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1 Diversity, Complexity, Stability and Pest Control Author(s): William W. Murdoch Source: Journal of Applied Ecology, Vol. 12, No. 3 (Dec., 1975), pp Published by: British Ecological Society Stable URL: Accessed: 21/02/ :07 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. British Ecological Society is collaborating with JSTOR to digitize, preserve and extend access to Journal of Applied Ecology.

2 DIVERSITY, COMPLEXITY, STABILITY AND PEST CONTROL BY WILLIAM W. MURDOCH Department of Biological Sciences, University of California, Santa Barbara, California 93106, U.S.A. INTRODUCTION It may be possible to design crop systems (agroecosystems) so that insect pest problems and the need for active control measures are minimized. This paper suggests ways that ecological theory and field evidence about population stability can contribute to the design of crop systems. The ecological theory, that diverse communities are more stable than simple communities, merits consideration for a number of reasons. First, the trend in agriculture has been towards more and larger monocultures (e.g. Potts & Vickerman 1974). If the stability and hence the dependability of our crop systems is correlated with their diversity, this is an unfortunate trend. Secondly, for a variety of reasons chemical pest control faces an uncertain future, and the major alternative, integrated control centered on the use of natural enemies, should make use of any available strong ecological theory. (Environmental pressure and restrictive legislation in the U.S. are reducing the use of some chemicals and probably increasing the cost of research and development. The problem of pest resistance is likely to increase. Furthermore, there is some evidence that the rate of production of new chemicals, and research into their development, are slowing down.) Finally, there is evidence that many of our activities simplify natural (unmanaged) communities and, where we wish to preserve these areas, the diversity - stability theory could be important in management. In this paper I contend that (a) there is no good evidence to support the diversity-+ stability theory either in crop systems or in natural communities, (b) natural systems are more stable than crop systems in major part because their component species are coevolved, (c) crop systems are so different from natural communities that different 'rules' govern the stability of the two types of systems, (d) in artificial systems (laboratory, models and some crops) there is evidence that physical and spatial complexity confers stability, and this might be a useful principle for crop systems and (e) we should maintain naturally diverse systems because simplified natural systems are unstable. I am concerned here with insect pests and especially with crop design for integrated pest management (IPM). These ideas have been dealt with in part by other authors, especially van Emden & Williams (1974), who come to some of the same conclusions. Agriculture and stability Before discussing factors that might increase stability we need to ask two questions. First, what kind of stability is desirable in crop systems? Secondly, what kind of stability is discussed by ecological theory? The farmer certainly wants stability in the sense of dependable, consistent high yields (or at least profits); but this is not a useful variable for us to examine directly, though it is 795

3 796 Diversity, complexity, stability and pest control obviously affected by pest control. Farmers have in fact used instability as a major tool in pest control; indeed much insect pest control has been, and still is, based upon a 'catastrophe strategy'. Such a strategy attempts to disrupthe pest, driving it to densities as near extinction as possible, using techniques such as frequent application of insecticides. It specifically does not rest upon the idea of regulating the pest population by factors whose effects are density dependent. If such a catastrophe strategy were to remain the basis of pest control, ecological ideas about stability probably would not be very relevant. However, the failures of this strategy, particularly the development of pesticide-resistant strains of insects and mites, have resulted in a swing to alternative techniques, epitomized by integrated pest management. IPM also uses disruptive techniques, and sometimes its practitionerseem unclear as to whether they are pursuing a disruptive or a stability strategy. But to the extent that control by natural enemies is a central tactic of the programme, then IPM is based on a stability strategy, one that emphasizes continuity of the populations of the pest's enemies, and perhaps also of the pest populations, rather than local extinction of the pest. Ecological theory about stability is relevanto pest control by natural enemies because this control strategy recognizes that even local extinction of the pest is highly improbable, so it attempts to regulate the pest at low densities by a continuously present set of natural enemies. Unfortunately, none of the stability theory I will discuss promises to keep pests at an acceptably low average density, a difficulty that ecological theory has hardly approached (see van Emden & Williams 1974). The question of what we mean by stability in real systems (the second question raised above) is vexing. I will refer to stability as it occurs in three situations: in pest control, in natural populations and communities, and in mathematical models of populations and communities. In each of these situations stability can be defined more or less unambiguously. The difficulty is that 'stability' may not have the same meaning in all situations. However, the consequences of each of these three types of stability may be similar enough that we can use the concept here, and apply it to pest control. Stability in pest control, and in natural populations and communities, can be taken to mean restricted fluctuations in pest population density through time. Populations that fluctuate less through time and avoid extinction make up more stable communities. Instability, i.e. large fluctuations, implies periods of heavy pest damage in crop systems. For stability of insect enemy species we might require in some cases only the continuous presence of these enemies. This requirement would be subsumed under the definition of 'restricted fluctuations'. Statisticsuch as the coefficient of variation, or variance of log density can provide measures of instability. There are other definitions of stability that one could use (e.g. return to a previous mean density following perturbation), and one could use the term 'constancy' rather than stability to refer to restricted fluctuations; however, the term stability in the ecological hypotheses about diversity and stability has traditionally referred to restricted fluctuations and infrequent extinctions. In mathematical models of populations, stability has several well defined meanings: (1) return to the equilibrium density after a small perturbation (neighbourhood stability); (2) return to equilibrium after a large perturbation (global stability); (3) rapid rate of return to equilibrium; (4) return to a limit cycle; (5) the retention of previous stability properties when small changes are made in the model (structural stability). Yet none of these mathematical definitions quite corresponds to our previous definition of stability as restricted fluctuations, used above. Herein lies a difficulty in applying theoretical results to our everyday, commonsense notion of the stability of real populations. However, the

4 WILLIAM W. MURDOCH 797 difficulty probably is not as serious as it seems. The tendency of a population to return to equilibrium following any degree of perturbation probably is associated with its tendency to exhibit restricted fluctuations. Some support for this comes from May (1973). In referring to the stability of models below, I will have in mind return to equilibrium, and usually neighbourhood stability in particular. Several models also examine the mechanisms that modify the range of conditions over which neighbourhood stability occurs. Thus models that exhibit stability over a wider range (for example those that can handle a large change in prey density or a wide range of birth rates) are called more stable. This is a property we would like our pest control systems to have and is likely also to be associated with more restricted fluctuations. Species diversity and stability-th evidence Species diversity here is measured by number of species. The abundances of the species tend to be more even in those communities with many species, though this is not always the case. Three main lines of evidence have been adduced to support the idea that more species causes greater stability (Elton 1958; Pimentel 1961; Krebs 1972; Goodman 1975). Natural v. artificial systems Natural systems, which are generally more diverse than artificial systems, are more stable than such artificial systems as crops or laboratory populations. A comparison of natural systems (a) The tropics, especially tropical rain forests, are more diverse and more stable than simpler temperate communities. (b) Simple arctic ecosystems, exemplified by lemming populations, are less stable than more diverse temperate communities. Mathematical models It makes good intuitive sense that a system with many links, or 'multiple fail-safes' is more stable than one with few links or feed-back loops. For example, if a herbivore is attacked by several predatory species, the loss of any one of these species will be less likely to allow the herbivore to erupt than if only one predator species were present and that predator disappeared. The message of this analysis for crop systems appears to be quite clear. If true, it would suggest the following: monocultures are dangerously unstable because their pests have few enemy species (examples of the reduction of enemy species can be found in Potts & Vickerman (1974) and Odum (1971, Table 6-2)). So we should design agroecosystemso that their diversity is increased. Thus, instead of one crop we should have a mosaic of several crops. For insect pest control we should allow weeds, trees and hedgerows to survive because they add diversity to the system. In these ways one hopes to recapture for crop systemsome of the stability properties of natural communities. But there now seems to be good reason to reject the above analysis. Much of the evidence has been discussed by van Emden & Williams (1974), and I simply summarize it here. First, there is no convincing field evidence that diverse natural communities are in general more stable than simple ones. For example, various papers by C. J. Krebs show that fluctuations of microtine rodents (e.g. lemmings, field voles) are as violent in the temperate zone as they are in the Arctic (Krebs & Myers 1974). There are anecdotal

5 798 Diversity, complexity, stability and pest control reports that populations of insects and mammals in the tropics undergo enormous fluctuations and even local extinctions (Goodman 1975; Gray 1972; N. G. Smith, personal communication). The trouble with such comparisons is that many variables are not measured. We really should compare natural communitiesimilar in all respects except their diversity. Such comparisons are well nigh impossible, but the existing data suggest no correlation between stability and diversity, or an inverse correlation (Murdoch, Evans & Peterson 1972; van Emden & Williams 1974). Turning to species diversity in agriculture, the situation is equally equivocal. While there are many examples where the addition of diversity (e.g. mixed cropping, adding overwintering species for parasites) has increased stability, in the sense of reducing pest outbreaks, there seems to be no general correlation between diversity and stability in agriculture (Smith& Reynolds 1968; Way 1972; van Emden & Williams 1974; Watt 1965). Neither is there really conclusive evidence supporting the theory from a comparison of laboratory systems with different diversities (Hairston et al. 1968; van Emden & Williams 1974). In summary, the only valid conclusion to be drawn from a comparison of different communities of the same type (e.g. comparing natural communities with other natural communities) is that no correlation has been found between number of species (or any more complex measure of diversity) and stability. Finally, the intuitive notion that more trophic links ought in theory to produce more stability has been undermined by recent, admittedly simple, mathematical models (e.g. May 1973). In fact, adding more species generally causes stability to decrease (by the loss of species). It should be noted that if more complicated sorts of interactions were to accompany the additional species (e.g. 'switching' in predators), such a conclusion need not hold.- However, the analysis does lead us to reject a simple theoretical claim of diversity-+stability. This analysis is not meant to suggest that monocultures are necessarily preferable to mixed cropping or that hedgerows and weeds are never useful in insect pest control. It simply argues that diversity per se is not useful in agriculture. However, it will generally make sense to add whatever species are needed to ensure the continuity of the enemy species of insect pests, provided that such enemies are an integral part of the control strategy. Natural versus artificial systems One line of evidence remains from the list enumerated above, namely that simple, artificial communities, such as crop and laboratory systems, are less stable than natural communities, which in general have more species (and therefore greater diversity) than artificial systems. This line of evidence seems irrefutable in the face of the massive instability exhibited by artificial communities. But artificial and natural systems differ in a number of ways; there is no compelling reason to suppose that the difference in diversity is the one that causes the difference in their degree of stability. If the difference in diversity between natural and artificial communities does not explain at one stroke the difference in stability, there is yet something to be gained by comparing these two types of systems, which differ in other fundamental and obvious respects. Three differences between natural and agricultural communities are as follows. (1) We disrupt, even destroy, agricultural communities more frequently and more massively than those natural systems we think of as stable.

6 WILLIAM W. MURDOCH 799 (2) The component species of natural systems are co-evolved (co-adapted), and this is usually not true of agricultural communities. (3) Agricultural systems are not only more simple, but even the natural (non-crop) part of the community is simplified by human activities. The first point is obvious, clearly causes much of the instability crops, and needs no further discussion. However, many crop systems, even when they are not being disrupted by humans, are highly unstable, and I have in mind here particularly the eruption of insect pests. I believe that differences (2) and (3) are responsible in large part for this instability. Specifically, I sugges that natural systems are more stable than crop systems because their interacting species have had a long shared evolutionary history. During that history, plant species that were especially vulnerable to herbivores have disappeared, as have predators that were unable to reap a consistent harvest from their prey. Species are thus co-adapted, those that are eaten having sufficient defense for their survival while those that attack have 'kept up' with such defences but have been unable to overwhelm them. The interactions are everchanging, but inevitably the more stable have survived. In contrast with these natural communities, the dominant plant species of a crop system is thrust into an often alien landscape. The crop is invaded by a more or less haphazard and frequently disrupted set of species that, on average, must have had a relatively brief shared history. Furthermore, the crops have undergone radical selection in breeding programmes, often losing their genetic defence mechanisms. No doubt the major herbivores have also undergone rapid evolution in response to the rapidly changing crops, so that their enemies now face a different kind of prey. In addition, the selective regime, from irrigation to pesticides, has changed and is continually and rapidly changing so that the species come to be more and more a haphazard assortment of genotypeshaphazard to the extenthat the interactions between species are no longer such dominant or consistent selective forces as they are in natural systems, because human interference comes to have such a powerful selective force. Point (3) above notes that the breaking of co-evolutionary links is made more severe because the biota of crop systems is simplified relative to the native community (e.g. few plant species are allowed to survive). Thus, many of the species with which the pest interacted in natural systems are gone. This analysis suggests that in comparing natural and artificial communities ecologists have seized upon one variable (the number of species) and ignored other critical variables such as the kinds of species and interactions. The analysis leads to a further conclusion. If the sorts of interactions that occur in crop communities are fundamentally different from those in natural co-evolved communities, and if co-adaptation is central in explaining the stability of natural systems, we can hardly expect to transfer unalloyed the principles discovered in natural systems to the management of crops. Thus we must expect differences in the rules governing stability in the two types of systems. Natural communities provide the wrong model for crop systems and we must look elsewhere for principles of crop management. However, where the crop is a lightly managed ecosystem, such as some forests, and thus quite similar to a natural community, the deviation from a natural community and its organizing principles will be less marked than in, say, a cotton field or vegetable patch. The analysis also suggests that, because 'artificial' systems (laboratory communities and mathematical models) share with agricultural systems the characteristic that they are less rich in the peculiar co-evolved quirks that arise during the co-evolution of interacting species, they can therefore serve as useful models for agricultural systems.

7 800 Diversity, complexity, stability and pest control Physical complexity and stability Predator-prey and insect parasite-host models form one area of ecological theory relevan to pest control by natural enemies. Recent work in this area points consistently to the conclusion that patchiness in space (one aspect of complexity) contributes to the stability of the interaction. (This apparent consistency needs to be treated with caution because of differences in the structure of different models.) Model 1 The first line of evidence suggests that when the predator-prey interaction is unstable it can be stabilized by breaking it up into two (and probably more) subsystems that have different environmental conditions and that are weakly linked to each other (St Amant 1970; Levins 1969; Maynard Smith 1974). Thus, the classical Lotka-Volterra model of a population of prey and one of predators, with time lags added, can be written d = ah(t - At) - bp(t - At)H(t - At) dt(1 dp= cp(t-at)-dp(t-at)h(t-at) dt where H is the number of prey, P the number of predators, a and c are respectively the prey birth and predator death rates, b is the predator's attack rate and d the efficiency which prey are converted to predators, and the time lag has length At. Because of the time lags, the populations are unstable, showing larger and larger fluctuations with the passage of time until one of them goes extinct. This system can be stabilized simply by breaking it into two parts, subscripted 1 and 2 in equations (2), and by adding terms that representhe random movement of individuals from one sub-system to the other: dh1 = alh1(t-at)-b1h1(t-at)p1(t- At) + ah2(t- At) dp = c1p1 (t-at) +d1hl(t-at)p1(t-at) + flp2 (t-at) dt ~~~~~~~~~~~~~~~ dh2 = a2h2(t- At)-b2H2(t - At)P2(t - At) + yh1(t - At) dp2 = c2p2 (t -At) + d2h2(t- At)P2(t -At) + bp1 (t- At) dt Immigration into each sub-system from the other sub-system is described by the third terms, while emigration is in each case incorporated into the parameters a and c. Notice that the parameters, as well as the symbols for prey and predator densities, have different subscripts, indicating not only that the system is broken up into different areas, but that there are different environmental conditions in each area. This is a crucial aspect of the stabilizing mechanism. This complete system is more stable because fluctuations in each sub-system are out of phase and are of different period and amplitude (St Amant 1970). Provided coupling (i.e. migration) is weak, and the time lags not too long, damped oscillations (stability) result. Note that we would not expect patchiness to produce stability unless the parameter values differed in the different patches.

8 WILLIAM W. MURDOCH 801 Model 2 The second set of evidence concerns the effect of patchiness on the stabilizing properties of the predator's functional response, which is the number of prey taken by the average predator per unit time, as a function of prey density. This is the second term in equations (1). That simple model assumes that each predator takes a constant fraction of the available prey. The functional response is of particular interest because it can change rapidly in response to changes in pest density. To be stabilizing (i.e. to cause density dependent mortality), the functional response usually will have to be an increasing, sigmoid, function of prey density (type 3, Holling 1959). Given a model of functional response, one way of testing for stability would therefore be to examine the second derivative to see if it is positive at low prey densities. This frequently is very difficult and furthermore gives no indication over what range of prey densities the response is density-dependent. To solve this problem Oaten & Murdoch (1975) proposed (1) a criterion for distinguishing a density dependent response and (2) a measure of the range over which it is density dependent. Where f(h), the functional response, is the number eaten when prey density is h, the risk run by the average prey isf(h)/h. The risk is increasing (i.e. the response is densitydependent) as long as f'(h) >f(h)/h. This criterion is much easier to calculate than the second derivative. In addition it yields a measure, hm, which is the largest pest density for which the criterion holds. Thus hm gives the range over which the functional response is likely to stabilize. For type 3 responses, hm is always greater than h at the inflection point. (In some modelsf(hm) can be used as a measure of stabilizing potential.) We have used the criterion and measure to evaluate the effect of patchy prey distribution in a number of models, both with only one prey species and with two (or more) prey species. The basic notions common to all of these models are that the prey occur in patches that are separated in space, that the predator tends to spend longer in more rewarding, i.e. denser, patches, and that the predator must spend time 'in transit' going between patches. Consider, first, an individual predator facing a pest population distributed among many patches with varying numbers of pests (H1, H2...) in each patch, and mean density per patch, h. We assume that within a patch the predator causes destabilizing mortality, i.e. it has a type 2 functional response (Holling 1959). When the predator enters a patch and eats prey the number of prey there declines, so the predator is frequently leaving patches, but leaves patches with few prey sooner than it leaves patches that have many prey. Each time it leaves and moves to another patch it 'wastes' X time units in transit. Now, as h, the average pest density in a patch, increases (i.e. as total pest density increases) the predator finds an increasing fraction of patches with many pests. It therefore wastes less and less time in transit as average pest density increases. This increase in efficiency with pest density tends to cause the functional response, averaged over all patches, (f(h)), to be density dependent. This model is written f(h) = G(h)/{S(h) + bg(h)+ T} where b is the average time taken to handle prey, G(h) is the average number eaten in a randomly chosen patch and S(h) is the average time spent searching (not including handling time) in a randomly chosen patch. G(h) and S(h) are complicated functions that incorporate both searching behaviour in a patch and the effect of the decrease in pest density in the patch as the predator feeds there, but these details need not concern us here,

9 802 Diversity, complexity, stability and pest control The range of prey densities that can be stabilized increases as T increases (and as b decreases) for given assumptions about G(h) and S(h). These conclusions hold over the wide range of detailed models G(h) and S(h) investigated (Oaten, Murdoch & McNulty, in preparation; Oaten, in preparation). Of course, this predator never catches as many prey as in the contiguous case. We also showed that the degree to which prey are unevenly distributed among patches has little effect on stability, a conclusion that holds only for predator-prey systems where the predator's numerical response is not tightly coupled to prey density. Thus, the functional response becomes stabilizing because the pest population is distributed among patches separated in space. In the model, the further apart these patches are, the greater is the range of pest density that can be stabilized. But two consideration show that there must, in real situations, be an optimum distance between patches. First, in real systems transit time could become so large that the predator would spend all of its time in transit. Second, the intensity of predation at hm, namely f(hm), at first increases with X at least in some cases, but declines at large values of T. Model 3 Our conclusion about the separation of patches in space is corroborated by a model of predatory behaviour when two species of pests are available. Predators switch between prey if the relative frequency of attacks upon a species increases faster than does the relative frequency of the species in the environment (Murdoch 1969; Murdoch & Oaten 1975). Where Ni is the number of individuals of species i eaten per unit time and Hi is the density of species i, N1/N2 = ch1 /H2 where c is an increasing function of H1 /H2. It has been shown experimentally that switching occurs when the two prey species occupy different areas in the predator's habitat, and the predator responds to variation in the prey's relative density by spending an increasing fraction of its searching time in one area as the species there becomes relatively more abundant (Murdoch, Avery & Smyth 1975). In the experiments, this also resulted in density-dependent mortality upon each prey species. This mechanism can be modelled, and the model shows that, if the mechanism is operating, switching always occurs and the functional response is likely to be densitydependent (Murdoch 1975b). We can then add transit time to the model; that is, the predator now 'wastes' some time travelling between the two areas. It is reasonable to assume that total time spent in transit (average transitime multiplied by the number of visits) decreases as total pest density increases. The model then shows that the addition of transi time always increases the likelihood that the functional response will be densitydependent. Furthermore, it never decreases the range of pest densities over which stability is possible. Transit time will cause an increase in the range over which stability occurs if the total time spent in transit declines over a broad range of pest densities. Again, it appears that intermediate values of average transitime maximize the range of pest density that can be stabilized. These mechanisms are modelled by first generalizing the Holling 'disc equation' to two (or more) prey species N1 Hla a 1 +ajb1hj +a2b2h2 L = H2a2 N 2 r 1 + a1b1h1 + a2b2h2

10 WILLIAM W. MURDOCH 803 where ai is the rate of search (or fraction of area covered per unit time) for species i, and bi is the time taken to 'handle' an individual of species i. The time spent in predation is set at unity. Then let 4, the fraction of search time spent in area 1, be an increasing function of H1 /H2. The time spent searching in area 2 is 1-4). T is total time spent in transit between areas and can be taken to be T V where T is the average transitime for one visit and V is the number of visits to both areas. The model then becomes N = (1 -T)Hlalb 1-ajb1H14-a2b2H2(1-4) A stabilizing (sigmoid) functional response is not a necessary outcome, though it is a possible outcome for any increasing function 4 and decreasing function T, depending on the values of the other parameters. The response is more likely to be stabilizing upon H1 when a, <a2, bl <b2 and H2 is large. Model 4 A theoretical conclusion, known for some time, is that environmental heterogeneity that produces refuges for some of the prey population is stabilizing. (For a review see Murdoch & Oaten 1975.) A refugeffect can also result from non-random movement of prey and predators across a continuously varying environment (Comins& Blatt 1975). Refuges always produce stability in simple models in which a constant number of the prey are in the refuge, and the effect is similar but weaker if a proportion of the prey has a refuge. Hassell & May (1973) show that in parasite-host systems a very uneven distribution of the host population over the area can produce a refugeffect. There is also field and laboratory evidence in support of the idea that refuges are stabilizing. Some of the evidence is reviewed in Murdoch & Oaten (1975). Connell (1970) has shown this effect for barnacles and seashore snails in the field. Laboratory evidence comes from Huffaker (1958) and from Pimentel, Nagel & Madden (1963). Taken together, these models sugges that, through a variety of mechanisms, physical complexity in the environment is likely to add stability to predator-prey and hostparasite systems. In particular, they suggesthat absolute refuges, or restricted movement, or large distances between 'patches' is desirable. Pest control and the scale of physical complexity Is any of the above theory relevanto real problems of pest control? Perhaps it can be of some limited use, though it hardly provides a blueprint for the design of crop systems. The temptation is to substitute for the diversity-+stability wisdom a call for farmers simply to add physical complexity to their fields, on the grounds that physical complexity adds stability; but this advice is too vague to be much use. The conclusion seem to be robust, in that they hold true for a wide range of different models, and they are consistent with what little experimental data we have. However, the models present us with several suggestions about pest control and stability, rather than with a single unambiguous message. While the suggestions are not conflicting, they are unclear about the appropriate scale of patchiness that might be desirable for each mechanism. Certainly the scale is not the same in each case. I now take each set of model results and suggest how they might be used. Note that in each case the models suggest that there is an optimum scale at which the suggestionshould be implemented. Model 1 suggests that sub-populations of pest and enemy species should be spatially

11 804 Diversity, complexity, stability and pest control separated but should be linked by migration at a rate that is 'not too high'. This suggests growing the crop in blocks with empty spaces, other crops, or barriers to insect dispersal in between. Further, the blocks should be somewhat different environments, which probably would arise from natural heterogeneity in a field, but could be enhanced by minor differences in fertilization or sowing time or sowing density, etc. The optimal size of such blocks (and the best type of barrier) would depend upon the mobility of pest and predator, and probably could be discovered only by experimentation with each crop. Maynard Smith (1974) discusses a variety of detailed models of blocks (or patches) of environment that are linked by migration in a variety of ways. Some of these models might serve to stimulate field experiments. The remaining models recommend patchiness on a smaller scale, i.e. within blocks of the crop. Model 2 requires spatially separated clumps of pests, much smaller in area than would be covered by an enemy individual in a day's feeding. Such clumps need not be wholly distinct-areas of high density surrounded by areas of low density would suffice. This type of clumping might be achieved by planting a mixture of crop strains that differ slightly in their susceptibility to the major pest. Or it might even be useful to have in each block a few small areas of a crop strain that is more susceptible to pest attack than is the major strain that is planted in most of the field. Model 3, incorporating predator switching, suggests than an alternative prey species, especially on a crop or plant species that is a short distance from each block of the crop, might enhance the stability of the pest-enemy interaction. (The interplanting of alfalfa with cotton perhaps exemplifies one technique.) However, to be most useful the density of the alternative prey should decrease as the pest increases, and vice-versa. One possible solution to this problem is to develop artificial alternative 'prey' which could be added to the crop. Hagen & Hale (1974) discuss several artificial diets that have been successful in attracting adult predators and parasitoids, raising their densities, and causing egglaying. Probably it would be difficult, but perhaps not impossible, to develop alternative prey for both adult and immature predators. An alternative tactic may be useful for mosquito control. Fox (1975) has shown that a population of back-swimming bugs (Notonecta) in streams feed mainly on insects that fall on to and are trapped on the surface of the water. She was able to maintain the Notonecta population at high density, and cause it to reproduce 'out of season' by adding surface prey (Tribolium larvae). Thus, in mosquito control it might be possible to manipulate alternative surface prey for invertebrate predators. I note, in passing, that the conventional wisdom in biological control is that highly specific parasites are the best enemy species, and that general predators are not usually thoughto be as useful. While there may be some empirical evidence for this belief, it is not based upon detailed experimental analysis of a wide range of pest control situations. Further, recent work on insect cotton pests in California suggests that general predators are the major controlling agents (Ehler & van den Bosch, personal communication; Ehler, Eveleens & van den Bosch 1973). Model 4, which consists of both mathematical models and laboratory experiments, and is confirmed by field work, shows that refuges for the prey are stabilizing and further suggests that marked clumping of the prey (i.e. highly variable density in space) can operate to produce refuges. Again, the appropriate scale here probably is small, i.e. withinblock. This set of results suggests some of the same tactics as did model 2, e.g. small patches of susceptible crop strains within each block. It also suggests that it would be useful to release the pest on to the crop whenever its numbers become 'too low', a tech-

12 WILLIAM W. MURDOCH 805 nique already employed successfully in greenhouse crops by Hussey & Bravenboer (1971). If these models and suggestions clearly do not provide a blueprint for crop design, perhaps they can serve as a guide to trying out some experimental designs. Very little work has been done on the design of crop systems that tries to use ecological theory, and at this point there would seem to be enough ideas to warrant such a programme. The ideas suggested here may turn out to be impractical. Nevertheless, chemical pest control is failing at an accelerating rate and increasing dependence will be placed on IPM. At the same time, the conventional ecological wisdom concerning diversity and stability can no longer be offered to pest managers as a theoretical base, and it is important to explore alternatives. Such alternative theory now exists, and it is time to see if it is useful. Other aspects of diversity and complexity I concentrated above on the role of complexity in predator-prey interactions and its relation to pest control by enemies. The crop-pest interaction is itself a predator-prey interaction. But it seems difficult to apply the principles at this crop-pest level because individuals of the crop do not move about, and crop distribution constrained by the needs of efficient cultivation. However, there is some evidence that here, too, physical complexity can be a useful stabilizing factor, although biological features produce the complexity. Briefly, there is evidence that anything that prevents the rapid spread of the pest organism through susceptible segments of the crop enhances stability, and also lowers the infestation rate. The intermixing of trees of a non-susceptible age, or trees of a different species, seems to have operated in this way to reduce the infestation rate of spruce budworm on susceptible individuals of Canada balsam fir. Growing trees in small stands set apart from each other had the same effect (Morris 1963). There is anecdotal evidence that mixing different genetic strains of cereals in a single field reduces the spread of disease. If this type of physical complexity, albeit sometimes obtained by biological (e.g. genetic) diversity, is stabilizing, it could be used in conjunction with those techniques for stabilizing the pest-enemy interaction discussed above. Diversity and conservation Lest the above be taken as an argument for abandoning or simplifying natural ecosystems, I note that, given that there are good reasons for preserving such ecosystems (Murdoch 1975a), the analysis favours keeping them as close to their natural diversity as possible. Since it is thought that a full complex of co-adapted species is what makes natural communities more stable than artificial systems, it is clearly good strategy not to simplify these interactions. At the same time, we can expect simple natural communities to be as self-maintaining as more diverse natural communities. SUMMARY (1) It should be possible to design agroecosystems to reduce the severity of insect pest problems. Ecological theory about stability should be relevant whenever pest control relies heavily on the action of insect enemies (predators and parasites). (2) To pursue such a control strategy the crop system should contain enough plant species to maintain continuity of the enemy species (and perhaps sometimes of the pest

13 806 Diversity, complexity, stability and pest control species). However, current evidence from (a) agriculture, (b) a comparison of different natural ecosystems, (c) laboratory communities and (d) mathematical models does not support the more general hypothesis that species diversity per se enhances stability. Thus, unless additional species contribute to the action of natural enemies, the addition of diversity, qua diversity, is not likely to be a useful strategy in agriculture. (3) It is suggested that the marked instability of agroecosystems (and other artificial communities), in contrast with the stability of natural communities, results from the frequent disruption of crops by humans and from the lack in crop systems of co-evolutionary links between the interacting species. This second feature of crops is caused by the haphazardness of the collection of species on any given crop field, the changing selective regime imposed by humans, and the fact that crops have lost many species that were present in the previously existing natural communities. Thus, I conclude that natural communities, whose stability results from their complement of co-evolved species, provide a poor model for the design of crop systems. By the same token, laboratory and mathematical models, like agricultural systems, are relatively poor in co-evolved peculiarities, and such models may therefore be useful in yielding insights about agricultural systems. (4) Recently formulated mathematical models of predator-prey systemsuggest that physical complexity, especially a patchy distribution in space, enhances population stability. This result is supported by some meager evidence from the laboratory and field. A major difficulty in applying this principle to agriculture centres on the scale on which patchinesshould be incorporated in fields of crops, but field experiments could examine this question. (5) Throughout the discussion, stability is assumed to be desirable in crop systems, being translatable into reduced pest fluctuations and pest damage. However, ecological theory is almost silent on the question of how to obtain both stability and an acceptably low average density of pests. (6) Some of the tactics suggested here achieve density dependence at the cost of lowering the overall predation rate at low pest densities. This trade off will be worthwhile if the predators can thus keep the pest at low densities. ACKNOWLEDGMENTS I am grateful to Patrick McNulty for stimulating discussions on this topic and to Joseph Connell, Allan Oaten, Maria Macduff, Ralph Slatyer, Steve Schroeter and Brian Trenbath for critically reading the manuscript. The research reported here was supported by grants from the National Science Foundation. REFERENCES Connell, J. H. (1970). A predator-prey system in the marine intertidal region. I. Balanus glandul and several predatory species of Thais. Ecol. Monogr. 40, Comins, H. N. & Blatt, D. W. E. (1975). Predator-prey models in spatially heterogeneous environments. J. Theoret. Biol. (In press). Ehler, L. E., Eveleens, K. G. & Bosch, R. van den (1973). An evaluation of some natural enemies of Cabbage Looper on cotton in California. Environ. Ent. 2, Elton, C. S. (1958). The Ecology of Invasions by Plants and animals. Methuen, London. Emden, H. F. van & Williams, G. F. (1974). Insect stability and diversity in agro-ecosystems. Ann. Rev. Ent. 19, Fox, L. R. (1975). Factors influencing cannibalism, a mechanism of population limitation in the predator Notonecta hoffmanni. Ecology (In press).

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