Figure 1. Agents are spheres projected onto a plane. This schematic shows the upper hemispheres of a grazer (lower left) and three plants. The cutaway shows the agent viewpoint. The grazer's world consists of itself, the landscape, and one plant. The plant's world includes itself, the landscape, one grazer, and two competing plants.
Figure 2. Gecko displays the landscape plane, with circles denoting the agent spheres. The green agents are ``plants'', yellow are ``grasshoppers'', and purple are ``spiders''. The plants at the middle right have settled into a broken hexagonal pattern, where mutual crowding deadlocks their growth. Grazing aids formation of the hex pattern. At the upper left corner, an uncrowded large plant is filling the open space around it with children.
Figure 3. A trophic cascade, population and biomass graphs for an unusual Gecko run. There are three distinct phases in this run. At time 0, 200 plants of child radius are randomly strewn across the resource-producing site. Coincident seeds immediately die off. The rest begin reproducing about time 350. At this point 15 random grasshoppers are introduced, and the two species uneasily coexist. At time 2000, 5 random spiders add a third trophic level to the system, and dampen the grasshopper/plant dynamic. The scale on the y axis is discussed in the text--one unit spider biomass = 1.2 grasshopper = 3.5 plant. The match to qualitative theoretical prediction is indicated by the straight line mean values for plants and grasshoppers. Grasshoppers are depressed after spider introduction, but this is not discernable at this scale. Mean plant values for the introductory segment are for a plant population allowed to grow to carrying capacity undisturbed. Carrying capacity plant biomass is about 155,000.
Figure 4. Population graph of a stable three-species food chain of plants, grasshoppers, and spiders. Table 1 gives the parameters of this scenario, and Figure 2 shows a snapshot.
| Agents | |||
|---|---|---|---|
| Plant | Grasshopper | Spider | |
| introduced | 200 at time 0 | 15 at time 350 | 5 at time 500 |
| minimum radius | 2.05 | 2.05 | 1.72 |
| child radius | 2.04 | 2.19 | 2.76 |
| breed radius | 7.51 | 3.55 | 4.72 |
| eats | sunwater | carbos | proteins |
| converts to | carbos at 10% | proteins at 33% | cproteins at 85% |
| tax | 0.0154 biomass3/4 | 0.365 biomass3/4 | 0.120 biomass3/4 |
| growth rate | 3.06% | ||
| veer | 3.77 radians | ||
| smell radius | 2.09 x current radius | ||
| digestive time | 6 timesteps | ||
| hibernating time | 15 timesteps since last ate | ||
| hibernating tax | 0.006 biomass3/4 | ||
| Landscape | |
|---|---|
| sites | 1 |
| size | 170.0 x 170.0 |
| production function | 1.0 sunwater per unit area per timestep |
| resource cap | 1.0 sunwater per unit area per timestep |
Table 1. Stable Grassland parameters. Some parameters use typical values found in nature, others were set by trial and error and algorithmic improvement.
Figure 5. Three plant species. This scenario matches Figure 4, except that the initial plants are evenly divided between three species, identical except for breeding radius (br) of 4.7, 6.0, and 7.5. This is a big difference. A br6.0 plant fixes twice the biomass of a br4.7, and a br7.5 four times that of a br4.7, before it can breed, while all start from seeds of the same size. The br4.7 plants appear to take over the field as they reproduce first, then gradually become marginalized by the larger plants. None tend to extinction.
Figure 6. Three plant species snapshot. Species br4.7 has been marginalized at the upper right edge, br6.0 has the lower left corner, and br7.5 the upper left, with most areas intermingled.