Interspecies Connection Models

In the Bak-Sneppen model studied in the previous chapter there is no explicit notion of an interaction strength between two different species. It is true that if two species are closer together on the lattice, then there is a higher chance of their participating in the same avalanche. But beyond this there is no variation in the magnitude of the influence of one species on another. Real ecosystems, on the other hand, have a wide range of possible interactions between species, and as a result the extinction of one species can have a wide variety of effects on other species. These effects may be helpful or harmful, as well as strong or weak, and there is in general no symmetry between the effect of A on B and B on A. For example, if species A is prey for species B, then A's demise would make B less able to survive, perhaps driving it also to extinction, whereas B's demise would aid A's survival. On the other hand, if A and B compete for a common resource, then either's extinction would help the other. Or if A and B are in a mutually supportive or symbiotic relationship, then each would be hurt by the other's removal. A number of authors have constructed models involving specific speciesspecies interactions, or "connections." If species i depends on species j , then the extinction of j may also lead to the extinction of i, and possibly give rise to cascading avalanches of extinction. Most of these connection models neither introduce nor have need of a fitness measure, barrier, viability, or tolerance for the survival of individual species; the extinction pressure on one species comes from the extinction of other species. Such a system still needs some underlying driving force to keep its dynamics from stagnating, but this can be introduced by making changes to the connections in the model, without requiring the introduction of any extra parameters.