Are Food Webs Divided into Compartments?

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  • Are Food Webs Divided into Compartments?Author(s): Stuart L. Pimm and John H. LawtonSource: Journal of Animal Ecology, Vol. 49, No. 3 (Oct., 1980), pp. 879-898Published by: British Ecological SocietyStable URL: http://www.jstor.org/stable/4233 .Accessed: 02/05/2014 19:35

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  • Journal of Animal Ecology (1980), 49, 879-898

    ARE FOOD WEBS DIVIDED INTO COMPARTMENTS?*

    BY STUART L. PIMMt AND JOHN H. LAWTON

    Environmental Sciences Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37830, U.S.A., and Department of Biology, University of York,Heslington, York YOI 5DD

    England

    SUMMARY

    (1) In general, randomly constructed model food webs are less likely to be stable the more species they contain, the more interactions there are between species, and the greater the intensity of these interactions.

    (2) Intriguingly, it has been argued (May 1972, 1973) that for a given interaction strength and web connectance, model food webs have a higher probability of being stable if the interactions are arranged into 'blocks' or 'compartments'; this has been coupled with the prediction that complex food webs in the real world may be similarly compartmented.

    (3) Alternative food web models are briefly described. These incorporate biologically more realistic assumptions, and do not neccessarily predict that food webs are more likely to be stable if they are divided into blocks.

    (4) Compartments exist in food webs if the interactions within the web are grouped into subsystems: that is, if species interact strongly only with species in their own sub- systems, and interact little, if at all, with species outside it.

    (5) Drawing on a number of alternative approaches, we test the null hypothesis that real food webs are not significantly more compartmented than chance alone dictates.

    (6) Analyses of published food webs show that subsystems can only be detected where the webs span major habitat divisions, for example a forest and a prairie, or adjacent freshwater and terrestrial habitats. These compartments are imposed by the natural histories of the component species. There are no grounds for believing that dynamical constraints, i.e. a requirement for persistent natural food webs to be stable, play any part in imposing compartments.

    (7) On a finer scale, we find no evidence for compartments in any of the food webs examined. Polyphagy in higher trophic levels may lead to a merging of detritus and grazing food chains, immediately above the level of the primary consumers. Polyphagy similarly generates non-compartmented food webs in assemblages of phytophagous in- sects. Several well documented food webs from other habitats are not noticeably com- partmented.

    (8) The implications, and limitations, of these results are discussed in the light of the general notion that loosely coupled subsystems promote ecosystem stability. On present

    * Research supported by the United States National Science Foundation's Ecosystem Studies Program under Interagency Agreement No. DEB 77-25781 with the U.S. Department of Energy under contract W-7405-eng-26 with Union Carbide Corporation. Publication No. 1566, Environmental Sciences Division, ORNL.

    t Current address: Department of Biological Sciences, Texas Tech. University, Lubbock, Texas 79409, U.S.A.

    0021-8790/80/1000-0879$02.00 ?1980 Blackwell Scientific Publications

    879

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  • evidence, we conclude there are neither adequate theoretical nor convincing empirical grounds for believing that food webs are divided into compartments.

    (9) These conclusions require more detailed testing using food web data which specify not only the presence, but also the strength and temporal variation of the interactions.

    INTRODUCTION

    Arguably the most important insight to emerge from May's (1972, 1973) analysis of model food webs is that complexity begets instability, not stability. In general, randomly constructed model food webs are less likely to be stable the more species they contain, the more interactions there are between species, and the greater the intensity of those interactions. Ecological communities persist in the real world despite, not because of, their complexity.

    Real food webs are not random assemblages of species. Hence we can ask: what are the special features of real, as opposed to random food webs which tend to make the former stable and the latter unstable? The answer seems to be several things. For example, the stability of real food webs is probably enhanced by low levels of connectance between species (Rejmanek & Stary 1979); the absence of biologically absurd linkages of the type species A feeds on B, which feeds on C, which feeds on A (Pimm 1979a, b); special constraints on biomass transfer (DeAngelis 1975); a limit on the number of trophic levels (Pimm & Lawton 1977; Lawton & Pimm 1978; Pimm 1979a); a low frequency, and special patterns of omnivory (Pimm & Lawton 1978; Lawton & Pimm 1979; Pimm 1979a); and a non-random (patchy) distribution of prey and predators (Hassell 1978). One other important possibility, suggested by May (1972, 1973), has not yet been explored in detail; namely that when food webs are divided into blocks, or compartments, the probability of the resulting food webs being stable is greatly enhanced. Following May, both McNaughton (1978) and Rejmanek & Stary (1979) have recently proposed that division into discrete subsystems promotes the persistence and stability of two very different assemblages of species, plants in an African grassland (but see Lawton & Rallison 1979), and populations of aphids and their associated natural enemies. A contrary point of view has been put by Murdoch (1979) who argues that most well studied natural communities do not appear to be divided into loosely coupled subsystems.

    In this paper we examine the structure of real food webs, to see if they are, or are not, divided into compartments. The webs are defined by binary data: a feeding link either exists, or it does not. Our analysis is therefore modest and preliminary, taking no account of the strength or the seasonal variation of the feeding links. If compartments can be shown to exist using binary data they will remain in more sophisticated descriptions of food webs. If compartments can not be identified using binary data, the case for the existence of subsystems within food webs is weakened, but not destroyed. We return to this problem briefly in the Discussion.

    Two extreme hypotheses encompass possible web structures in the real world. (1) The 'reticulate hypothesis': species interactions are uniformly distributed (homo-

    geneous) throughout the system, subject to the minimal biological constraints outlined below.

    (2) The 'loosely coupled subsystem hypothesis': only species within a particular sub-

    system interact. Between subsystems (called 'blocks' by May 1973, and 'compartments' by Pimm 1979a) there is little interaction. (In this paper, when we use the term sub-

    Are food webs compartmented? 880

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  • S. L. PIMM AND J. H. LAWTON

    system we shall be referring to this idea and not to any other subset of species within a system.)

    The two hypotheses are illustrated in Fig. 1. Of course, food webs in the real world will neither be completely compartmented, nor totally reticulate: but if the notion that blocking promotes stability has any substance, real food webs should be more compart- mented than chance alone dictates.

    Deciding what chance alone dictates is not completely straightforward, because asking a computer to draw an unconstrained random food web, for example, leads to all sorts of biological absurdities: predators with nothing to feed on; autotrophes (plants) in the middle of food chains; excessively large numbers of trophic levels; thermodynamically impossible loops of the type A feeds on B, feeds on C, feeds on A, and so on. Cohen (1978) and Pimm (1979a, 1979b) discuss these problems in detail; Pimm (1979b) presents an algorithm for generating constrained random webs without biological absurdities. The key null hypothesis in this paper is that within the limits imposed by minimal biological constraints, real food webs are not significantly more blocked (compartmented) than chance alone dictates.

    A closer look at the prediction that blocking enhances the stability of model food webs

    May (1972, 1973) argued from considerations of connectance (the proportion of possible species interactions that are non-zero) and interaction strength (the magnitude of the non-zero interactions) that 'for a given interaction strength and web connectance (models) will do better if the interactions tend to be arranged in blocks'. By 'better' May meant more likely to be locally stable, and hence more likely to persist. His com- parisons are based on the fraction of models that are asymptotically stable, the same criterion we have used elsewhere (Pimm & Lawton 1977, 1978) to make predictions about the design of food webs. However, May's comparisons are between blocked models and completely randomly organized models. When we exclude many of the biologically unreasonable phenomena found in completely random model food webs (see above) his intriguing result no longer holds. Indeed, completely compartmented models with a given level of connectance have the least likelihood of being stable (Pimm 1979a). The distinction between May's result and Pimm's result is important. The former specifically predicts that compartments should be present in real food webs, the latter that they should not.

    Note both Pimm and May (and authors cited therein) agree that low connectance enhances a model's chances of being stable. As connectance is lowered, models will tend to become more compartmented. However, connectance and blocking are independent; when the former is fixed the latter can vary extensively (Fig. 1). The destabilizing influence of high connectance should not be attributed to a lack of compartmentalization.

    Whether May's or Pimm's result is a more accurate description of the real world is probably best settled by an analysis of real webs rather than a pedantic discussion of their models' assumptions. Finding out what happens in real webs is one of the principle objectives of this paper.

    May's result is a specific example of a general class of models predicting structure in food webs for dynamical reasons. It is important to realize that the same structures, or patterns (e.g. blocking) might just as easily be generated by biological, or natural history constraints. Examples in the real world of food web structures predicted by stable models would then merely be consistent with the requirements for stability; they would not be a consequence of those requirements. Compartments in food webs could presumably be

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  • Are food webs compartmented?

    (a) 3

    (b) 3

    FIG. 1. Two webs with identical numbers of species, connectance, species on which no other species feed (top-predators), species which feed on nothing else within the web (basal species) and species feeding on more than one trophic level (omnivores). System (a) is a

    compartmented system, (b) is not.

    generated, for example, because species within a habitat are more likely to interact with other species within that habitat, rather than those outside it. Each habitat requires a set of adaptations from its component species, with specialization precluding extensive interactions between habitats. For similar reasons, feeding on detritus might preclude feeding on live plant material and vice versa with the corollary that species in the grazing and detritus food chains should be separate (Odum 1962, 1963).

    Obviously, subsystems whose boundaries correspond to different habitats might arise for either dynamical or biological reasons or both. For an unequivocal demonstration of dynamical constraints forcing food webs into blocks we must look at whether sets of species are compartmented within habitats. But what is a habitat? We cannot answer this objectively, but feel we can come sufficiently close for present purposes. Defining a habitat depends entirely on the size and activity of the organism(s) in question (Elton 1966). Southwood (1978) neatly illustrates the problem by correlating the size of an animal with its range. Thus, the individual grasses and shrubs in a field may represent separate habitats for herbivorous insects; but a lark will view the same grassy field as a different habitat from the nearby wood, and ignore changes in the abundance of the field's constituent grasses and shrubs; finally, a predatory hawk may include both the field and the nearby wood in its territory. What constitutes a habitat will depend very much on the taxonomic group of the organism and its trophic position. Conceivably a system may be compartmented at one trophic level but reticulate at the next.

    A SEARCH FOR COMPARTMENTS COINCIDENT WITH HABITAT BOUNDARIES

    In this section we will consider whether species interactions are more frequent within than between habitats. First, we will examine insects and whether their interactions form subsystems whose boundaries correspond to differing resources: plants in the first

    example, gall forming insects in the second. Despite widespread interest in ecosystem stability, the data available to answer our questions are few, a point to which we will

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