Proc. Nat. Acad. Sci. USA Vol. 71, No. 10, pp. 4169-4172, October 1974

The Compression Hypothesis and Temporal Resource Partitioning (feeding strategies/competition/ecological niche) THOMAS W. SCHOENER Biological Laboratories, Harvard University, Cambridge, Massachusetts 02138 Communicated by Edward 0. Wilson, June 13, 1974

ABSTRACT Contingency models of feeding compare Optimal diet the energy per unit time gained from utilizing a resource unit of a particular kind (food types, habitat patches, Existing models of optimal diet relate selectivity to food abun- time periods) against that energy/time expected if the unit is skipped. Optimally, an' animal should reject the dance in two fundamentally different ways. Firstly, the opti- particular unit if and only if the former energy/time is less mal diet can be governed by contingency feeding,-in which the than the latter. Consequently, food or habitat types animal weighs the per-unit-time energy gain from an item of should be excluded if the prospect of finding and con- food if caught and eaten against the expected gain if that item suming better types is sufficiently high. In contrast', is skipped and only better items are searched for and con- feeding periods should be skipped only if it is less costly to wait than to feed. sumed. Secondly, the optimal diet can be governed by re- In situations of high food abundance, contingency stricted feeding, in which extent of an animal's fixed require- models imply that animals should bemaximally specialized ments or fixed opportunity to feed determines how selective it with respect to food or habitat type, but maximally should be. generalized with respect to time period. As food decreases at- in abundance, food and habitat types should be added to Models of contingency feeding have received the most the diet or itinerary, but time periods should be omitted tention in the literature so far (1, 4-6, *). They maximize the from feeding activity. In contrast, animals with fixed ratio of the expected net energy gained per item of available caloric intake should broaden diet, habitat, and feeding (= encountered) food to the expected time to find, catch and times as abundance decreases. eat an item of available food. This ratio is According to contingency models, competitors cannot cause item kinds to be dropped from the diet, but because they" can affect the values of patches once found, can E pie - CT cause habitat kinds to be dropped from the itinerary. YT= diet [1] Competitors also reduce the'value of feeding during'par- E pits + T77 ticular time periods, but ordinarily fairly severe depletion diet must occur before it is optimal'to feed no longer in -a period frequented by competitors. These arguments imply that temporal resource par- where e1 is the net energy (potential minus pursuit and han- titioning on a diel basis should be relatively rare. In fact, dling-swallowing costs) for a single item of Type i; t, is the specialization according to feeding period should differen- time to pursue, handle, and swallow a single item of Type tially occur in animals of limited abilities to use or process available food,- whereas that need not be the case for food- i; pi is the frequency of Type i in the environment (availabil- type or habitat specialization. It should also occur in ity), T. is the mean search time per item of available (en- animals sensitive to and found in variable climates. countered) food, and C. is the cost per unit search time. T, = K/D, where 1/AK is a rate of search and D is food density MacArthur and Pianka's (1) model of optimal feeding hy- (4, 5). Notice that summations are over only those item kinds pothesizes that a decrease in food abundance, as might be actually eaten. Models very similar in structure and basic caused by the invasion of a competitor, should decrease the concept to Eq. 1 have been derived by Charnov* and Pul- range of habitat patch types an animal utilizes but should liam (6). not affect the range of item kinds in its diet. This proposition YT ia Eq. 1 is written as a ratio of expectations that are was later labeled the "compression hypothesis" by Mac- taken per item of available food; exactly the same expression Arthur and Wilson (2) and related to the first stages of re- results- if expectations are per item eaten. To see this, let source partitioning. However, Pianka (3) has pointed out pi' be the abundance of Item Kind i in the diet and T/' be the that dimensions along which species divide resources can be time between items of food actually consumed. Then sub- three classified under general headings: food type, habitat, stitute pi. = p/(p)i for Pt and T7,,' = K/D( pi) for T, and time. MacArthur and Pianka's treatment deals with diet diet selectivity of resources arranged along the first two types of into Eq. 1. The numerator and denominator are now differ- dimensions but does not consider time. This note (1) rederives ent, but the 1/Z p, cancel to give the same ratio as before. the yet still diet compression hypothesis from a more general, x should be we very simple, model of optimal foraging; (2) asks how reduction To determine whether Item Type eaten, whether with x is than without in food abundance, as might be caused by competitors, affects need to know YT greater YT the range of diel feeding activity times; and (3) discusses the implications of these models for the theory of resource par- titioning. * E. L. Charnov, unpublished manuscript. 4169 Downloaded by guest on September 26, 2021 4170 Zoology: Schoener Proc. Nat. Acad. Sci. USA 71 (1974)

it. In symbols, x should be eaten if and only if maximizes YT, subject to the constraint that the total feeding p ei + -CT8ET - time equals some fixed period. This animal, which maximizes pxez pie, C8T8 the energy gained during a fixed amount of feeding time, is an diet >diet ~~~~~~~[2] a, Pits + pxtx + T8 E-pti + T8 "energy maximizer" (8). In both these kinds of restricted feed- diet diet ing, what determines selectivity is the extent of the fixed caloric requirement or fixedd opportunity to feed. where the summations are taken over all items eaten except Onlv very simple models of restricted feeding exist so those x. fart. items of Type Inequality 2 reduces to They apply to sit-and-wait feeders or passive searchers, who pie, - C8T8 Z Nje1 -CUKA because they perform many activities simultaneously with e> diet diet food search and search inexpensively, are not charged for tz E piti + T8 Z Nft, + KA search time and energy. Selectivity in these models can diet diet clearly be seen to be related to fixed requirements or op- Notice that the expression right of the inequality sign is portunity, as follows. Fix the total number of food items an written two ways, one involving relative abundance (the animal would encounter during a feeding period. Then the pi), the other absolute abundances (the N1). The rightmost greater the requirements during that period, the more kind expression is obtained from Eq. 1 by substituting E N/A for of food must be taken, or the greater the time to feed, the more kinds can be taken. In these simple models, no account is D and Ni/E Ni for Pi, where N is the absolute abundance of taken of the possibility that while feeding on a particular item Item Type i in area A and the summations are taken over all another item might be missed; rather, they assume that feed- item kinds, whether in the diet or not. ing time is small relative to exposure time. Verbally, Inequality 3 says that Type x should be included if and only if the energy gained per unit time while catching Optimal habitats and the compression hypothesis and consuming it (ex/tx) exceeds the average energy per unit Since MacArthur and Piank4 model habitat selection as con- time gained by skipping the item and looking for and con- tigency feeding, we limit the following discussion to that kind suming better items. MacArthur (7) has given a simpler and of model. The general equation (Eq. 1) for contingency feeding more specific version of this statement. The effect of a lowering can'be used to model optimal utilization of randomly en- of food abundance (D) is to increase T8 and thereby lower YT. countered patch types simply by redefining the symbols: This in turn makes it more likely that previously rejected item es is now the energy gain from feeding in Patch Type i, ti is the kinds (such as Type x) will now be included in the diet. Here, time spent feeding in one such patch and T8 is the travelling selectivity decreases as the chance of finding something better time between two available 'patches. Just as for items, an after skipping an item decreases. Charnov* has elegantly animal can be thought of as accepting or rejecting patches employed derivatives to show that with decreasing abun- depending on their ei/t1. dance item kinds are added to the diet in decreasing order of MacArthur and Pianka's graphical arguments can easily be ei/ti. adapted to our algebra. An overall decrease in food abundance Contingency models are not as general as they might look, can lower e/t for patch kinds. If this can be represented in however, because they make the strong assumption that D Inequality 3 by a proportional reduction in each e, then this (food density) is constant during the time the animal is trying decrease cannot cause a patch type formerly included in the to maximize YT. An example which fits this assumption is itinerary to be now dropped. However, it can (but need not) that of a territorial feeder that forages over some but not all of cause habitat types excluded in the itinerary before the de- its uniform territory during the time between renewal of food. crease to be included after. Hence decreasing food abundance If it does not cross its path (like an efficient lawn mower), it can lower selectivity for both food types and habitats. De- will encounter food at constant D. However, imagine that the creasing food abundance overall, however, may not cause a animal feeds at maximum YT but runs out of unperused area proportional drop in e/t if different proportions of time are before the next renewal period. It has then gained a certain spent searching in each patch type, or even if the same propor- number of calories, but that number may be insufficient to tion is spent searching. If no time were spent searching, then meet its requirements. Then the animal would have to go over ej and ti would be reduced by the same amount, and In- the now depleted area, picking up items formerly rejected so equality 3 if true before would be true after density reduction; as to avert starvation. Rather than that, an optimal feeder whereas if Inequality 3 were false before reduction, it' could would have picked up those items to begin with, gauging its easily be true after reduction. Hence, as MacArthur and overall selectivity on the basis of how much energy it requires. Pianka argue, pursuers should more consistently show the The object of this animal's feeding strategy is to maximize IT. habitat expansion after reduction of food than searchers. subject to the constraint that the energy gathered must be a Competitors act differently from an overall decrease in certain amount. This animal, which minimizes the time spent abundance'in that they diminish the abundance of certain, gaining a fixed amount of energy, is a "time minimizer" (8). possibly preferred, item kinds and do this in certain patch We also might imagine an animal whose ceiling on the amount types more than others. As Inequality 3 shows, the decision as of energy it can process is high relative to that available. Such to whether to include Item Type x does not depend on the an animal could be limited, however, by the time it has to feed. Again, that animal, if it feeds at maximum YT, may t See refs. 4 and 8. However, somewhat similar models, which do finish perusing its area before the end of its feeding period. not consider time, are used by animal nutritionists; these gen- Such an animal could have gathered more total energy if it erally take the form of linear programming models where nutri- widened its selectivity such that the entire area was covered tional constraints can easily be formulated. See Westoby for a just by the end of the feeding period. Here, the optimal feeder review (9). Downloaded by guest on September 26, 2021 Proc. Nat. Acad. Sci. USA 71 (1974) Compression Hypothesis and Temporal Resources 4171

item's abundance (either relative or absolute), so that reduc- But this inequality is obviously always true, provided only ing the abundance of Item x cannot cause that item to be that e, > - W,. Hence, unless feeding in a given time period dropped. The only possible change from such a reduction is results in a greater loss of energy than waiting, feeding should that some other items may be added. Hence optimal diet take place, according to this model. should expand or remain constant during the initial stage of A second way to approach the problem is to apply to time competition. But optimal habitat is different. A specialized periods the verbal translation of Eq. 3 given above. This asks competitor may deplete some patches to the extent that they whether the energy per unit time gained by feeding during are effectively absent, thereby raising T8, or on the right of some period (e_/t,) is greater than that gained by not feeding. Inequality 3, reducing the No. But far more importantly, a But "not feeding" in this context is waiting. Clearly, on these competitor preferring Patch Type x will actually reduce ex/t,. grounds alone feeding should almost always be favored be- Therefore, Inequality 3 may be true for e,/t_ before com- cause no energy is ingested while waiting. petition, but after competition, since e./tx is reduced, may no These considerations imply that temporal specialization longer hold. Thus preference of a competitor for Patch Type x should vary with food abundance in exactly the opposite can cause it to be dropped. This basic difference between manner to food or habitat specialization. In situations of very items (value once found unchanged by competitors) and high food abundance. only the best item kind is taken and patches (value once found changed by competitors) is what only the best patch type is foraged in. Hence specialization on underlies the compression hypothesis. However, inasmuch as food type and habitat is at its maximum. But under situations competitors reduce the worth and availability of patch types, of greatest food abundance, there should be no time during they can, as for diet, decrease overall selectivity if favorable which feeding results in a greater loss of energy than waiting. habitat is limitedT. Hence temporal specialization is at its minimum. With de- creasing food abundance, item kinds and habitat types are Optimal activity times added, but it is possible that food availability becomes so Let us now try to contrive a model for contingency feeding low during certain periods of time that it is less expensive to where instead of items or patches we have periods of time. wait those periods out. Hence food and habitat type broaden Kinds of periods may be defined by a cluster of factors (which while diel activity periods shrink as abundance decreases. affect energy expended) and need not simply correspond to The effect of a competitor is like that for patches, however, continuous hours of the day. The expected net gain per period in that ex/tl during preferred periods of time is lowered. If of time is ex/tx is lowered too far, then time periods can be dropped. In this respect feeding times of competitors should diverge Eefip - E Wipi, act inact like habitats. But the degree of food depletion necessary to cause time periods to be omitted may be greater than for where ei is the energy gained while feeding in a period of Type of feeding must be is the energy habitats: the profit (now negative) actually i, pi is the frequency of periods of Type i, Wf less than that of waiting. This circumstance is certainly pos- (including maintenance costs) lost while waiting through a sible, especially under severe climatic conditions, but probably period of Type i rather than feeding, E sums over all periods act is often unlikely if that profit were initially positive. In con- during which feeding activity occurs and E sums over all trast, especially if food is abundant, selective depletion of inact certain habitat types can easily tip the balance in favor of periods of inactivity. The expected time per period of time is other, nondepleted types, thereby resulting in habitat shift. just E tipi, where ti is the duration of a period of Type act + inact Of course, it is possible that animals will not be as generalized i. Hence, with respect to time as contingency models imply, if by being so generalized they gain more food than they can process. eipj - EI Wipi Such or animal with a fixed caloric act inact animals, any requirement, YT = should specialize with respect to time as food abundance tip. [4] act + inact increases, just as they should for food or habitat. Thus con- tingency feeders and restricted feeders should react in oppo- To determine whether periods of Type x are worth including, a in food Williams contingency model following Eq. 2 asks whether site ways to changes overall abundance. (10) reports that during poor weather when yield from the best E eipi + expz- E Wspi feeding periods is less, certain animals (daddy-longlegs, act inact cattle) enlarge their activity times. Such animals are behaving Ex tips as if they have a fixed caloric quota. act + inact E ejpj - E Wipi - Wxpx Application to resource partitioning act inact [5] Species can partition resources only if it is adaptive for their

acta+t+pninact individuals to specialize on some interval of a resource axis. If the species are too similar upon coming together, they must t Incidentally, we can imagine, just as for diet, that animals also diverge in order to coexist. feeding at maximum YT run out of patches before satisfying The compression hypothesis, generated by contingency their Then selectivity will have to decrease. requirements. again, models, applies to divergence only during the first, nonevolu- It is also easy to that habitat patches, especially when imagine that not are not encountered randomly. If the animal knows where tionary stages of species overlap. It says habitats, large, in the various patches are, selectivity will vary with the time spent food types, should diverge. As we have seen, time periods feeding even when there is no overall shortage of suitable foraging such models should be like habitats rather than food types. area (5). However, the amount of resource competition required to Downloaded by guest on September 26, 2021 4172 Zoology: Schoener Proc. Nat. Acad. Sci. USA 71 (1974)

cause an animal to drop certain periods of time from its ac- grazers (11) and parasites, morphological change should be tivity should be considerably greater. particularly effective in allowing specialization by food size. Natural selection may be expected to change a species' Change in susceptibility to secondary compounds can likewise phenotypes and thereby change its ei and ti by changing allow specialization by food type (12). Morphological changes abilities to find, catch, and consume various kinds of food. such as in body proportions can help animals specialize on Unless an initial behavioral divergence is rapidly fixed geneti- habitat types (3). In contrast, for animals with internal ho- cally, such selection can divert the course of resource parti- meostasis, it is harder to imagine what sort of phenotypic tioning from its initial trend. To understand what sort of change would greatly facilitate specialization according to time partitioning finally results, one thing we need to know is the periods, which are largely characterized by climatic factors. feasibility of specialization along various resource dimensions. Temporal specialization based on temperature, for example, Contingency models tell us that food and habitat types should occur commonly only among poikilotherms in variable should be skipped if better ones are sufficiently likely to be climates. found. No such possibility exists for time periods, thereby A recent survey (13) of modes of resource partitioning disfavoring temporal specialization. This alone leads us to within 81 associations of sympatric species largely supports expect that temporal resource division may be rare. However, the theoretical arguments of this section. The commonest kind animals with limited abilities to process food or limited re- of resource partitioning is by habitat, followed by food type. quirements would probably find it maladaptive to feed at all Time is a distant third. In fact, partitioning by daily activity times when energy can be gained, contrary to predictions of time is widespread only in terrestrial poikilotherms. contingency models. These animals (such as time minimizers) should specialize on time periods just as they should specialize I thank R. B. Huey for comments on a previous draft. Sup- on habitats and food types. Animals (such as energy maxi- ported by NSF Grants B019801X and GB37731X. mizers) not limited in these ways may still specialize on food type or habitat, provided that enough undepleted foraging area is available. But they should not specialize on time. In 1. MacArthur, R. H. & Pianka, E. R. (1966) Amer. Natur. short, specialization is less favored overall for time periods, 100, 603-609. and when it occurs should usually be in animals especially 2. MacArthur, R. H. & Wilson, E. 0. (1967) The Theory of Island Biogeography (Princeton Univ. Press, Princeton, limited in their abilities or needs to utilize food. N.J.). Habitat specialization should be especially favored if 3. Pianka, E. R. (1969) Ecology 50, 1012-1030. patches are large relative to the home ranges of individuals 4. Schoener, T. W. (1969) Amer. Natur. 103, 277-313. (T8 very small in Eq. 1). For most vertebrates, macrohabitat 5. Schoener, T. W. (1971) Annu. Rev. Ecol. Syst. 2, 369-404. 6. Pulliam, H. R. (1974) Amer. Natur. 108, 59-74. specialization is feasible whereas a great degree of food-type 7. MacArthur, R. H. (1972) in Geographical Ecology (Harper specialization is not: the small energy gained per item re- and Row, New York), chap. 4. quires that many be eaten, and if animals are too specialized, 8. Schoener, T. W. (1969) Brookhaven Symp. Biol. 22, 103-114. T8 will be too large. The situation is different of course for 9. Westoby, M. (1974) Amer. Natur. 108, 290-304. food "items" of many herbivorous insects, just as micro- 10. Williams, G. (1962) J. Anim. Ecol. 31, 23-42. 11. Schoener, T. W. (1968) Ecology 49, 123-141. habitats should be treated by vertebrates as food items. 12. Freeland, W. H. & Janzen, D. H. (1974) Amer. Natur. 108, Finally, the degree to which ei/ti differs among resources 269-289, and included references. helps determine whether specialization can occur. Except for 13. Schoener, T. W. (1974) Science, 185, 27-39. Downloaded by guest on September 26, 2021