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.