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Lagniappe #1

FIGURE 1: Local oscillations in the predator-pest dynamics are shown. At the start, a patch of pests (blue) in the upper left corner of the environment is being invaded by predators (red). This patch is consumed by predators, and then disappears as another patch in the lower left is consumed by predators.

CA Modeling of Apparent Competition

Eric Klopfer

Several mechanisms have been proposed (Holt 1977, Holt and Kotler 1987, Holt 1987) by which a shared predator can mediate the reduction or exclusion of one prey species by another (apparent competition). A novel twist on this idea is that one prey species can act as a spatio-temporal corridor for the predator to reach the other prey leading to a reduction in that prey's numbers ("quantitative apparent competition") or even to its elimination ("qualitative apparent competition"). The key elements in this mechanism are that interactions are local, and dispersal is short-range.

In this work, interest focuses on a target prey species, with high birth rate and a non-target species, which provides an additional resource for a predator which is introduced to control the pest. It is shown that the non-target prey species can facilitate the control of the pest, and that this role is enhanced when interactions are localized. Thus, models that do not account for the localization of interactions may underestimate the potential for control, or may overestimate the impact of the predator on the non-target prey species. These results have important implications for the theory and practice of biological control.

Figures 2-8 follow. See Apparent Competition and Biocontrol for the accompanying text.

FIGURE 2: Transfer diagram for the three species model showing probabilities of moving from one state to another. Parameters are defined in the text.

FIGURE 3: Time series for a local dispersal model demonstrating qualitative apparent competition (Here b1=.008, b2=.006, d=.004, d1=.08, d2=.04, beta=.001, beta1=.2, beta2=.1, delta1=.005, and delta0=.0001). When the pest and non-target prey are introduced concurrently the pest displaces the non-target species (a). When the pest and predator are present the two species persist, going through several initial large oscillations and later smaller oscillations (b). When all three species are introduced together (c), the pest is driven extinct and the non-target species persists with the predator.

FIGURE 4: Time series for global dispersal model demonstrating for the same parameters given in Figure 3. As in the global dispersal situation, when the pest and non-target prey are introduced concurrently the pest displaces the non-target species (a). Similarly, when the pest and predator are present the two species persist, however the oscillations damp through time (b). For this dispersal regime, there are two alternative outcomes when all three species are introduced together. When initial densities are low, the non-target species is driven extinct and the pest persists with the predator (c). When initial densities are high, the pest is driven extinct and the non-target species persists with the predator, as in the local dispersal case (d).

FIGURE 5: Regions in which pests and/or non-target prey persist for the global dispersal parameters in Figure 4. Three initial prey densities were used (.05, .1 and .15 for each species), paired with a range of initial predator densities (0 through .5 at intervals of .02). The winning species for each combination of initial densities was determined by running the model 4 times for 10,000 generations for each parameter set and noting which prey species was present at the end. For each trial only one species remained at the end. In the upper region that species was the non-target prey. For the middle region the winner was sometimes the pest and sometimes the non-target species. At the lowest densities the pest always persisted.

FIGURE 6: Densities of the predator, pest and non-target prey over time demonstrating quantitative apparent competition. When dispersal is global (a), the density of the non-target prey is approximately the same as it is for the mean field model (.13). However, when dispersal is local (b), the density of non-target prey similar to the mean field density when pests are absent (.17).

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