experiment
to acclimate to the surroundings.The fish generally
ranged from 70 mm to 80 mm total length (the
mean + SE was 73.5 ? .06). All animals were starved
for 24 h to standardize hunger. Ten fish were used
in an experiment since this led to more normal
feeding behavior. If only one or a few fish were
used, the feeding procedure often frightenedthem
and produced erratic results.
The designated prey population was then introduced and distributedabout the pool by hand mixing
the water. The fish were accustomed to being fed
in this manner and, as long as there were a number
of fish in the pool, would boldly advance toward
the experimenterstirringin the prey. An investigator observed the experimentfrom a platform 12
ft above the pool and noted when the fish began
feeding. The fish were permittedto feed for a predetermined amount of time (discussed later) and
were netted and sacrificed. Stomach contents were
examined immediatelyto minimize digestion of the
prey.
A number of pilot experimentsnot reported here
were performedto arrive at combinations of pool
size, number of fish, and duration of experiment
that assured a constant selection pattern during the
experiment (i.e., the prey distributionis not distorted to the point that the fish changes its prey
II
2.5 ? 0.07
20
108?--3.5
5 @c50
III
1.9 ? 0.04
20
37?4-1
5 @ 125
IV
1.4 ? 0.05
20
18?--0.7
5 @ 200
selection accordingly). Because the work was carried out in a greenhouse at differenttemperatures,
activitylevels in the fish and thereforeexperimental
duration were affected. These times, ranging from
5 min to 30 s, are reported with the temperatures
in the results.
The effectivedensity of prey
Ecologists commonly compare the distributionof
prey in the stomach of a predator to that sampled
from the environmentin order to make inferences
regarding food preferences or availabilities. The
obvious problem with this sort of analysis is to
distinguishsatisfactorilywhat foods were available
but passed up, from those in the environmentbut
not really available or encountered. We have attempted to eliminate some of these problems by
using a single prey species in a simple environment.
Thus, the role of body size is not confounded with
factors such as differentmorphologies, movement
patterns,and environmentalcomplexity,which also
influence relative availability or frequency of encounter. Body size, however, clearly will influence
visibilityand thereforethe effectivedensityof a given
size class. Since the theoryis concernedwith a choice
of diet breadth based on the prey actually encountered (i.e., f[x]), we must determine the effective
proportionsof prey in this system.
The visual field of fish is roughly spherical with
about a 200 posteriorblind segment (depending, of
course, on body conformation; Trevarthen 1968,
Protasov 1968). Not all of this field is used with
similar effectivenessin locating prey; naturally the
binocular region appears to be heavily relied on.
So long as the field is used in a similar manner for
detectingdifferentsize prey, however, a ratio of the
field volumes computed as spheres should indicate
the relativevisibilityof the various prey sizes.
To determine these ratios reactive distance was
measured for each prey size. Fish from the experimental populations were isolated in a 1-mX 12-cmX
12-cm trough. Light and water claritywere similar
to the experimentalconditions. The fishwere starved
for 24 h and then single prey were introduced out
of the visual range of the fish. The distance from
which the prey was firstdetected was noted. The
mean (? SE) distance of reaction for Class I is
51.5 ? 1.8 cm; Class II, 40.8 + 1.5; Class III,
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EARL E. WERNER
1046
AND DONALD
Ecology, Vol. 55, No. 5
J. HALL
3. Stomachratiosfor a uniformdistribution
at low density.The data are ratioscomputedfromthe mean
numberof preyeaten per class relativeto thatof Class I; thereare 10 fishper experiment
TABLE
Experiment
1
2
3
4
Time
(min)
5
5
5
5
Temperature
(OC)
10
10
15
15
Density
I
25/class
25/class
50/class
50/class
Mean + SE
1
1
1
1
1
35.4 + 1.5; and Class IV, 24.6 + 1.4. The majority
of observations originated from two fish but a
number of others tested showed similar results.
In the pools the fish searched from about middepth so the reaction distances all considerably exceed the distance to the surface or bottom. In fact,
except for Class IV in the large pool, all reaction
distances exceed the pool depths. In this case then,
the appropriate visual field ratios are for volumes
of spheres cut by two parallel planes. By definite
integralthisvolume is found to equal 27r a(r2 - a/3),
where r is the radius and a the distance from middepth to the surface or bottom. The ratios of these
volumes relativeto that of Class I are (I-IV respectively), 1, 0.63, 0.47 and 0.22. The differencein
these values for the two pool sizes is always < 0.02.
By the theory, at extremely low densities prey
should be taken as encountered (i.e., T. large,
equation 5). Ivlev (1961) has amassed a large
amount of experimentalevidence with fish supporting this contention by showing that electivityapproaches zero with decreasing prey density. If relative visibility is the main factor determiningthe
effectiveproportionsin our system,then fish offered
a uniformdistributionat low density will consume
prey in the ratios given earlier. Four pilot experiments were set up to test this hypothesis;two each
at 25 and 50 prey per size class. The ratios of
numbers eaten in each size class to that of Class I
did not differ at the two densities (Table 3).
The means of all four experiments are (Classes
I-IV respectively), 1, 0.83 + 0.1, 0.54 + 0.04, and
0.27 + 0.1.
II
Class
0.67
0.92
1.04
0.70
0.83 + 0.1
III
0.42
0.60
0.61
0.53
0.54 + 0.04
IV
0.08
0.28
0.36
0.38
0.27 + 0.1
Only Class II deviates very much from the theoretical ratios. It appears that the discrepancy is
caused by permittingthe fish to feed too long. By
the end of the experimentsvirtuallyall of Class I
was eaten. As a result the distributionwas biased
to the smaller classes, particularlyII; i.e., more prey
of Class II appeared in the diet than would be expected with an unchanging distribution.
In a second series of experimentsprecautionswere
taken to prevent this bias. These experimentswere
ended within 1 to 3 min to check that the selection
pattern was consistentthrough time. Seven experiments showed consistent results at each duration
(Table 4). In these the numbers of smaller prey
were compensated according to the reciprocal of the
ratios obtained in the initial experiments,i.e., so
that the effective distributionshould be uniform.
Thus, the visibilityhypothesiscan be tested under
a distributionof differentform. The prey populations were constructedfrom a base of 25 of Class I,
and thereforeconsisted of 25, 30, 46, and 93 prey
of I-IV respectively. If the ratios from the pilot
experiments are correct, the fish should then encounter prey sizes in equal proportions. The means
of the ratios for the seven experimentswere as follows (I-IV respectively), 1, 0.86 + 0.1, 0.96 + 0.2,
and 1.05 + 0.2.
The values for III and IV are very close to the
expected ratio of 1 and bear out the good agreement of the original and theoreticalratios. Class II
is underrepresentedin the diet because the original
ratio of 0.83 was too high for the reasons given
earlier. If we compute the ratio for Class II based
4. Stomachratios for experiments
designedto give a uniformeffectivedistribution
at low density(based
on 25 Class I prey). The data are ratioscomputedfromthe mean numberof preyeaten per class relativeto
thatof Class I; thereare 10 fishper experiment
TABLE
Experiment
1
2
3
4
5
6
7
Time
(min)
1
2
2
2.5
2.5
2.5
3
Temperature
(OC)
13
13
11
14
14
14
13
Mean ? SE
Class
I
II
1
1
1
1
1
1
1
1
0.61
0.82
1.30
0.50
0.75
0.91
1.11
0.86 + 0.1
III
0.82
0.63
1.00
0.80
0.93
0.64
1.94
0.96 ? 0.2
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IV
0.64
1.21
1.75
0.36
1.33
0.62
1.50
1.05 ? 0.2
Late Summer 1974
SIZE SELECTION
BY THE
BLUEGILL
1047
Stomachratiosforexperiments
designedto give a uniformeffective
distribution
at low density(based on
20 Class I prey). The data are ratioscomputedfromthe mean numberof preyeaten per class relativeto that
of Class I; thereare 10 fishper experiment
TABLE 5.
Experiment
1
2
3
4
5
6
7
8
Time
(s)
Temperature
(OC)
30
45
45
45
45
45
45
45
18.5
18.8
19
18
18
18
18
18
I
Mean + SE
1
1
1
1
1
1
1
1
1
Class
II
1.00
0.72
0.53
0.76
1.33
0.84
1.30
0.66
0.90 ? 0.1
IV
0.66
1.00
1.40
0.28
0.87
0.52
0.50
2.00
0.90 ? 0.2
never passed up unless the fish is absolutelysatiated;
it appeared from the platformthat the fish actively
searched during the experiment. Ivlev (1961) has
also noted the strong preferenceshown by fish for
the largest prey available.
The mean number of prey (all sizes) eaten per
fish for a given experimentwas multiplied by the
handling time to obtain total time spent handling
prey. This was subtracted from the duration of
the experimentto obtain the search time. The frequency distributionof prey (f[x]) seen in this inThe assessment of costs
terval of search time was reconstructedon the basis
The currency used in the theory was time and of the mean number of Class I prey eaten per fish.
some estimatemust be made of costs in these terms. The numbersof prey encounteredin the other cateTo measure handling time, fish which had been gories can be estimated using the relative visibility
deprived of food for 24 h were isolated in aquaria. ratios.
Prey were introduced into these aquaria both inThe patterns of size selection
dividually and in groups. Handling time was meaAll elements of the model can now be estimated
sured with a stop watch and taken to be the time
from strikeuntil searching recommenced. Virtually and used to predict the optimal breadth of diet for
no pursuit is necessary when fish are capturing a given experiment. We can thereforeproceed to
cladocerans and thus handling time is quite short. experimentswhere prey selection is considered as
Handling time tends to increase as hunger declines, we systematicallyvary search time (T,). Accordbut these experimentsare too short for this com- ingly, prey distributionswere offered over a considerable range of densities and the patternsof seplication to be significant.
From 12 to 24 observations,divided between two lection observed.
This series of experimentswas performed when
fish (67 and 70 mm), were made for each prey size.
The mean handling time (+ SE) for sizes I-IV re- temperatureswere somewhat higher in the greenspectively were 1.26 ? 0.1, 1.17 -+ 0.1, 1.23 + 0.1, house and with only three prey sizes (I, II, and IV)
and 1.02 + 0.1 s. A mean value of 1.2 s will be to reduce the work of counting prey. Because of
used as the handling time per particle (k) in the these changes we repeated experimentsat low prey
densities, i.e., where no selection occurs but prey
considerationswhich follow.
Search time is much more difficultto quantify, are taken as encountered. Since activity levels of
since we are interestedin how long it takes to find the fish were much higher because of the temperaa given array of prey, whether they are eaten or turechange, i.e., feedingwas more rapid, experiments
not. With two assumptionswe can arrive at search were shorter. As a consequence fish at low prey
time (T,) indirectly. First, we assume a fish takes densities captured very few prey, often only two to
all of the Class I (largest) individuals encountered. three prey per fish. Because this introducesa conSecondly,we mustassume all time not spenthandling siderable sampling variation, eight repilcate experipreywas spentsearching. Since the experimentswere mentswere performed.A uniformdistribution(equal
run for short periods with hungry fish, neither of numbers of each class) was used in all experiments
these assumptionsis unrealistic. Large Daphnia are except these eight at low density. In the latter the
on the results of the second set of experimentswe
find that it averages 0.71 + 0.1. The deviation of
this value from the theoretical(0.71 + 0.1 vs. 0.63)
is very close to that found for III and IV, which
appear to hold very well. For the purposes of this
paper, then, we will assume the visual field ratios
to be 1, 0.71, 0.54 and 0.27. With these data it is
possible to estimate f(x) or the proportions of
differentsize prey encountered by a fish given the
actual proportionsplaced in the environment.
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EARL E. WERNER
1048
AND DONALD
prey population offered was constructedto give a
uniformeffectivedistribution(prorated from 20 of
Class I), because the expectation of encounteringa
Class-IV prey otherwisewas quite small and introduced furthervariation. These differences in no
way hinder comparisons with the model as long as
appropriatef(x) functionsare used in each case.
The resultsof these eight experimentsat low prey
density indicate that the fish are nonselective and
take prey as theoreticallyencountered (Table 5).
The ratios in the stomachs(I, II, and IV respectively)
were 1, 0.9 + 0.1, and 0.9 + 0.2. These values are
not significantly
differentfrom 1, the resultexpected
if prey are simplyeaten in the proportionsthat they
are seen.
At higher prey densities the fish consumed more
prey, and as a result the variation between fish and
between experimentsdropped markedly. Therefore
fewer experiments are needed to demonstrate a
given selection pattern. A uniformdistributionwas
offered,and thus, the effectivedistributionwill be
1, 0.71, and 0.27, as indicated earlier. Four experiments were performedat intermediatedensities;one
at 50, two at 75, and one at 200 prey per class.
Similar selection patternswere obtained in three of
these experiments,where a large number of I and II
were eaten in very nearly expected proportions-to
the virtual exclusion of Class IV. In one of the
experimentsat 75 prey per class three fish ate only
Class I and biased the results considerably. If the
seven other fish alone are considered, the number
eaten per fish and the proportionsconcur with the
results of the other three experiments(Table 6).
Two experimentswere performed at still higher
densitiesof 300 and 350 prey per class. The results
of the two experimentswere practicallyidentical and
indicate a strongselection for Class I (Table 6).
The significanceof these patternsis best demonstrated in comparison with the relative visibility
Ecology, Vol. 55, No. 5
J. HALL
12
4.,..............-:,.;,-B
:M
IC
I
I
D
:I
I
FIG. 4.
The mean numberof each size class eaten
per fish. The top histogram(a) is the mean of the
eightexperiments
at low density.The threehistograms
in
panel (b) represent(fromleftto right)the experiments
at 50, 75 (mean of two experiments),
and 200 preyper
class. Similarly,(c) depictsthe experiments
at 300 and
350 per class. The durationof an experimentcan be
found in the precedingtables. Superimposedon the
histogramsof mean numbereaten is a stippledarea
representing
the expected numbersin the stomch if
itemswere eaten as encountered.These were computed
fromthe visual field ratiosusing the numberof Class
IV actuallyeaten as a base. Thus a deviationfromthe
expectedshows positiveselectionfor that size class.
and highdensitiesgivena uniformdistribution.
The data
at intermediate
6. Stomachratiosforexperiments
are ratioscomputedfromthe mean numberof preyeaten per class relativeto thatof Class I; thereare 10 fish
per experiment
TABLE
Time
(s)
Temperature
(OC)
1
2
3
30
30
30
24
23
25
4
60
22
1
2
30
30
25
25
Experiment
*
Density
densities
Intermediate
50/class
75/class
75/class
*
200/class
Mean + SE
Highdensities
300/class
350/class
Mean + SE
I
Class
II
IV
1
1
1
0.60
0.52
0.32
0.07
0.04
0.08
1
1
0.62
0.58 ? 0.02
0.01
0.04 + 0.01
1
1
1
1
0.60
0.22
0.23
0.23 + 0.01
Experiment3 computedwiththreefishdeleted,discussedin text.
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0.04
0.05
0.05
0.05
Late Summer 1974
SIZE SELECTION
BY THE
profile. For this purpose we compute from the
average number of Class IV eaten per fish the expected representationof I and II if prey are taken
as encountered(i.e., no size selection). The expected
numbers are shown as the stippled area in Fig. 4
for the experimentaldistributionsused in each case.
The total histogramsare the mean number of each
size class eaten per fish. Experimentsat equivalent
densitiesare combined and an average used.
The experimentsrepresentedin Fig. 4 are grouped
in the three panels by selection pattern. Those experimentspresented in panel (a) were designed to
provide a uniform effective distributionof prey.
There is clearly very littledeviation from that in the
stomachs. The fish thereforeexhibited no selection
at this densityof prey. In panel (b) if no selection
occurred we would expect the proportions in the
stomach to be 1, 0.71, and 0.27, since a uniform
distributionwas offered. In fact the smallest prey
(IV) is neglected by the fish; 80% of the fish over
all experimentscontained no Class IV at all. The
proportionsof Classes I and II in the stomach are
close to that of the expected encounter ratios; the
numbers of II being only slightlyunder that predicted. This pattern is repeated with high fidelity
over a range of densities from 50 to 200 prey per
class. Thus the fish are selecting the larger two
prey sizes in contrastto the patternseen in panel (a).
The remainingtwo experimentsin panel (c) showed
a marked dominance of Class I in the stomachs.
The results again are very repeatable from one experimentto the next.
We have shown, then,that we can force the bluegill to change its diet breadth by essentiallyeliminating one size class at a time. We have done this
by manipulating primarily the density of prey in
the environmentand thereforesearch time. It is
not clear how discretethe changes in diet will be as
prey abundance changes. The proportion of II at
high densitiesis much reduced,thoughnot as sharply
as was the case with IV in going from low to intermediate densities. This may be due in part to the
fact that the size differencebetween I and II is not
as great as that between II and IV. Or, perhaps over
a range of densities proportions in the diet will
change gradually: this may explain the fair number
of Class II eaten at high densities. On the other
hand, the stabilityof the pattern over considerable
ranges of density,as shown in panel (b), may indicate a more discrete shift in diet. Overall, however, the trend in selection follows the theory.
Moreover, the bluegill can adjust the breadth of diet
to prevailing conditions literally after some few
seconds exposure to a prey population, and this is
of obvious adaptive advantage. These data are generally in accord with the results of Ivlev (1961).
BLUEGILL
1049
o~a
t
20
b
e.
100
200
300
400
Search Time
groupedby selectionpattern
FIG. 5. The experiments,
as in Fig. 4, are plottedagainstthe search time (sec)
scaled for each experimentto the time requiredto encounterthe standarddistribution.A mean (+ SE) is
plotted for the experimentsat low density;otherwise
are plotted.The dashed lines are
individualexperiments
the pointswherethe selectionpatternshould changeas
in
for the standarddistribution
theoretically
determined
if T8 < 29 s only the largest
this system.Accordingly,
prey (I) should be eaten, and if T. > 29 s the two
largest(I and II) should be eaten. If T. > 295 s any
selectionis suboptimaland prey should be taken as
encountered.
He held relative densities constant and demonstrated that electivityby carp increased as absolute
densityof the prey population was increased. It is
not possible to determine from his data, however,
if prey are eliminatedfrom the diet in sequence by
profitability.
Comparisons with the theory
It now remains to demonstratequantitativelythat
the changes in diet are related to the costs associated
with foraging. The results of each experimentprovide an estimate of a prey distributionseen by a
fishand the requisitesearch time. The handlingtime
and prey weights are also available. Using a discrete version of the theorypresentedearlier, we can
determine from these data the optimal breadth of
diet for this system.
In order to facilitate the comparison with the
model, all of the experimental data are scaled to
give the search time for a standarddistributionbased
on 10 prey of Class I. Thus, search time (T8) was
computed for each experiment as detailed earlier
and scaled by (T,/number Class I eaten) 10 giving
the search time for the encounter of a distribution
based on 10 prey of Class I. The differencesbetween
experiments,then, are reduced to two matters: the
search time and the selection pattern. The appropriate relative abundances (f(x)) based on 10 Class-I
prey were substitutedin the model along with the
handling time and prey weights to determine the
theoreticalpoints where diet breadth should change
as search time increases. These points are indicated
by the dashed lines in Fig. 5, which offersthe comparison of experimental results with these predictions. The search time for the standard distribution
was determinedfor each experimentand plotted in
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1050
EARL E. WERNER
AND DONALD
J. HALL
Ecology, Vol. 55, No. 5
Fig. 5 against the selection pattern (a, b, and c of
Fig. 4). In each case the selectionpatternexhibited
in the experiments falls within the region where
that pattern is deemed optimal by the theory. At
least under these conditions it appears that the
400
mechanisms of size selection in the bluegill are
integrated so as to allocate time expenditure optimally in feeding with respect to the biomass
(energy) consumed.
The relation of search time to density in the q3 300environmentis of interestin this light. In Fig. 6
we have plotted T, (search time) against densityfor
the experimentsat 18'-250C. The relationis strongly
concave. Observations from the platform indicated
200that the rate of movement and general intensityof
search was much greaterat the higher densities. At
F~~~~~~~
it
low densities the fish moved slowly and very deliberatelyin short runs of 4-6 body lengths with a
definitepause in between. At high densitiesthe fish
100
rushed wildly about pausing only instantaneously.
This is another indication that the fish are treating
and a more extensive
these densitiesvery differently
study should provide insighton the mechanisms of
size selection and the searching procedure. The
0.3
0.5
0.6
0.1
0.4
0.2
densities used in these experimentsare low relative
to published field data for zooplankton, though the
Class I/ Liter
prey, particularlyClasses I and II, are considerably
FIG. 6. The search time (s) to encounterthe stanlarger than found in most limneticsituations.
dard distribution
based on 10 Class I preyplottedagainst
densityof Class I/liter. The data are for experiments
DISCUSSION
at temperatures
between180-250C. Means (? SE) are
wererunat equivalentdensities.
has
proved givenwhereexperiments
The theoryconcerningoptimalforaging
The curve is drawnby eye.
useful in qualitatively interpretingcertain results
from the field and has contributed fundamentally
to the theory of species distributionsand numbers toral habitat probably sees prey in any quantityonly
(MacArthur 1972). Most optimal foraging models for a short time at dawn and dusk. At these times
proposed fall in the realm of qualitativemathematics; many of the prey are active in the water column;
their usefulness in a quantitative sense is contro- during periods when light intensitiesare higher the
versial. Usually the models are considered too prey are less active or in the sediments. Thus, time
simple and general to apply to actual situations. As is likelyto be a very importantcost in the economics
MacArthur (1972) notes, the naturalist's intuition of feeding. Even in the spring and early summer
and experience with the organisms is needed to when food is more abundant, breeding activitiesare
judge the suitabilityof these efforts. This intuition very time-consuming(e.g., Clark and Keenleyside
should be used to match the tractabilityof simple 1967) and compete with foragingtime. This study
models to appropriate real situations in order that indicates that the bluegill is keenly responsiveto the
directtestsof the theorycan be managed. This will time required to search for and handle prey. Thus,
greatly aid in delimitingthe importantcosts to an the time budget alone may provide a good firstapanimal. Possibly, as Schoener (1972) has suggested, proximationin gaining insighton the economics of
a family of such simple (i.e., tractable) models of prey choice by fish.
a particular phenomenon, which adequately handle
We used a much simplifiedsystemto demonstrate
limited situations,will be the best approach to the that diet breadth changed with search time. A large
complexityof these problems.
number of factorswill complicate this picture; most,
Our primarypurpose was to demonstratethat the however, can be conceived of as affectingeither
theory may account for the size selection of prey search time or the effectivedensity of prey, and
by fishes. Moreover, this systemwas simple enough these in no way limit the implicationsof the theory.
that a quantitativetest of the theory was possible. For instance, changes in light intensitywill alter
Our rationale was that the bluegill in a typical lit- the relative visibilityof prey. A decrease in light
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Late Summer 1974
SIZE SELECTION
BY THE BLUEGILL
1051
(or increase in turbidity)may act as a relativerefuge and Levins 1967) and species packing. The possifor larger prey because attenuationof contrastwill bility that we can begin to predict the diet of the
make them relatively less visible than before bluegill from simple predicates is importantin this
respect. This will enable us to explore more precisely
(Lythgoe 1966).
Temperatureeffectscan also be important.At the questions of overlap in the diet both between species
same prey densityand distributionan increased diet and between size classes of the same species. This
breadth at 140 over that at 230C is shown (e.g., should provide some quantitative notions of tolerTables 3 and 6 may be compared at 50 prey per able overlap that could be compared for different
class). In both cases if time budgets are constructed environments.With some work on effectivedensity
the selection patterns correspond to that predicted and searching rates in the limneticzone these sorts
by the model. The fish at lower temperaturessimply of analyses could be of immediate use. To effecsearch more slowly, and the diet breadth is adjusted tively explore cases where the benthos is foraged
so that time allocation is optimal under these con- or other situations where larger food is consumed,
ditions. Results of this sort may point to inter- we need more informationon the maximum prey
actions of time and energy expenditure as costs. size a fish can consume and the relation between
Wohlschlag and Juliano (1959) in a study of the prey size, fish size, and handling time. Our current
seasonal metabolism of the bluegill hypothesized study of these relations for several species of the
that the increase in expenditureover standard me- Centrarchidaemay enable a much broader applicatabolism for comparable swimmingactivityis rela- tion of the theory.
tively much greater at the colder temperaturesin
ACKNOWLEDGMENTS
the range where we are working. Energy expendiWe are gratefulto the membersof theecologygroups
turemay set limitson the searchingrate; withinthese
of Iowa,
and theUniversity
limits it is clearly advantageous to allocate time at MichiganStateUniversity
whose commentshave greatlyimprovedthispaper. Part
optimally. Unfortunatelyour data here are not of this work was accomplishedwhile the seniorauthor
extensive.
was at the Universityof Iowa and the assistanceof
The structureof the environment,both temporally Robert L. Conley at that institutionis gratefullyacand spatially, will also have a marked effect on knowledged.Special thanksgo to Thomas Shuba for
thestudy.The Michigan
diet breadth. It is likelythatthe bluegill'sdiet breadth invaluableassistancethroughout
Departmentof Natural Resourcesdonatedsome of the
changes considerablyduring a day, with the periods fishused in the study.
of increased and decreased availability of inverteThis workwas supportedin partby grantsGB 15665,
bratesmuch as Orians and Horn's (1969) blackbirds. 31018, 35988 and GI 20 from the National Science
Physical structurein the environmentwill decrease Foundation.
searching effectivenessand consequently broaden
LITERATURE
CITED
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