Aggregation heterogeneity and spatial variation in practice

What, then, can be said about the role of spatial variation in practice? The stabilizing effects of heterogeneity were demonstrated famously, long ago, by Huffaker (1958; Huffaker et al., 1963), who studied a system in which a predatory mite fed on a herbivorous mite, which fed on oranges interspersed amongst rubber balls in a tray. In the absence of its predator, the prey maintained a fluctuating but persistent population (Figure 10.16a); but if the predator was added during the early stages of prey population growth, it rapidly increased its own population size, consumed all of its prey and then became extinct itself (Figure 10.16b). The interaction was altered, however, when Huffaker made his microcosm more 'patchy' (creating, effectively, a metapopulation, though the term had not been coined at the time). He spread the oranges further apart, and partially isolated each one by placing a complex arrangement of vaseline barriers in the tray, which the mites could not cross. But he facilitated the dispersal of the prey by inserting a number of upright sticks from which they could launch themselves on silken strands carried by air currents. Dispersal between patches was therefore much easier for the prey than it was for the predators. In a patch occupied by both predators and prey, the predators consumed all the prey and then either became extinct themselves or dispersed (with a low rate of success) to a new patch. But in patches occupied by prey alone, there was rapid, unhampered growth accompanied by successful dispersal to new patches. In a patch occupied by predators alone, there was usually death of the predators before their food arrived. Each patch was therefore ultimately doomed to the extinction of both predators and prey. But overall, at any one time, there was a mosaic of unoccupied patches, prey-predator patches heading for extinction, and thriving prey patches; and this mosaic was capable of maintaining persistent populations of both predators and prey (Figure 10.16c).

Subsequently, others, too, have demonstrated the power of a metapopulation structure in promoting the persistence of coupled predator and prey populations when their dynamics in individual subpopulations are unstable. Figure 10.17a, for example, shows this for a parasitoid attacking its beetle host. Figure 10.17b shows similar results for prey and predatory ciliates emergent spatial patterns metapopulation effects in mites, beetles and ciliates

Figure 10.16 Hide and seek: predator-prey interactions between the mite Eotetranychus sexmaculatus and its predator, the mite Typhlodromus occidentalis. (a) Population fluctuations of Eotetranychus without its predator. (b) A single oscillation of the predator and prey in a simple system. (c) Sustained oscillations in a more complex system. (After Huffaker, 1958.)

Eotetranychus Sexmaculatus

• Typhlodromus o Eotetranychus

Figure 10.16 Hide and seek: predator-prey interactions between the mite Eotetranychus sexmaculatus and its predator, the mite Typhlodromus occidentalis. (a) Population fluctuations of Eotetranychus without its predator. (b) A single oscillation of the predator and prey in a simple system. (c) Sustained oscillations in a more complex system. (After Huffaker, 1958.)

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Figure 10.17 A metapopulation structure can increase the persistence of predator-prey interactions. (a) The parasitoid, Anisopteromalus calandrae, attacking its bruchid beetle host, Callosobruchus chinensis, living on beans either in small single 'cells' (short persistence time, left), or in combinations of cells (four or 49), which either had free access between them so that they effectively constituted a single population (persistence time not significantly increased, right), or had limited (infrequent) movement between cells so that they constituted a metapopulation of separate subpopulations (increased persistence time, center). Bars show standard errors. (After Bonsall et al., 2002.) ( b) The predatory ciliate, Didinium nasutum, feeding on the bacterivorous ciliate, Colpidium striatum, in bottles of various volumes, where persistence time varied little, except in the smallest populations (30 ml) where times were shorter, and also in 'arrays' of nine or 25 linked 30 ml bottles (metapopulations), where persistence was greatly prolonged: all populations persisted until the end of the experiment (130 days). Bars show standard errors; different letters above bars indicate treatments that were significantly different from one another (P < 0.05). (After Holyoak & Lawler, 1996.)

Figure 10.18 Long-term population dynamics in laboratory population cages of a host (Plodia interpunctella), with and without its parasitoid (Venturia canescens). (a) Host and parasitoid in deep medium, exhibiting coupled cycles in abundance, approximately one host generation in length. (b) The host alone in deep medium, exhibiting similar cycles. (c) Host and parasitoid in shallow medium, unable to persist. (d) The host alone in shallow medium, able to persist. The deep medium provides a refuge from attack for a proportion of the host population that is not present in the shallow medium (see Section 10.5.2). All data sets are selected from several replicates showing the same pattern. (After Begon et al., 1995.)

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(protists), where, in support of the role of a metapopulation structure, it was also possible to demonstrate asynchrony in the dynamics of individual subpopulations and frequent local prey extinctions and recolonizations (Holyoak & Lawler, 1996).

A study providing support for the a refuge for a moth stabilizing powers of a physical refuge is illustrated in Figure 10.18, based on the same Plodia-Venturia host-parasitoid system as that in Figure 10.1c. In this case, hosts living deeper in their food are beyond the reach of the parasitoids attempting to lay their eggs in them. In the absence of this refuge, in a shallow food medium, this host-parasitoid interaction is unable to persist (Figure 10.18c), although the host alone does so readily (Figure 10.18d). With a refuge present, however, in a deeper food medium, the host and parasitoid can apparently persist together indefinitely (Figure 10.18a).

In fact, though, the distinctions between different types of spatial heterogeneity may not be as clear cut in real systems as they are in mathematical models. Ellner et al. (2001), for example, examined a system of predatory mites, Phytoseiulus persimilis, feeding on herbivorous mites, Tetranychus urticae, feeding on bean plants, Phaseolus lunatus. On individual plants and on a single 'continent' of 90 plants (Figure 10.19a), the system had no long-term persistence (Figure 10.19c). However, when the Styrofoam sheet supporting the plants was split into eight islands of 10 plants, connected by bridges that limited the mites' powers of dispersal (Figure 10.19b), persistence was apparently indefinite (Figure 10.19d, e). It would be easy to jump to the conclusion that stability was increased by the eight-island metapopulation structure. But when Ellner et al. examined mathematical models of the system that allowed the various aspects of the altered layout to be investigated one by one, they could detect no significant effect of such a structure. Instead, they suggested that the enhanced stability arose from a different aspect: a reduction in the predators' ability to detect and respond to prey outbreaks on individual plants - a prey 'refuge' effect that could arise in the absence of any explicit spatial structure.

One major problem in making pronouncements about the stabilizing role of aggregation of risk is that although, as we have seen, there have been wide-

more mites: a metapopulation or a refuge?

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Didinium Attacking Its Prey

Figure 10.19 The population dynamics of the predatory mite, Phytoseiulus persimilis, and its herbivorous mite prey, Tetranychus urticae. They interacted either (a) on a single continent of 90 bean plants, the dynamics of which are shown in (c) (a, predators; o, prey), or (b) in a metapopulation of eight islands of 10 plants. For the latter, the dynamics of two replicates are shown in (d) and (e), where persistence (stability) is clearly enhanced. (After Ellner et al., 2001.)

Figure 10.19 The population dynamics of the predatory mite, Phytoseiulus persimilis, and its herbivorous mite prey, Tetranychus urticae. They interacted either (a) on a single continent of 90 bean plants, the dynamics of which are shown in (c) (a, predators; o, prey), or (b) in a metapopulation of eight islands of 10 plants. For the latter, the dynamics of two replicates are shown in (d) and (e), where persistence (stability) is clearly enhanced. (After Ellner et al., 2001.)

ranging surveys of the data on spatial distributions of attacks, these data generally come from studies of very short duration - often of only one generation. We do not know if the observed spatial patterns are typical for that interaction; nor do we know if the population dynamics show the degree of stability that the spatial patterns might seem to predict. One investigation that has examined population dynamics and spatial distributions over several generations is that of Redfern et al. (1992), who made a 7-year (seven-generation) study of two tephritid fly species that attack thistles and the guilds of parasitoids that attack the flies. For one host, Terellia serratulae (Figure 10.20a) there was evidence of year-to-year density dependence in the overall rate of parasitism (Figure 10.20b), but no strong evidence of significant levels of aggregation within generations, either overall (Figure 10.20c) or for parasitoid species individually. For the other species, Urophora stylata (Figure 10.20d), there was no apparent temporal density dependence but good evidence for the aggregation of risk (Figure 10.20e, f), and, to repeat a pattern we have seen before, most heterogeneity was contributed by the HDI component. It cannot be said, however, that the patterns of this study fit neatly, overall, to the theory we have outlined. First, both hosts were attacked by several parasitoid species - not one, as assumed by most models. Second, the levels of aggregation (and to a lesser extent the HDI or HDD contributions) varied considerably and apparently randomly from year to year (Figure 10.20c, f): no one year was typical, and no single 'snap-shot' could have captured either interaction. Finally, while the relatively stable dynamics of Terellia may have reflected the more demonstrable direct density dependence in parasitism, this appeared to be quite unconnected to any differences in the aggregation of risk.

The effects of spatial heterogeneities on the stability of predator-prey dynamics are not only of purely scientific interest. They have also been the subject of lively debate (Hawkins & Cornell, 1999) in considering the properties and nature of biological control agents: natural enemies of a pest that are imported into an area, or otherwise aided and abetted, in order to control the pest (see Section 15.2.5). What is required of a good biological control agent is the ability to spatial heterogeneity and the most effective biological control agents

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Figure 10.20 Attacks by parasitoids on tephrytid flies (Terellia serratulae and Urophora stylata) that attack thistle flower-heads. The dynamics of the populations are shown for T. serratulae in (a) and for U. stylata in (d). Temporal density dependence of parasitoid attacks on T. serratulae (b) is significant (r2 = 0.75; P < 0.05), but for U. stylata (e) it is not (r2 = 0.44; P > 0.05); both fitted lines take the form y = a + b log10x. However, whereas for T. serratulae (c) there is little aggregation of risk of parasitoid attack within years (measured as CV2 > 1 for aggregation), with U. stylata (f) there is far more, most of which is HDI (no shading) rather than HDD (dark shading). (After Redfern et al., 1992.)

reduce the prey (pest) to a stable abundance well below its normal, harmful level, and we have seen that some theoretical analyses suggest that this is precisely what aggregative responses help to generate. Establishing such a link in practice, however, has not proved easy. Murdoch et al. (1995), for example, noted that the California red scale, Aonidiella aurantii, an insect pest of citrus plants worldwide, appeared to be kept at low and remarkably stable densities in southern California by a parasitoid introduced to control it, Aphytis mellitus. The existence of a partial refuge from parasitization for the red scale seemed a plausible hypothesis for how this was achieved: on bark in the interior of the trees, rates of parasitism were very low and scale densities high, seemingly as a result of the activities of ants there that interfered with the searching parasitoids. Murdoch et al., therefore, tested this hypothesis by a field experiment in which ants were removed from a number of trees. Parasitization rates in the refuge did increase, and scale abundance declined there (Figure 10.21), and there was some evidence that parasitization rates, and scale abundance, in the population as a whole were then more variable. But these effects were only slight and apparently short term, and there was certainly no evidence that scale abundance overall was increased by any diminution of the refuge effect.

Figure 10.21 Results of a field experiment to test the hypothesis that the parasitoid Aphytis mellitus maintains the abundance of the California red scale, Aonidiella aurantii, at stable low levels because of a partial refuge from parasitization in the interior portions of citrus trees, where ants interfere with the parasitoids. When ants were removed from blocks of trees (time of removal indicated by the arrow), the fraction parasitized in the refuge tended to be higher (a), and scale abundance there was lower (b), but outside the refuge ('exterior') the fraction parasitized was only marginally more variable (c), and scale abundance was only more variable over one relatively brief period and tended to be lower than on control trees (d). (After Murdoch et al., 1995.)

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Moreover, Murdoch et al. (1985) had earlier argued that, in general, pest populations persist after successful biological control not as a result of aggregative responses, but because of the stochastic creation of host patches by colonization and their subsequent extinction when discovered by the agent: essentially, a metapopulation effect. Waage and Greathead (1988), however, suggested that a broader perspective could incorporate both aggregative responses and metapopulation effects. They proposed that scale insects and other homopterans, and mites (like Huffaker's), which may reproduce to have many generations within a patch, are often stabilized by asynchronies in the dynamics of different patches; whereas lepidopterans and hymenopterans, which typically occupy a patch for only part of a single generation, may often be stabilized by an aggregative response. In fact, though, with biological control, like predator-prey dynamics generally, building convincing links between patterns in population stability of natural populations and particular stabilizing mechanisms - or combinations of mechanisms - remains a challenge for the future.

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