of “across-diagonal” plus–minus links in the web. Because the product of their interaction is always negative, adding more summed negative terms increases the chances that this eigenvalue will be negative (Allesina and Pascual, 2008). More specifically, adding shared pathogens to the food web significantly increases the proportion of negative cross-product terms relative to positive product terms produced by competition (where negative times negative = positive!). This effect generalizes: As we increase the species diversity of the web, destabilizing competitive interactions will increase at a maximum rate of (n2 − n)/2, whereas potentially stabilizing shared pathogen interactions increase at the significantly faster maximum rate of n2.
Similar effects arise when we consider parasites with complex multiple host life cycles. These infectious agents confound traditional concepts of food-web structure because they feed on several different trophic levels within different host species during the course of their life cycle. They also act as food resources to species on different trophic levels as they pass through their free-living stages. Usually, <1% of the energy-rich, free-living infective stages of a parasite ever manage to infect a host; the other 99% are eaten by planktivorous species. Parasites with this type of life cycle can again be incorporated into food-web models. Initial results with matrix models of the form described above suggest that such parasites will also have key stabilizing effects on the structure of food webs because they also add pairwise sequences of “plus–minus” resource–consumer interactions at every stage of their life cycle, and these will consistently increase the probability that the dominant eigenvalues of the linearized system will be negative. Furthermore, generalist parasites with complex multihost life cycles also introduce long circular loops of relatively weak links into the web; theoretical analysis by Neutel et al. (2002) suggests that these may also be important in imparting stability to food webs.
Thus, generalist parasites and those with complex life cycles potentially play important roles in regulating the relative abundance of their free-living host species. Whereas generalist species with direct transmission are likely to be buffered from extinction by the rescue effect of at least one host remaining abundant, parasites with complex life cycles will depend highly on the host species in the life cycle to which they are most specifically adapted. The trematode and acanthocephalan species that are recorded as adult worms from scores of vertebrate host species often depend entirely on a single species of mollusk or amphipod that serves as their intermediate host. Thus, snails or other invertebrates that invade natural ecosystems and replace crucial host species within the complex life cycles of parasites may lead to losses of parasite diversity that cascade throughout the food web.