Recipe for the week of Oct. 14

The Cook Book

Recipe for the week of October 14 - 20

The Good, the Bad & the pRedators, revisited

This week Eric Klopfer is guest chef here in the Kitchen. He offers a follow-up report on a three-species ecological model for biocontrol originally investigated with the CAM8 mixmaster last winter. Whereas the CAM8 version used density-dependent state values for the predator and two types of prey, Eric's new implementation involves only presence or absence of each type within a cell. Nevertheless the observed behavior is qualitatively the same, confirming in this instance that the two modeling approaches are essantially equivalent. [Technical note: the two animated gif sequences on this page fill nearly 1Mb, so those with slow connections should look over the text until the data is downloaded to a local cache, after which they will loop in real time.]

Apparent Competition as a Result of Spatial Interactions

These are simulations of a presence-absence cellular automaton model for a single predator and two prey. One prey (blue) is a pest while the other (green) is not. The pest is characterized by its higher birth rate. The predator (red) is present in order to control the pest, and thus attacks it more aggressivlely than the non-pest, which does not always need to be present.

Our first animation demonstrates possible dynamics of the predator-pest system. In this example the predator is unable to control the pest because the predator always leaves a few pests behind in its wake. This sequence, showing 15,000 generations, is reminiscent of forest fire models.

Here is a graph of the above dynamics over a longer time scale (100,000 generations). The oscillations are quite noticeable and seem to persist a long time.

Three Species Dynamics

When the non-pest species is present it can provide access to the isolated pockets of pests that are not accessible in the two species model. While the two prey do not compete directly, and coexist in the absence of the predator, when the predator is present it now drives the pest extinct. The non-pest can then persist with the predator, and this two species system is stable to reintroduction of the pest (i.e. the pest is again eliminated if it is reintroduced).

Our second animation shows this case over about 30,000 generations. The pest is reintroduced after it goes extinct at about 20,000 generations and again at the end.

The graph below shows that the system of predators and non-pests is stable to the reintroduction of pests. The pest is initally eliminated, but is reintroduced several times. After each reintroduction it is again eliminated.