As the system gets closer to the refuge, the combination of a lower bound on the scale population and the rapidity with which it can increase when under protection from the ants combine to frequently produce chaotic oscillations, and the collision between the boundary of the chaos and the basin edge causes the population to crash, in a basin or boundary collision . The basic dynamics are illustrated in cartoon form in figure 8b. To the extent there exists evidence to support the ideas of chaos and basin or boundary collision as represented in figure 8, we display some data in figure 9. The expectation from a chaotic approach to a basin boundary collision is complicated and requires a far more dense data set than we currently have, but what is available certainly supports the idea that, as the system approaches the refuge, it undergoes complicated and relatively unpredictable behavior within a hysteretic zone. A complicating issue is the fact that the scale insect population density is the main determinant of the probability of infection, and that density increases as the refuge is approached. As the refuge is approached, we expect an increase in total scale population and an increase in the fungal infection rate. With the increase in total scale population we expect an increase in susceptible scales as the refuge is approached. Within the refuge, we expect the signal of flickering , which, in this case, would result in a bimodal distribution of bushes, dutch buckets many with no infection and many with high infection with few intermediates. That is precisely the pattern suggested by the data presented in figure 9.

At the periphery of the refuge , we generally have very few scales and low levels of disease incidence. Moving further into the refuge area, we see a gradual buildup of disease incidence , culminating in bimodality when we arrive at a distance of 0–1 meters. What is not immediately obvious from this analysis is that there are really three qualitatively distinct outcomes at a local level, which is to say on a particular coffee bush. If the bush is very close to the Azteca nest, the ants forage vigorously and, therefore, the scale insects are highly protected from the beetle predator. Consequently, they build up very high local populations, and are subjected, eventually, to the white halo fungus disease, effectively eliminating the entire population . At the other extreme, when the coffee bush is far removed from the ant nest, the scale insect is constantly attacked by the adult beetles and never is able to build up a substantial population. Therefore, it would appear that either very close to an Azteca nest or very far away from an Azteca nest thegreen coffee scale is kept under control. However, in the real world, there is no such thing as only far away or very near; many coffee bushes are neither. The result is a complex system in which the Azteca ant forms a reaction or diffusion Turing-like pattern-forming complex that acts as a pilot structure, driving the spatially dependent direct control system. The ant exerts a behavioral restriction on the beetle , but the phorid exerts a behavioral restriction on the ant , causing what has been referred to as a trait-mediated cascade of effects and imposing a hypergraph-like structure on the system . The concentration of ants creates refuges within which the adult beetle predator is restricted from active predation but within which the pest, the scale insect, builds up very dense local populations, the consequence of which is a high attack rate of the white halo fungus disease. Regulation of this herbivore is therefore effected through a complex system involving a Turing process, nonlinear indirect interactions, critical transitions, hysteresis, chaos, basin or boundary collisions, and a hypergraph, all elements of the burgeoning field of complex systems.

The elements of the system are illustrated in figure 10. Note the central role of the Azteca ants. It is worth emphasizing that these ants are obligate tree nesters, which suggests that the trend to eliminate the shade trees in the system, thought to be a modernizing effort, completely breaks down this complex system. An interesting complication emerges as we understand the importance of these two obvious natural enemies of the scale insect . We began by proposing a predator–prey driven Turing mechanism to generate the clustered distribution of ant nests, a clear application of what has previously been noted; predator–prey systems distributed in space can generate Turing-like patterns. The predator was the phorid parasitoid, and the prey was the Azteca ant. However, the spirit of the Turing mechanism involves only generalized reaction and diffusion terms, wherein the reaction is thought to be a coupled positive or negative effect. And in the present example, there are two clear negative effects on the ant through the attack on its food. Both the predatory beetle A. orbigera and the white halo fungus are enemies of the scale insect, the main food of the Azteca, and therefore both constitute a negative effect. It has been independently suggested that either the beetle or the fungus could be the repression agent that generates the Turing-like pattern. Evidence from a combination of modeling and empirical observations suggests that either could be true. If the beetle is the cause of the pattern formation, it is an especially interesting situation in that the beetle population itself is dependent on the existence of the spatial pattern for its own survival but is the cause of the formation of that pattern in the first place .Perhaps the most directly obvious of the three pests is the infamous coffee berry borer, because of its habit of drilling directly into the seed, which is the basic commodity that goes to market. It emerged as a major pest in the 1980s and is regarded as far more important, on most farms, than the green coffee scale.

The literature on the coffee berry borer is now enormous because of its sometimes devastating effect . A variety of natural enemies have been reported, including the fungus Beauveria bassiana , anole lizards , birds , possibly bats , and parasitic Hymenoptera . But, by far, the most obvious natural enemies are ants. There is now a substantial literature documenting the general category of ants as major predators on this seed-eating herbivore . As in the case of the predacious beetle on the scale insect, some rather casual observations can easilyconvince one that, in particular, the Azteca ants are major predators to the coffee berry borer, and a variety of detailed studies support that conviction . However, further examination reveals another major ant predator, Pheidole synanthropica, a rather large-body species that nests in the ground but forages vigorously both on the ground and in the coffee bushes. Detailed observations established that this species is a major predator of the berry borer. It takes the berry borer approximately 1–2 hours to completely burrow into the fruit , which means it is unprotected and unable to escape the predacious activity of the ants for that period of time. Both Azteca and P. synanthropica, grow bucket if they encounter a berry borer trying to burrow into a seed, grab the borer by its posterior end and pull it out of the fruit. Azteca tends to simply throw the borer off the tree , whereas P. synanthropica almost inevitably takes the borer back to its nest. Therefore, we might say that Azteca is mainly a general antagonist to the berry borer, whereas P. synanthropica is definitely a predator . The consequences of this difference are quite important. Although Azteca provides some protection to the coffee from the ravages of the berry borer, when the borer is simply thrown to the ground it can easily climb back up and try again to bore into the seed. Indeed, there is some reason to suspect that the borer actually prefers to burrow in seeds that are protected by ants, presumably taking advantage of the ant’s mutualistic behavior toward the scale insects and protecting it from other predators that may attempt to enter the seed in which it is eating endosperm and creating the new generation of berry borers. However, this strategy is compromised by other species of predators that can directly prey on the borers when they are thrown to the ground, one of which is P. synanthropica. And this species is highly aggressive, limiting the activity of the smaller species . These species offer considerable regulatory potential because they are capable of entering the coffee seed through the hole that the borer makes . One group is the twig-nesting complex, including the genus Pseudomyrmex , and Procryptocerus scabriusculus, all adept at entering hollow arboreal structures because they normally nest in hollow twigs . Other small arboreal ants capable of entering the hole made by the berry borer include the arboreally nesting Solenopsis picea, which nests in superficial structures, such as moss, surrounding the branches of the coffee bushes . On the ground, a variety of ground foraging ants, including Pheidole protensa , and a variety of other species in that same genus are small enough to enter the borer’s hole. Of particular interest is the well-known Wasmannia auropunctata , which nests and forages on both the ground and arboreally . There are many other potential ant predators in the system, but these are the ones we have studied in particular. Azteca clearly dominates over P. synanthropica, and both of them dominate over the smaller species in the system, reducing their nest density significantly . In summary, there are at least six species of ants that are predators on the coffee berry borer, suggesting that ants represent an excellent natural enemy to regulate the coffee berry borer. However, the foregoing natural history suggests that the system is not so simple. Although several of the smaller arboreal species could be effective predators on adults, larvae and pupae of the berry borer within the fruit on the bush, they are effectively unable to engage in such predation if Azteca or P. synanthropica ants are around. Fruits that are not harvested tend to dry out and fall to the ground, providing a refuge for the beetles during the dry season but also being exposed to the potential predation from the smaller ants . However, those smaller ants have dramatically reduced populations if they are forced to compete with P. synanthropica, which, because of its larger size, is unable to penetrate the borer hole in the fruit. In other words, the whole system seems to be operating in a complicated fashion with potential predators interfering with one another but perhaps acting in an emergent fashion to at least partially regulate this key herbivore, the coffee berry borer.Adding to this complication is the phorid fly. As was noted earlier, this fly has an important trait-mediated effect on the Azteca ants, the foundation of the Turing patterns we seem to see at a large scale and effectively contributes to the maintenance of the major predator of the green coffee scale . However, because, as all evidence suggests, the Azteca ants so dominate the coffee bushes where they forage that the smaller ants are unable to persist there, we might expect the same sort of trait-mediated cascade we saw with the control of the green coffee scale. Indeed, in controlled laboratory settings, the coffee berry borer has its success rate of penetrating coffee fruits reduced in the presence of the phorid flies. The importance of this effect is in the addition of what has been referred to as vertical biodiversity to the system , the smaller ants who had been effecting control over the berry borer were restricted from doing so by the action of the Azteca, but when the phorids were introduced, the smaller ants again became effective predators. Although the Azteca ants reduced the effectiveness of berry borer predation from these smaller ants , the phorids reduced the effectiveness of the Azteca in reducing the effectiveness of the smaller ants in their effectiveness in controlling the berry borers, a similar trait-mediated cascade that we saw for the green scale control. All of this is summarized in figure 12. It is tempting to conclude something like “the more ants the better.” However, cascading indirect effects sometimes can have unexpected consequences, meaning that such a conclusion ought to be tempered with more careful analysis.