Vim$226213x'=:rerm'2.3.ug;gmm..322a a“; . A. ‘ A , ON THE BREADTH 0F DIET IN FISHES Thesis for the Degree of Ph. D. MICHIGAN STATE UNIVERSITY EARL EDWARD WERNER 1972. 0-7639 IIIIHIII IIIIIIIIIIII II 31293 This is to certify that the thesis entitled ON THE BREATH 0!“ DIET IN PISHES presented by Earl E . Werner has been accepted towards fulfillment of the requirements for Majo ofessor , ___ ~BINDERS 'e '\ "em MICEIEAIU l ' r.' :.. ABSTRACT ON THE BREADTH OF DIET IN FISHES BY Earl Edward Werner Certain patterns of prey selection exhibited by fishes can be clearly attributed to a preference for larger sizes. Moreover, characteristic growth phenomena appear also to bear some relation to size of available prey. There are indications that clarification of the role of prey size in both selection and growth lies in considerations of forag- ing efficiency. These issues are discussed and related to the broader "fitness" of fish. Accordingly, a model is developed to explore the role of search and handling "costs" in the selection of prey if a range of different size prey are available to the pre- dator. It is hypothesized that natural selection will favor those individuals allocating time between these costs in a way which will optimize the energy return. These con- siderations are formulated for both a coarse— and fine- grained environment. Some consequences of the model are explored and discussed in terms of the breadth of the diet, the energy return, and the allocation of time. Finally, a short perspective on the species composition problem in the aquatic community is developed. ON THE BREADTH OF DIET IN FISHES BY Earl Edward Werner A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Zoology 1972 ACKNOWLEDGEMENTS Dr. William E. Cooper is largely responsible for the total environment which proved a constant source of stimu— lation throughout this study. His considerable contribu- tion of support, time, and enthusiasm are deeply appreciated. Especial thanks are also due to Dr. Donald J. Hall who showed steadfast interest in the progress of the study and made invaluable contributions at various junctures. I also wish to extend my appreciation to Drs. Robert G. Wetzel and Herman E. Koenig for their time and assistance. Many forma- tive discussions can be traced to Ivan Valiela, Quentin Ross, Hal Caswell, and Patricia Werner. Bodil Burke contributed in a diversity of ways. The author was supported in various stages of the re- search by a NDEA Title IV fellowship and National Science Foundation Grants GB 15665 and GB 31018X (Coherent Areas Research Project in Freshwater Ecosystems) and GI-ZO (Design and Management of Environmental Systems). National Science Foundation Grants GB 3459, 6505, 8510, and 20962 to some permutation of D. J. Hall and W. E. Cooper supported the research leading to this study. ii TABLE OF CONTENTS Page LIST OF FIGURES. . . . . o . . . . . . . . . . . . . iv THE PROBLEM. . . . . . . . . . . . . . . . . . . . . 1 SIZE AND FISH PREDATION. . . . . . . . . . . . . . . 4 Evidence for Size—Selection by Fish . . . . . . 4 Prey Size and Growth in Fishes. . . . . . . . . 12 THEORY O I O O 0 O 0 O O O O O O O O O O 0 O O O 9 O 17 The Argument. . . . . . . . . . . . . . . . . . 17 Handling Time 0 O O O O O O O 0 G O O O O O 0 O 20 Search Time and a Coarse-Grained Environment. . 21 Search Time and a Fine—Grained Environment. . . 25 The Breadth of the Diet . . . . . . . . . . . . 30 The Biomass Return. . . . . . . . . . . . . . . 33 The Allocation of Time. . . . . . . . . . . . . 37 DISCUSSION . . . o . . . . . . . . . . . . . o . . . 40 CONCLUSIONS. . . . . . . . . . . . . . . . . . . . . 52 LITERATURE CITED . . . . . . . . . . . . . . . . . . 54 iii FIGURE 1. LIST OF FIGURES Relationship of food size to fish size based on data from the bluegill (HCW), and the pike and perch (Popova, 1967). . . . . . . . . . . . Mean percent composition of the 200plankton by species biomass in the Cornell ponds for three nutrient levels . . . . . . . . . . . . . . . . Standing crop of the fish populations in September (less the young-of—the-year) plotted against the mean standing crop of invertebrates )>0.01 mg. dry wt. over the course of the summer(fromHCW)............... Hypothetical search (b) and handling (a) time curves for a coarse-grained situation (curves on a per unit biomass basis). . . . . . . . . . A size-frequency distribution of prey with an arbitrary diet cross—hatched. . . . . . . . . . Typical curve of the time to biomass ratio as x recedes from b to a. The Optimal diet includes items from 2 to b. . . . . . . . . . . Ratios of B/N and'X1Tg7E for an exponential prey distr ibution o O O O O O O O O O O O O O O 0 {1'1 Diet breadth (Q) as a function of search time for prey distributions that are uniform, follow l/x, or where N = 0.9 N (similarly for 0.7). x+l x Curves as in Figure 7 indicating the effects of k on the return from diets of given breadths. . iv Page 10 10 24 24 29 29 36 36 THE PROBLEM Delimiting the manner in which an animal exploits the available food resources is an informative approach to a number of important ecological and evolutionary problems. Extracting energy from the environment is a preeminent concern of all animals and consequently many critical eco- logical interactions revolve about this activity. There is an obvious correlation between the effectiveness of a species' foraging habits and that Species' "fitness" in a given environment. Thus, in evaluating an organisms per- formance relative to competitors, 3 study of food and forag— ing habits is often quite rewarding. Moreover, comparative studies of coexisting forms sharpen our insight on the ways in which species partition the environment. The study of food habits can similarly begin to de— lineate the nature and extent of an organism's broader influence on the structure of the community. Recent studies of certain predator-dominated systems clearly indicate a general pattern. Paine (1966), Hrbacek (1962) and Hall, Cooper, and Werner (1970, hereafter HCW) have affected sig— nificant changes in communities through the direct manipu- lation of predator populations. Harper (1969) and Brooks and Dodson (1965) report similar observations where com- munities were surveyed sometime after the introduction of new species. Generally, increases in the number of species, and the evenness in their apportionment are attributed to predation on otherwise dominant species. Thus the pre- dator influences in some degree (depending on the predator and the system) the expression of competitive relations among a whole subset of prey. In this paper I explore some patterns in prey selection exhibited by certain fishes. Particular attention is paid to the bluegill sunfish (Leppmis macrochirus) which was seen to have a pervasive influence on community structure in small ponds (HCW). Traditionally, efforts to provide a quantitative foundation for prey-predator interactions have stressed the number of prey eaten per unit time as related to prey and predator densities. Usually it is assumed or experimentally determined that all prey are identical. The types of problems outlined above, however, demand that our theories account for which items or what range of items are consumed. In large measure, selective feeding by the predator is responsible for the sorts of community changes noted. Further, indiscriminant feeding will generally be less than efficient on the predatorkspart. Prey size is clearly important in selection by the bluegill and other aquatic predators (HCW, Brooks, 1968). This indicates a quantity common to all prey species which may provide the basis for a first approximation to a theory of prey selection. In addition, competitive advantage among the zooplankton appears to be related to size (Brooks and Dodson, 1965). This would seem to be a rich arena for the develOpment of ecological theory whereby the action of competition and predation could be related through the common quantity of size. Hopefully, from a study of prey selection along these lines important statements bearing on the structure of the aquatic community can be made. SIZE AND FISH PREDATION Evidence for Size-Selection by Fish The pioneering observations of Hrbacek (1958, 1962) on the zooplankton associations of Poltruba backwaters initiated considerable interest in the effects of size- Selective predation by fish. More recent work in Eastern European ponds and backwaters (Straskraba, 1965; Gurzeda, 1965; Grygievek, §E_a1,, 1967) and the works of Brooks and Dodson (1965), Galbraith (1967) and HCW have confirmed Hrbacek's hypothesis. These studies have all shown dis- proportionate predation on Iarge dominant zooplankters resulting in a compensatory increase in smaller forms. In the following section evidence for prey selection by size in fish is reviewed. Finally a rationale for size selec- tion is provided. Trophic apparatus or behavior may clearly limit the range of prey available to a predator. In some cases this limitation is quite strictly determined by structures such as gill rakers or very stereotyped behavior (many inverte- brates fall in this category). Hinde (1959) has noted, however, that in parallel with birds, fishes generally exhibit a considerable catholicity of diet. They are also capable of a high degree of learning and discrimination. Choice of food items regularly changes in response to a fluctuating prey community. The range of prey sizes that can be handled, however, is clearly related to the size of the predator. The mean size of prey taken generally increases with the size of the fish (Ricker, 1932). In some cases the increase occurs rather discretely during ontogeny due to changes in behavior, habitat, etc. The bluegill, for instance, changes from planktophage to benthophage habits (and consequently to larger prey) between 31 and 40 mm std. length (HCW). Other- wise the relation is fairly direct with a slope usually less than 1. The range about this mean is quite large and characteristically reduced at the extremes (Figure 1). The restricted range consumed by the smaller fish is, of course, a consequence of the dimensions of the mouth. The largest fish tend to ignore an increasing proportion of the small prey. Especially, then, through the intermediate predator sizes a wide range of prey sizes are taken. For a fish attaining the size of the bluegill, this range will encompass practically all the invertebrates in most lakes and ponds. Abundant anecdotal and some experimental evidence in- dicates that preference for larger items in the acceptable range is quite strong when these are available. For instance, selection of larger items is inferred from the community changes noted by Hrbacek (1962), Brooks and Dodson (1965) .Ahoma .m>omomv Souwm 6cm exam may cam .Azomv Hanmmsan map aoum mumo co comma muflm away on mNHm boom Mo QHQmGOAumawm A mmDOHm H meme 62m nmE 62m boom 532:- I dim boom 5 owes—I BZIS P003 and Gurzeda (1965). In the presence of fish/large zoo- plankers were much reduced or lost while small species increased and became the dominants. Galbraith (1967) followed the same change after introduction of a faculta- tive planktivore (Salmo gairdneri) to lakes that had been poisoned. Careful measurement of size of zooplankton con— sumed by the fish revealed that greater than 80 percent of the diet consisted of animals larger than 1.3 mm while half of the Daphnia in the lake were less than 1.3 mm. Actual observations on feeding in swarms of Daphnia also indicated the selection of only the larger ones. Gurzeda (1965) found strong selection for larger items in both the zooplankton and benthos. He reports that the larger size prey were always exploited first. This was particu- larly well documented when the fish (carp fry) switched from the preferred benthos to the plankton. In the pond experiments at Cornell (HCW) Ceriodaphnia dominated the zooplankton in all ponds in the absence of fish. When fish (bluegills) were introduced Ceriodaphnia disappeared while large compensatory increases in rotifers, Bosmina and chydorids occurred. All of the latter are smaller than Ceriodaphnia. These changes in community com- position are portrayed in Figure 2. Surveys of the ponds several seasons after the fish were removed showed that Ceriodaphnia had regained its dominant position. FIGURE 2 Mean percent composition of the zooplankton by species biomass in the Cornell ponds for three nutrient levels (LN is low, MN medium, and HN high) with (F) and without (NF) fish (from HCW). FIGURE 3 Standing crop of the fish populations in September (less the young—of-the-year) plotted against the mean standing crop of invertebrates >.0.01 mg. dry wt. over the course of the summer (from HCW). "I" ‘ .Ill.a|\\ Standing Crops of Classes I- IV (8 drv welsh!) 10 FIGURE 2 W OHlsh oMedlum . 0000‘ 51.0!» O W O 4000- ‘b 0 30(1)“ ‘A zooo-I . ' 1) III) IIXIX) 10500 Number of Purllrtles >0.01mg dry weight FIGURE 3 ll 11 Similarly prey taken from the benthos were the larger species. Dragonflies, damselflies, the large midges and amphipods in particular were the most vulner- able. Comparisons of size or age distributions of given species populations in ponds with and without fish further substantiated the size selection. Populations in ponds with fish were considerably more skewed to smaller indi— viduals. For instance, 2nd through 4th instars of the midge Chironomus tentans do not differ in appearance, habitat, etc., but considerably in size. The second in- star, however, was rarely found in the fish guts while the 3rd and 4th often comprised 50—90 percent of the diet by weight. When all species were lumped and categorized only as to particle size (mg. dry wt.) the pattern of prey selection across the nine populations was remarkably con- sistent. Comparing the size—frequency distributions in the fish stomachs to that in the environment again confirmed the extreme selection for Iarge prey. Several instances indicated, however, that density and relative proportions influenced the patterns in size selection. Other investigators have noted size selection in the laboratory. Ivlev (1961) reported it in several species Of fish and LeBrasseur (1969) and Parsons and LeBrasseur (1968) have observed it in juvenile salmon. Experiments by Brooks (1968) and D. J. Hall and myself (unpublished) also show clear preferences ranked by size in prey of similar 12 form and behavior. Other things being equal, one would intuitively expect a fish to take the larger item in a choice situation. Generally prey are simply grasped and swallowed, thus the time or difficulty involved in han- dling prey quite different in size is negligible. The difference in energy return is then essentially "profit". Prey Size and Growth in Fishes The evolutionary "rationale" for this characteristic selection appears straight forward. Growth in fishes is an exceptionally plastic character (Brown, 1957). It is not uncommon for individuals or populations to "stunt" at a particular size for a number of seasons. Either release from density stress (Beckman, 1941) or different environ- ments (HCW) will promote large, size-conditioned differences in growth rate relatively independent of chronological age of the fish. This may greatly affect time to maturity and in some cases size at maturity (Martin, 1952). Moreover, the faster a fish grows the faster it sheds potential pre- dators and numerous other mortality factors concentrated on the small. Many studies of fish populations show very good survivorship for large size classesIbecoming increasingly poor for smaller ones (e.g., McFadden and Cooper, 1964). Laboratory growth studies have further demonstrated the advantage of an individual gaining a slight size edge in a cohort. Dominance then permits this individual to gain a 13 greater share of the resources which allows in turn a faster growth and enhanced dominance. This positive feed- back builds a widening competitive gap for the advantaged individual. It is quite clear that this is a relevant factor in the real world. Stream salmonids sort out pre- ferred feeding spots on the basis of size-determined dominance hierarchies (Jenkins, 1969). Thus natural selec- tion would tend to favor individuals picking up the larger energy "packets" when given the choice. There are a number of references to size of available prey determining growth in the literature. Unfortunately the majority of these are anecdotal and provide no data on other factors which influence efficiency (i.e., total and relative abundances, availability, etc.). Parker and Larkin (1959) and LeCren (I958) mention that bursts of growth can be expected when larger particles of food be- come available, e.g., when a fish switches from planktonic to benthic food. Martin (I952) and Kerr and Martin (1968) have compared lake trout populations feeding on plankton and fish. Where plankton constituted an important part of the diet growth was slower and ultimate size less than in the piscivorous population. They conclude that the differ- ence is due to the relative efficiency of exploiting the respective resources. Paloheimo and Dickie (1966) arrived at a similar conclusion when a review of laboratory growth studies indicated a great difference in growth efficiency 14 on different types of food. The data suggest that the important factor was the particle size that the food came in. A higher growth—efficiency was thought to be corre— lated with an equivalent weight of larger particles because of decreased energy expended in foraging. The role of prey size was transparent in the Cornell experiment. Fish populations, initially identical, were harvested after a season's growth in ponds held at three inorganic nutrient levels. The populations increased 371, 560 and 932 percent in dry weight at the three treatments (three replicates at each level showed almost no variance in total dry weight). Attempts to correlate this produc- tion to total benthic and benthic plus p1anktonic~produc- tion resulted in no reIationship whatsoever. When we chose In) relate the mean standing crop of only those prey larger than 0.01 mg. dry wt. to the fish, however, the expected relationship occurred (Figure 3). Thus the growth of the fish was directly related to‘a small frac— tion of the total invertebrate community--specifically the larger size classes. Larger prey may be energetically more useful or quali- tatively better food on a per weight basis as Karzinkin (1952) argues. Surface to volume ratios alone would sug- gest that an equivalent weight of zooplankton would contain a greater proportion of undigestible parts (carapace) than say fish or large insect larvae. The evidence here is 15 equivocal though and no clear patterns are yet evident. There seems to be little doubt, on the other hand, that considerations of foraging efficiency bear importantly on the prey selection and growth exhibited by fish. In a series of papers Kerr (1971a, b, c) has evalu- ated more recent studies and constructed a growth model that includes a foraging metabolism or cost of searching. Search cost is measured as swimming metabolism over the time required to obtain a given ration. This time is obtained from estimates of prey density, visual limits, and swimming speeds. He found that growth efficiency I 4 "91...... . decreases with a reduction in prey density and prey size. Simulations of lake trout growth resulted in patterns corroborating those obtained from the field (Martin, 1970) where composition of the diet had changed. It was con- cluded that growth in the field would be related to the size distribution of available prey. Glass (1971) has also evaluated the metabolic cost of searching in this case from laboratory experiments. These approaches tend to become somewhat cumbersome as the model "grows". And, although fairly good resolu- tion on certain aspects of the problem is afforded, the models are still constructed around a single or mean prey size. The question of selection of a range of prey from a wider available distribution is not approached. Large prey are generally much less abundant than small and 16 consequently a complete diet of the largest prey is not usually feasible, or necessarily efficient. The argument for efficient feeding seems reasonable and thus should provide some direction in assessing factors mediating the range of prey sizes consumed. What seems to be lacking is a model of the relations of these factors to selection-— simple enough that the ecologist can "think" with it and yet complex enough to bear some relation to the real world. The model should also indicate measurements that can be applied in direct tests of the theory. THEORY The Argument The fundamental predicates of natural selection and a limiting environment often lead the ecologist to study the economics of an animal's situation. Thus many paral- lels in viewing problems have developed between ecology and economics (MacArthur and Pianka, 1966; Tullock, 1971). This is not surprising since the central predicate of eco- nomics is also a "law of scarcity”--otherwise questions of allocation are not at issue. It is postulated in this case that the predator optimally allocating time and/or energy in feeding (with respect to return) will be favored by natural selection. Less time or energy spent feeding per unit return can mean less exposure to enemies, enhanced growth, more resources available to mate selection, breed- ing activities, etc. The reasonableness of the postulate, however, belies the difficulty of rendering the approach fruitful. A great deal of care is required in interpreting "optimal strategies" when the system is very complex and little known. Spurious results are expected since, in reality, the problem is certainly one of suboptimization. An animal would most 17 18 likely optimize foraging efficiency subject to any number of possible constraints varying in importance for a given situation. For instance, it may be important to concur- rently minimize exposure to predation, maximize breeding potential, defend a territory, etc. Weighting these factors could greatly change a prediction of optimal diet derived from simpler assumptions. Of course, this also implies that it may be difficult to isolate a “pure activity" such as feeding in the field in order to directly test the predicted allocation of resources. The advantage of proceeding along these lines is that the predation process is cast in the light of its adaptive significance. This framework seems moreisatisfying, both pedagogically and in extending the horizons of the theory, than methods aimed primarily at prediction. The insight afforded is useful in making sense of the diverse feeding behaviors exhibited by animals, particularly when questions are asked of a different predator, environment, etc. With careful choice of situations, one can look for confirmation of the predictions from a relatively simple set of assump- tions; perhaps where various activities can be examined in a relatively isolated context. In more complex cases the predictions from a simple model can often be productively utilized as a base line from which to systematically explore the causes of deviations from the same. 19 In the following treatment I will pattern the hypo— thetical predator after certain characteristics of the bluegill, but these characteristics are general enough to be applicable to a large class of predators. When in the feeding mode, the predator will be imagined as "patrolling" or "cruising" its environment. A considerable number of prey relatively small compared to the predator are en- countered during a feeding bout. A fairly large number of these prey are necessarily required to sustain this type of forager and will be chosen from the wider range en- countered. The prey will differ in size over some given range and each is handIed individually rather than filtered, etc. It is assumed that size (biomass) is roughly a measure of the energy availed to the predator. In attempting an economic analysis of predation, costs must be affixed in some manner to the prey. For the predator envisaged as "patrolling" while feeding, minimizing the time spent procurring a given biomass of prey will also be ap— proximately equivalent to minimizing the energy outlay. Accordingly this initial analysis will be limited to the time budget of the predator. Obviously the rate at which items are "searched out" or encountered is important. The times it takes to find various prey greatly affects the composition of the predator's diet. It is well recognized, however, that the rate of capture increases at a diminishing rate with an increase in the density of prey. This is 20 generally attributed to the proportionately increasing time spent "handling" prey, i.e., subduing, preparing, eating, carrying to young, etc. (Holling, 1965; Salt, 1967; Royama, 1970). The time spent feeding then will be con- sidered to be simply proportioned between searching for, and handling, prey. Handling Time A fish feeding on particles much smaller than it will not be a "pursuer." The majority of these prey are so less mobile than the fish that they will usually be seen at fairly short range, oriented to, captured and swallowed whole. Over a considerable range of prey size, the time required to handle a particle should not vary much for this type of forager. Watt (1968) and Schoener (1969a) have argued for a similar assumption when prey are small relative to the predator and swallowed virtually intact. Initially it seems reasonable, then, to proceed as though handling time per particle is a constant. This assumption may be relaxed later. Personal observations indicate the handling time for the bluegill is relatively small--on the order of a few seconds. Clearly the time involved is only a factor if a large number of items are eaten or if the economics of taking a large number of small species as opposed to few large, but rarer, species is considered. The pond communities at Cornell 21 afforded prey to the fish that ranged over six orders of magnitude in dry weight (from Aga§_at about 20 mg. to rotifers at 10'6 mg.). Most of these were taken by the fish at one time or another, although rotifers very rarely and only by young-of-the year. It is easy to visualize how handling time would mount if smaller species are con- sumed; it takes about 103 adult Bosmina to provide a biomass equivalent to a single 4th instar midge (Chironomus tentans). And, at times, fish from the ponds could be found to contain many hundreds of prey as small as Bosmina to the virtual exclusion of larger particles. The constant k will be taken as the average time taken to handle any given prey. The handling time per unit bio— mass for a prey of size (biomass) x will, of course, be k/x. Search Time and a Coarse-Grained Environment In an environment that is patchy with respect to prey species or sizes (due to habitats, distribution, etc.) such that the predator can feed primarily in a given patch type, the search time will be taken as the time between encounters with the singular prey type. The search time per item Tx can then be assessed and again multiplied by l/x to convert to a unit biomass basis. The search time curve may assume any form for a given set of environments. Since small organisms are generally much more abundant than large, the curve will probably tend 22 to rise with x as in Figure 4. Addition of the search and handling time curves gives the total cost in time per unit biomass for the various prey sizes. The predator should concentrate on that prey size(s) (and therefore patch) having the minimum. The minimum will naturally change with fluctuations in density, vulnerability, etc., thereby necessitating that the predator switch to differ— ent prey (patches). The coarse—grained case may approximate the predator's economics in certain real world situations. Often species of fish exhibit facultative planktivory whereby feeding switches abruptly from benthos to limnetic zooplankton (Galbraith, 1967; HCW). Usually this can be related to changes in density of one or a few zooplankters seemingly rendering it efficient to exploit this particular food source. The density that elicits switching of course de- pends on size as the above model would indicate. Similar patterns can be seen in the utilization of specific habi- tats during insect emergences. An interesting example is the daily changes in "patch" exploitation by trout in some very simple alpine lake systems (D. J. Hall, personal comm.). Early mornings are spent feeding in the limnetic zone on virtually one species of calanoid copepod. As light in- tensity increases the copepod density wanes due to migration to the bottom. The trout then switch to patrolling the lake margins for much larger terrestrial insects. 23 FIGURE 4 Hypothetical search (b) and handling (a) time curves for a coarse-grained situation (curves on a per unit biomass basis). FIGURE 5 A size-frequency distribution of prey with an arbitrary diet cross-hatched. Time/Unit Biomass LI‘ 24 f (2‘) Pray SI :9 (X) FIGURE 4 /////////Ib 5 Pray SlzeIX) FIGURE 5 25 The evident inadequacy of this type of analysis lies in the assumption that search times are independently assessed for each prey type. Most situations faced by a predator will not be coarse-grained with respect to prey sizes to the extent indicated above. When the predator is "patrolling" a habitat (or mixture of habitats) a diversity of prey sizes will be encountered. Thus the distance traveled between two common small prey also contributes to the distance that must be covered to encounter the next large (but probably rarer) item. This contingency casts the problem quite differently and permits us a more accurate insight into the economics of prey selection. Search time and a Fine—Grained Environment In this section we assume the predator encounters prey roughly in proportion to their relative abundance in the environment. From the distribution of items seen, a diet is chosen which again optimally allocates search and han— dling time with respect to biomass gained. The encountered size—frequency distribution of prey, f(x), is arbitrarily truncated at the largest size (b) easily handled by the predator. For the bluegill over about 45 mm. this is a simple problem since virtually all invertebrates in the ponds would be included. Next arbitrarily define a certain interval of time spent searching, TS, such that a reasonably representative 26 sample of the prey distribution is encountered during this interval. Thus TS is the time it would take to search a certain area, number of crevices in bark, etc. and f(x) is the size frequency distribution of prey actually found. If the predator stops and consumes any of these prey.the handling time incurred over TS will simply be k times the number of particles eaten. The biomass accumulated over Ts is, of course, the sum of the number of items eaten times their respective biomass. Ample justification was provided in earlier sections for never passing up a large morsel if it should become available, particularly if handling time is not much greater than for smaller prey. The problem is then quite simply stated. The predator should always eat the largest items encountered and include smaller prey only as long as this results in an overall increase in efficiency. If the forager minimizes the ratio of time to biomass over the interval Ts, and the distribution f(x) is representative, this will be tantamount to operating most efficiently over— all. Thus the predator is weighting the increase in handling cost incurred over TS by including successively smaller prey (relative to the biomass they contribute) against the efficiency of instead spending that time searching for larger prey. If the predator taries too long handling numerous small item§,large prey further on are lost to it. More precisely, if the distribution f(x) is defined over the interval [a, b] as in Figure 5, the biomass gained 27 over TS when the predator consumes items as small as size x is b B =f 6f(6)d6 (1) x where 6 is the dummy variable for x. The cost, in time, for obtaining this diet will be the search time TS plus the handling time. Handling time for the diet depicted in Figure 5 is simply k times the number (N) of items eaten where b N: f f(6)do (2) X The ratio of time to biomass is then b T + k .{ f(6)do S x .rb OfIGIdd X R = (3) A typical curve as defined by (3) is shown in Figure 6. The optimal breadth of diet can be obtained by differenti- ating (3) with respect to x and setting the derivative equal to 0. That is, when the derivative of (3) is 0 the composi- tion of the diet is such that time per unit biomass is minimal. Thus the value of x at this point (9) delimits the interval [2, b] whereby a predator operating at maximal efficiency should consume anything encountered within this range and ignore everything smaller. 28 FIGURE 6 Typical curve of the time to biomass ratio as x recedes from b to a. The optimal diet includes items from x to b. FIGURE 7 Ratios of B/N and -——§—— for an exponential prey distribution. Cur§$§si55 represent different values of TS where TS(5))'TS(4), etc. 29 Biomass Time/Unit ”L---- 3 Pray Size(x) FIGURE 6 20 10 _B__ / NIWk 10 I 20 Prey Slze(X) FIGURE 7 30 Accomplishing the differentiation and rearranging gives 1" ) [b H.) f(x) (xT +xk f(o d6 -'k of 6 6 s ’ x x 524% (4) b 2 (Ix 6f(6) do) Since f(x) is assumed defined over [a,b], (4) is 0 only when b b x T + xkf f(o) do - k f 513(6) do = o (5) S X x An explicit solution cannot be obtained from (5) since x also defines a limit of the integrals. However, it is possible to plot certain relationships which permit some insight into how the composition of the diet will change with varying search costs, prey distributions, etc. The Breadth of the Diet As one would expect, the optimum diet (R, b] depends on the relative rates at which biomass and numbers accumu— late as x recedes from b (smaller prey added to the diet). Biomass provides an approximation to the utility of the range of items eaten while the cost must be evaluated on the basis of numbers. The integrals in (5) represent, respectively, numbers and biomass. For simplicity, N and B can be substituted for these integrals bearing in mind 31 that the lower limit varies with x. Rearranging (5) then gives B N + Ts/k (6) X > I This indicates how the cummulative ratio of biomass to numbers is related to Q. The B/N curve is a function of the distribution f(x) always starting at the value of x at b and becoming smaller as x becomes smaller (i.e., at xb the ratio is xb f(xb)/f(xb) = xb). Since B/N is a weighted average starting with the largest it does not decline as fast as x, i.e., it always stays to the left of the x diagonal for all values of x after xb. The addition of the Ts/k ratio to the denominator of (6) weights the ratio so that the initial value at xb is-< xb. As B and N grow, however, the effects of TS/k will gradually be swamped out and the ratio in (6) will again fall to the left of the x diagonal. Clearly the solution to (6) occurs at the inter— section with the x diagonal. Figure 7 portrays these changes for an exponential prey distribution. From (6) it is apparent that the absolute magnitude of TS and k are of no consequence to the diet breadth, but rather it is their relative magnitude which is important. (Later it will be shown that absolute magnitude of k is reflected in the biomass gained per time unit.) Recall that TS is some arbitrary amount of search time and k the handling time per particle. Consequently the ratio of the 32 two holds no particular significance except in relation to the size—frequency distribution of prey encountered over TS. That is, for any given situation the relation between the time taken to search a certain area, volume, number of crevices, etc. and the size-frequency distribu- tion of prey actually encountered can be determined. This will then define a unique relation between Ts/k and B/N. It will be possible to explore the effects of changes in the abundance of items (without change in relative propor— tions) encountered per time unit alternatively by holding the distribution constant (and hence B/N) while increasing T8 or holding the ratio TS/k constant and changing the absolute values in the distribution (and hence the magni- tude of B and N). Either way it can be seen that this is equivalent to manipulating the search time required to encounter a given number of prey. Increasing search time naturally drives 4 back. As prey become successively rarer, the predator must broaden the diet to compensate (Figure 7). The magnitude of the change effected by vagaries in Ts' however, depends on the characteristics of B/N or the prey distribution. For instance, a given ratio of T; to k will have a greater effect on a distribution where large items are rare since B and N will be small initially. The larger B and N are initially the faster the effects of Ts/k will be swamped A out. In Figure 8, x is plotted against TS for several 33 distributions of different form. Clearly, the more uni— form the distribution of prey, the slighter the effect of increasing search cost on the breadth of the diet. As the distribution drops off sharply to large items, changes in search time when TS/k is small have a large impact on diet breadth. When TS/k is quite large significant changes in search time affect the diet very little. Thus both the time required to find prey and the way these prey are distributed are important to considerations of an optimal diet. The Biomass Return It was noted that the breadth of the diet depended on the characteristics of B/N and Ts/k' For a given B/N, however, any number of values of TS and k will give an equivalent value for the ratio and thus specify a unique diet. To this extent, then, the breadth of diet must be independent of the energy return. Although Ts's of 1000 and 100 and k's of 200 and 20 respectively will determine equivalent diets, the actual biomass obtained per unit time could not be even nearly equivalent. Going back to equation (6) it can be seen by rearrang- ing that kB 2(T + kN) s or (7) CD wrx> 34 The ratio on the left in (7) is actually the inverse of the time to biomass ratio initially set up in (3). According to (7), then, the actual value of the biomass to time ratio at optimum will equal the x delimiting the lower end of the diet divided by the handling cost. Hence the actual return in the example given above will differ by an order of magnitude despite the equivalent breadth of diets. Obviously, if k is l or time is scaled such that k is l, the return per time unit under optimal conditions will be simply equal to Q. In this case Figure 8 can be con— sulted to obtain not only the interval [9, b] but also a perspective on the biomass gained over various conditions (since this will follow Q). It is easily seen here how increasing the search cost affects the biomass foraged. Again the shape of the distribution, primarily the relative abundance of large items, is crucial. When large prey are relatively rare the return dips sharply as search costs are increased. For k £ 1, the curves in Figure 8 are multiplied by l/k to obtain the biomass/time value. Another way of visualizing the role of k is depicted in Figure 9 where again (6) is presented for an exponential prey distribu- tion. For any given x at optimum the biomass/time will be a line with slope l/k. Iseveral of these are plotted in Figure 9. To find the biOmass return one simply finds where 35 FIGURE 8 Diet breadth r?) as a function of search time for prey distributions that are uniform, follow 1/x, or where NX+l = 0.9 NX (similarly for 0.7) FIGURE 9 Curves as in Figure 7 indicating the effects of k on the return from diets of given breadths. N Prey Size a Q 36 N 0.9 9% 0.7 Seech Time (Ts) I?ICHflREI 8 Prey SlzeIXI FIGURE 9 37 the curve crosses the diagonal and reads off the value for this x on the l/k lines. In general any factor decreasing the breadth of diet for a given k will increase the return since this will result in a larger x at optimum. The Allocation of Time If a predator is feeding with optimal efficiency in accordance with the model, changes in the distribution of prey, the search cost, or the handling cost will precipitate changes in the proportion of time spent handling and search— ing while the animal is foraging. It may be useful in certain situations to measure this proportion directly. Generally this type of measurement would be more easily obtained than the other parameters in the model. Compara- tive measurements on coexisting species may then point to interesting problems in niche segregation, etc. The more formal background of the model will provide a first idea as to possible implications of these differences and critical points of analysis to be approached empirically. Specifically, the proportion of time spent searching relative to handling will be the time it takes to search out the given distribution, TS, divided by the handling cost per item, k, times the number of items actually taken from the distribution encountered. Thus we are interested in the changes in the ratio TS/kN as reflected by changes b in the diet (where N is again J. f(d) do). When only x 38 large prey are taken this ratio will be relatively large and diminish as smaller items are incorporated in the diet. Our immediate interests are not how this changes as the diet broadens with a given set of conditions but how the specific value at optimum breadth differs under changing conditions such as vagaries in search time and prey dis- tribution. For a given distribution and small TS/kratio the proportion of time spent handling is much greater and therefore the ratio TS/kN‘< 1. As search time is increased (holding the distribution constant) the optimal diet broadens and the proportion of time spent searching in- creases. The rate at which this proportion increases, of course, depends on the characteristics of the distribution jointly with the increased search cost due to the effect these have on changes in width of the diet. This is true up to the point where search costs are so high that virtu— ally everything seen should be eaten--at this point further increase is strictly a function of the increase in TS unconfounded by diet changes (i.e., k and N are constants). The nature of the distribution is particularly crucial to the more interesting case where changes in parameters still dictate a choice between items rather than consumption of everything seen. The proportion of time spent searching goes up slowest and only attains modest values for distribu— tion where prey are about equally abundant and the range of 39 size is small. This grades through to the extreme case in the other direction where large items are quite rare relative to small prey and there are very large differ- ences in the size of prey.‘ In the latter case large values of TS/kN can mount with relatively little change in the composition of the diet. If large peaks in the dis- tribution are included in the diet at some point, the ratio may drop and begin to rise again. That is, a steady over- all increase in TS may result in a fluctuating TS/kN ratio if the distribution is not well behaved. DISCUSSION "Simplicity of this kind is only an intermediate stage between previous and succeeding complexities." Poincare in Science and Hypothesis 1905. A purview across the diversity of feeding adaptations in animals, both morphological and behaviorial, leaves one somewhat timid in attempting generalizations on the strate- gies of allocating basic resources (time, energy). Moreover, particular activities, such as feraging, are seldom accom— plished in a pure state which would permit an unequivocal measure of such patterns. A few things can be noted, however, strictly on considerations of the relative size of predator and prey. Predators consuming prey large relative to themselves generally suck the juices from it (spiders, etc.) or tear it apart for consumption (raptors, canines, felines, etc.). Often the prey must be pursued; the difficulty of capture or time taken being a function of the prey species or size. Handling time will probably also be a function of prey size. As the prey become larger, the possibility that the predator may sustain some injury in subduing it grows. Optimal prey size(s) will hinge on factors such as these 40 41 weighted by the search costs (or probability of encounter) incurred in the particular situation. Where a single or few prey will satiate the predator it may be the first thing encountered that can be pursued with fair success should be attempted. Further, large "hunger cycle" effects (Holling, 1966) can be expected. Searching behavior and prey choice may both change significantly with large, rather discrete changes in hunger. This case is more dif— ficult to evaluate with the model considered here. At the other end of the spectrum, where prey are very much smaller than the predator, items can be easily swallowed intact. In view of the number it takes to sus— tain the predator, however, the cost levied in handling each .prey individually is simply insurmountable. Here one notes especially morphological adaptations built on some sort of filtering principle. Many fish (Brooks, 1968), the baleen whales, insect larvae, crustaceans and other invertebrates are thus equipped. In some cases either a particulate feeding or filtering strategy is opted for by the same predator as a response to prey density. This would be an interesting case to explore more fully from both an empiri- cal and theoretical standpoint. In Obligate filterers, optimal foraging would probably be most clearly related to the density of prey. Habitats or patches which provide the most biomass per unit time of items in the filterable range should be exploited. 42 Through the middle ground, items are usually handled individually and can be swallowed intact. A reasonably large number of prey must be taken and generally a range of sizes is available. Recognition of prey is often by sight and sizes can easily be discriminated. This type of situation is most usefully considered in the light of the foraging model. Handling cost will become a factor due to the number of prey taken. Also pursuit generally be- comes less of a factor since the predator is usually rela- tively more mobile. Comparisons with the real world may be most appropriate where diurnal cycles in prey activity, the tide, etc., result in a limited time when prey are available or where a large proportion of total time avail- able must be spent feeding. The latter situation often occurs during extreme seasons such as winter, the dry season, etc. In these sorts of situations foraging activity, .EE£.§Ev is likely to be practiced largely at the exclusion of others and the continuous feeding will minimize large hunger effects. High metabolic costs as in birds will often place similar constraints on the animal, particularly in the less productive seasons or in more saturated faunas where competition is great. On the surface, then, a number of birds, fish and perhaps some of the insectivorous mammals would fit in this category. Attempts at a more formal analysis of prey-predator systems have resulted in an extensive literature going back 43 to the early 1900's. The majority of these works seem to stem from basic notions advanced by Lotka (1925) and Volterra (1926) or the directions indicated by Nicholson and Bailey (1935) and Thompson (1939). Both approaches are founded in random encounter hypotheses and consider all prey (and predators) equivalent in all respects. Therefore numbers provide an adequate discription of the populations. Numbers eaten per unit time are then appro— priately related to the demographic parameters of the respective populations. Later authors have incorporated other factors and relaxed various assumptions while adher- ing to this central theme. In this paper I have attempted to construct a model providing insight into the problem of which different types of prey a predator consumes. Inevitably the real world avails a range of items and most predators practice some degree of discrimination. The quantity eaten was obtained by assuming that all prey encountered in the "elected" sizes would be taken. This could easily be weighted by some "catchability" factor reflecting unsuccessful attempts at capture for a more realistic picture (changing the range of items eaten in much the same way as increasing k). Also the prey distribution was assumed an "effective" density, i.e., those prey actually seen. Proceeding from some well substantiated observations on the selection of 44 prey by size in a number of fishes, it was postulated that this could be reasonably couched in cost-benefit terms. A considerable body of ancillary information on growth of fishes was aISO suggestive of the economic considerations in the selection of prey. Clearly, in arguments posed along these lines the prey must be considered to differ in some relevant feature(s). In cases where prey are all assumed equiva- lent, optimizing intake per time unit simply requires that everything encountered be taken. Thus the legitimacy of considering numbers as related to some encounter hypothesis utilized in the models mentioned above is apparent. The number eaten can then be related to a host of other factors affecting the probability of encounter such as accessi- bility (Bailey §t_al., 1962), hunger (Holling, 1966), learning (Ware, 1971), visibility, etc. Such factors can often be very effectively explored with this approach. Questions of strategy here must deal with the efficiency of certain modes of searching, selection of habitats affording the greatest probability of encounter, etc. In other words, search time should be minimiZed. A natural first step in broaching the question of a selection strategy is to consider all prey equivalent except in their handling Cost (including pursuit). That is, if all prey were approximately the same size but differ in the difficulty of capture or extraction. A well-known 45 example is the difficulty fish have in capturing copepods relative to cladocerans (Karzinkin, 1952). Another example might be woodpeckers excavating similar—sized larvae from different depth in wood. This latter case is an accessibility problem probably faced by all predators feeding predominantly on one prey type. Good examples of qualitative differences of this sort can be found in Errington (1946), Southern and Lowe (1968) Craighead and Craighead (1956). MacArthur and Pianka (1966) have advanced a strategy argument for this case. Here all prey are the same size but can be ranked by the time it takes to pursue, capture and eat the item. The optimal diet is determined by adding different prey by their rank to the diet until the decrease in search cost is overbalanced by the increase in pursuit cost on a mean time per item basis. The argument is presented qualitatively with no function provided for the hypothetical curves. Conversely, prey can be considered to all require roughly the same handling time but different in size or caloric value. This is, of course, the case made in this paper from evidence in fishes. Here an a priori ranking or "utility" is provided based on the size of the prey and patterns of prey selection by fish seem to corroborate this. Functions are indicated for assessing the economics of a given diet. Royama (1970) has looked at some special situations contrasting the efficiency of exploiting prey differing in 46 both handling and search costs. The efficiency is again weighted, however, in explOiting one prey type--much as in the coarse-grained analysis introduced earlier. Other investigators, notably Emlin (1966) and Schoener (1969a, b) offer models reflecting on prey selection incorporating a considerably more complicated set of factors. Both are concerned with time and energy. Emlin (9p, git.) looks at the contingency of eating one prey type relative to a dif— ferent one given a set of parameters describing the energy and time expended relative to the energy return. Schoener (pp. gig,) allows both prey and predator size to vary. The latter model is quite complex and it becomes difficult to sort our various influences. In general, the predator will not be feeding on one prey type or, if this is the case, it is often temporary. Consequently the breadth of the diet is of particular interest in regards to assessing the impact of the predator and the overlap in resource utilization by competing forms. The actual performance of a predator is related to the return/ time which is not necessarily evident from the breadth of the diet. From the model certain qualitative statements can be made about both of these considerations. For the most part, it was seen that the predator having a narrower diet, i.e., a relative specialist, may be responding (either day to day or evolutionarily) to an abundance of prey or a large handling cost. That is, 47 firstly, any factor contributing to a uniform increase in handling time relative to some search time will force a restriction in the diet. Only large items near the upper limit handled should be consumed where the ratio of search to handling time is lowered by an increase in k. MacArthur and Pianka (1966) also predict that predators having high "pursuit" to search ratios will exhibit more restricted diets. A possibility immediately evident is where prey must be excavated from material, extracted from a shell, etc. If the difficulty of this Operation is differ- ent in two environments corresponding changes in the width of diet of a predator found in both could be expected. Also, where factors favor a narrow diet, separation in the food niche should be cleaner. Perhaps this contributes to the extreme sexual dimorphism in species of woodpeckers (Selander, 1966) by reducing the intraspecific competition for a relatively narrow range of food items. It might also be argued that changes in the environment (e.g., proximity of refuges) or other factors affecting the "catchability" of all prey in roughly the same manner will produce similar results. That is, as the‘proportion attacked but missed grows, this is tantamount to increasing the handling cost per item by some factor. Alternatively, lowering the search time required to see a given distribution of prey allows the predator to specialize on a smaller range of large items. A more 48 productive environment is an example of a change in this direction. Gurzeda (1965) found carp in ponds to increas- ingly specialize on large items as density of the fish Stock decreased and/or artificial food was provided. Both, of course, permitted higher natural prey densities. A decrease in environmental complexity may also reduce search time. For instance, both Southern and Lowe (1968) and the Craigheads (1956) found environmental complexity crucial to the abilities of raptors to locate prey. Glass (1971) found in experimental situations that searching cost as measured by metabolism for the largemouth bass was less in a simpler environment. An increase in visual range as a result of changes in turbidity, etc. could be very important in this respect to the aquatic predator. Or, height above the surface for terrestrial predators hunting from perches. If those predators are feeding on the same prey, overlap in the diet should decrease as perch height diverges. Differential predator mobilities may lead to similar diet differences. The converse cases, higher search and lower handling costs, naturally tend to broaden the diet. Commonly, large prey are very much rarer than small. Characteristically the size-frequency distribution will show a preponderance of prey in the small classes with an attenuated positive tail. In some cases this has been adequately described by the log normal distribution (Schoener and Janson, 1968). Clearly the "desirability" of 49 a certain size prey is strictly conditional to the size, abundance, etc. of the larger prey available. The breadth of the diet will change as characteristics of the size— frequency distribution Of prey encountered differ. Other things being equal, an increase in the proportion of a large prey may free a smaller prey from predatory pressures. Changes in the distribution of small prey to the left of § should not affect the diet unless the situation approaches the coarse-grained case presented earlier. Then it is possible that larger items should be abandoned in favor of an exclusive diet of very abundant small prey. In an earlier section it was seen that the total biomass/time gained from an Optimum diet was equal to the factor l/k times the x delimiting the lower boundary of the diet. This, of course, is the quantity of ultimate concern in assessing the advantage of any diet or in compar— ing efficiencies of competing forms. If k remains constant, any change admitting a narrower diet increases the energy intake per time unit (e.g., decreased search time, greater proportion of large prey, etc.). From Figure 8 it is clear that the smaller TS/k is the greater the effect a given change will have on the return, particularly if k is small. When resources are quite rare (Ts/k large), a large change is required to produce much difference in the return. Or, if k is quite large, a significant increase in diet breadth gives minor changes in return (since biomass/time is a line 50 with slope l/k, a large k results in a slight change with x--see Figure 9). As a consequence of the above, one might expect pre- dators consuming prey which require large amounts of handling time or that are scarce to show a greater variance from the expected diet than a predator in the converse situation. Deviations from the optimum diet will not re- sult in large changes in return in these cases. However, a predator feeding on prey that are abundant and quickly dispatched (TS/k small and k relatively small) should be less "capricious" since significant differences in return may result. Thus fish consuming large numbers of zooplank— ton may show considerably more attention to the size of prey selected than a fish preying on'benthos for instance. It is, of course, in the zooplankton where size-selection has been so evident and Galbraith's (1967) study clearly shows how discrete this size—selection may be. Clearly as the composition of the diet changes the proportion of time spent handling and searching will also change. Some predators may be required to alter their tactics considerably on a day to day basis. The bluegill, for instance, was faced with extreme fluctuations in the zooplankton over the course of a week (HCW). Similarly, emergences in the benthos produced marked alterations in the relative abundance of prey available to the fish. 51 The predator must be constantly modifying its behavior accordingly in order to be at all efficient. Obviously a predator will be a "searcher" if Ts is very large relative to B, N, and k. If the range of prey sizes available is relatively small, generally this will indicate a situation where everything encountered should be consumed. The predator will spend most of its time searching and still pass up items only if the prey avail— able are very different in size. For instance, the prey available to the bluegill at Cornell ranged over 6 orders of magnitude in dry weight. Generally rotifers and zoo- plankton were quite abundant giving way to an extreme attenuated tail of rare large items. This wide range of relatively rare items provided the mainstay of the diet. In this sort of situation large changes in T8 will often precipitate little difference in diet if the next smaller category is considerably removed. The prOportion of time spent searching, however, may be considerable. When a preponderance of the time is spent handling prey it is likely to be the result of high handling costs, low search costs, or a distribution of prey differing very little in size. CONCLUS IONS In many ways, size may provide a toehold toward the resolution of some important questions facing aquatic ecologists. I will attempt to point to some of these possibilities in a very general way. If one were to study the interaction of two of the major processes responsible for community organization, i.e., competition and preda— tion, one would justifiably look for this interaction on as simple a background as possible. Ideally niche dimen- sions having the potential to segregate bona fide species would be relatively limited. Thus the competition problem would not be insurmountably complex. Similarly one would like the possibility of observing predation on this system in a relatively simple environment. Thus a few simple predicates should suffice in quantifying the predation component. Finally, one should like a quantity common to the expression of both processes by which to relate this way of selection and counterselection to appropriate species pOpulations. The fish—zooplankton associations, particularly of the limnetic zone, seem an eminently suitable choice of system by these criteria. It was noted earlier that size may 52 53 provide the "common quantity." There are indications that the large cladocera have a competitive advantage, presum— ably based on food processing capabilities, over the smaller species. For the most part, this is inference drawn from the numerous observations on natural systems where predation on the larger species results in a "blossom" of smaller species. As was noted earlier, removal of the predation pressure encourages dominance by the large species (HCW). It may be possible to quantitatively relate the advantage of larger species, via filtering rates, g3g,, to their respective sizes. Or, perhaps the application of known predation pressures on these communities may provide the most tangible meaSure of size-related competitive advantage (MacArthur, 1968). The advantage of size can then be weighted against the disadvantage due to predatiOn. Models of the sort I have proposed should aid in delimiting the sizes (species) which are subject to various predation pressures in given situa- tions. 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