Optimal Foraging and the Size Selection of Prey by the Bluegill
Transcription
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 REFERENCES Linked references are available on JSTOR for this article: http://www.jstor.org/stable/1940354?seq=1&cid=pdf-reference#references_tab_contents You may need to log in to JSTOR to access the linked references. Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at http://www.jstor.org/page/ info/about/policies/terms.jsp JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. Ecological Society of America is collaborating with JSTOR to digitize, preserve and extend access to Ecology. http://www.jstor.org This content downloaded from 129.175.106.167 on Mon, 09 Nov 2015 09:36:09 UTC All use subject to JSTOR Terms and Conditions 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. This content downloaded from 129.175.106.167 on Mon, 09 Nov 2015 09:36:09 UTC All use subject to JSTOR Terms and Conditions 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 This content downloaded from 129.175.106.167 on Mon, 09 Nov 2015 09:36:09 UTC All use subject to JSTOR Terms and Conditions 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 This content downloaded from 129.175.106.167 on Mon, 09 Nov 2015 09:36:09 UTC All use subject to JSTOR Terms and Conditions 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, This content downloaded from 129.175.106.167 on Mon, 09 Nov 2015 09:36:09 UTC All use subject to JSTOR Terms and Conditions 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 This content downloaded from 129.175.106.167 on Mon, 09 Nov 2015 09:36:09 UTC All use subject to JSTOR Terms and Conditions 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. This content downloaded from 129.175.106.167 on Mon, 09 Nov 2015 09:36:09 UTC All use subject to JSTOR Terms and Conditions 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. This content downloaded from 129.175.106.167 on Mon, 09 Nov 2015 09:36:09 UTC All use subject to JSTOR Terms and Conditions 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 This content downloaded from 129.175.106.167 on Mon, 09 Nov 2015 09:36:09 UTC All use subject to JSTOR Terms and Conditions 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 This content downloaded from 129.175.106.167 on Mon, 09 Nov 2015 09:36:09 UTC All use subject to JSTOR Terms and Conditions 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 the diet; little is known about this effect,however. Glass (1971) has demonstrated an increased ex- Brooks,J. L. 1968. The effectsof preysize selection by lake planktivores.Syst. Zool. 17:273-291. penditurefor returnwhen largemouthbass prey on Clark, F. W., and M. H. A. Keenleyside. 1967. Reguppies in environmentsmade successively more productiveisolationbetweenthe sunfishLepomis gibcomplex with wooden dowels. bosus and L. macrochirus. J. Fish. Res. Board Can. 24:495-514. All evidence also points to a patchiness of prey in space. The immediateresponse of the bluegill to Emlen, J. M. 1966. The role of time and energyin food preference.Am. Nat. 100:611-617. differentconditions with which it had no previous Galbraith,M. G., Jr. 1967. Size selectivepredation experience would indicate that the fish could adjust on Daphnia by rainbowtroutand yellowperch.Trans. the diet while moving throughpatches of different Am. Fish Soc. 96:1-10. quality. Depending on the pattern of the environ- Glass, N. W. 1971. Computeranalysis of predation energeticsin the largemouthbass, p. 325-363. In B. ment, however, this strategymay be inefficient.It Patten[ed.] Systemsanalysisand simulationin ecology, is easy to envision cases where poor areas should Vol. 1. AcademicPress,New York. be passed over and only the more profitablepatches Hall, D. J., W. E. Cooper, and E. E. Werner. 1970. searched (e.g., MacArthur and Pianka 1966). No An experimental approachto the productiondynamics and structureof freshwateranimal communities. doubt factors such as patch size and distribution Limnol. Oceanogr. 15:829-928. will influence diet breadth or patch utilization patIvlev, V. A. 1961. Experimentalecologyof the feedtern. Problems of scale as they pertain to these ing of fishes. Yale UniversityPress, New Haven, questions should be investigated. Conn. 302 p. These featuresshow how sensitiveniche breadthon Keast, A. 1970. Food specializationsand bioenergetic in the fishfaunasof some small Ontario interrelations the food dimensioncan be to environmentalchanges. waterways,p. 377-411. In J. H. Steele [ed.] Marine This, of course, is an important consideration in food chains. Oliver and Boyd, Edinburgh. developingtheoriesof limitingsimilarity(MacArthur LeCren, E. D. 1958. Observationson the growthof This content downloaded from 129.175.106.167 on Mon, 09 Nov 2015 09:36:09 UTC All use subject to JSTOR Terms and Conditions 1052 EARL E. WERNER AND DONALD J. HALL yearswith perch(Perca fluviatalisL.) overtwenty-two special referenceto the effectsof temperatureand changes in populationdensity. J. Anim. Ecol. 27: 287-334. Lythgoe,J. N. 1966. Visual pigmentsand underwater vision,p. 375-391. In Bainbridge,R., G. C. Evans, and 0. Rackham [ed.] Light as an ecological factor. BlackwellSci. Publ., Oxford. R. H. 1972. Geographicalecology.Harper MacArthur, and Row, New York. 270 p. MacArthur,R. H., and R. Levins. 1967. The limiting similarity,convergenceand divergenceof coexisting species. Am. Nat. 101:377-385. MacArthur,R. H., and E. Pianka. 1966. On optimal use of a patchy environment.Am. Nat. 100:603609. Orians, G. H., and H. S. Horn. 1969. Overlap in foods and foragingof four species of blackbirdsin the potholes of central Washington. Ecology 50: 930-938. Paloheimo,J. E., and L. M. Dickie. 1966. Food and growthof fishes.III. Relationsamongfood,body size, and growthefficiency.J. Fish. Res. Board Can. 23: 1209-1248. Ecology,Vol. 55,No. 5 Parker,R. R., and P. A. Larkin. 1959. A conceptof growthin fishes. J. Fish. Res. Board Can. 16:721745. Protasov,V. R. 1970. Vision and near orientationof fish. Israel ProgramSci. Trans., Jerusalem. 175 p. Schoener,T. W. 1969. Optimalsize and specialization in constantand fluctuating environments: an energytimeapproach,p. 103-114. In Diversityand stability in ecological systems. BrookhavenSymp., Upton, N.Y. 1971. Theory of feedingstrategies.Annu. Rev. Ecol. Syst. 2:369-404. 1972. Mathematicalecology and its place among the sciences. Science 178:389-391. Trevarthen,C. 1968. Vision in fish: the originsof visual framefor action in vertebrates, p. 61-94. In D. Ingle [ed.] The centralnervoussystemand fish behavior. Univ. Chicago Press,Chicago,Ill. Werner,E. E. 1972. On the breadthof diet in fishes. Ph.D. Thesis. MichiganState Univ. Wohlschlag,D. E., and R. 0. Juliano. 1959. Seasonal changesin bluegillmetabolism. Limnol.Oceanogr.4: 195-209. This content downloaded from 129.175.106.167 on Mon, 09 Nov 2015 09:36:09 UTC All use subject to JSTOR Terms and Conditions