As an acceptance test for the Gecko simulator, I modeled a trophic cascade in a food chain of ``plants'', ``grasshoppers'', and ``spiders''. Schmitz presents qualitative predictions and empirical results with the natural system on the Montana prairie [14]. Schmitz and Booth use this food chain on the one-dimensional Echo Gecko prototype [15]. The same food chain is the inspiration for the experiments presented here.
This food chain, dubbed Grassland, is simple. Plants grow, grasshoppers eat the plants, and spiders prey on the grasshoppers. Spiders and plants have no direct interactions. In the absence of grasshoppers, plant biomass is maximal, limited by resources (including space). This is a single trophic level. If grasshoppers are present, with no carnivores to limit their numbers, plant biomass is lower. This is two trophic levels. A third trophic level of spiders limits the grasshoppers. The plant biomass level in a three level system should lie between that in the one and two level systems. This is a trophic cascade, demonstrated in Figure 3.
To pass the acceptance test, the simulator must not only generate a qualitative trophic cascade of relative plant biomass in one, two, and three level systems, but do so consistently and stably, using plausible behaviors for the natural creatures. Qualitative here means that predictions are relative quantities. This theory provides no quantitative predictions, and population levels may be steady or cyclic about the relative levels predicted. Consistently means the trophic cascade is seen in all cases. Plausibility includes facing realistic energy inefficiencies between trophic levels.
Stably means that all species persist ``indefinitely'' with no extinctions. In the interests of computer time, I used 4000 timesteps as a stand-in for ``indefinitely'' for most experiments, or about 6 boom-bust cycles, or about 36 herbivore or 14 plant generations. This is admittedly not close to ``indefinite''. However, I studied many longer periods before selecting a ``sufficient'' 4000. The first one or two boom-bust cycles include initialization effects, but anything beyond that appears to be a self-perpetuating dynamic, subject to occasional extinction by demographic bad luck.
This is a challenging acceptance test. Natural systems of only three species arrayed as a three level food chain are rare, and don't include the Montana prairie system. Empirical studies were limited to a grasshopper nymph stage, about a month in the grasshopper life cycle, with no reproduction of grasshoppers or spiders. (Grass spreads asexually, even if it doesn't seed.) Thus, this first-pass abstract Grassland is not strongly based on the real system. As this is the empirical system used by Gecko's principal investigator, Oswald Schmitz, future elaborations of Gecko are expected to model it more faithfully, to permit empirical and theoretical development to inform each other. Although this test is difficult in some ways, three species is the simplest case of a multiple trophic level system. It was felt necessary to start here to demonstrate sufficiency of Gecko's basic mechanisms, before venturing into more complex and behaviorally specific ecosystems.
Gecko passes this test, as demonstrated in three species in Figure 3. The parameters used to generate this graph are given in Table 1, varied only by the grasshopper and spider introduction dates. Note that although it would make a prettier graph if the one-, two-, and three-species portions were of equal length, that scenario does not work. The grasshoppers must be introduced before the plants reach biomass carrying capacity, or the grasshopper/plant dynamic is too extreme to self-correct. The grasshopper population peaks, then goes extinct.
Finding parameters to perform this demonstration was tricky, not because the trophic cascade is difficult to generate in Gecko---that's a simple consequence of energetics, provided each trophic level has noticeable effect, and the ecosystem is stable enough to measure relative population levels. The difficulty lay in finding a model interchangeably operable in one, or two, or three levels, and stable in all three configurations, to permit direct comparison. In natural systems, local stability is not necessary for a three-level system to persist, as neighboring areas are a source of replacements in the common event of local extinctions. Also, natural species have a multitude of physiological and active behaviors for adjusting to the current state of their habitat, far beyond the simplistic repertoire given these Gecko agents. However, I wished to test that Gecko's spatial and energetic abilities alone were sufficient for this trophic cascade. Thus this test, though naturally inspired and naturally valid, is stringent, which makes it a compact test case. The trophic cascade result is highly robust.