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In English, this equation says that for a given habitat, there exists a carrying capacity, K, which is the right population level for this species. If the population rises above K, it will drop back down. If lower, it will grow. How fast the population grows or falls depends on how close it already is to K, and R, its growth rate. The population grows at its fastest, R, only when it is far below K. Near K, the population neither grows nor shrinks. (If R is high enough, the population oscillates, but we don't set R that high.) R values used in Chaparral range from 0.15 for Scrub and Raccoon, to 1.7 for Otherbug. There are some R=0's as well, but more on that below. The ecologically savvy will notice that we don't really know what values to use for R. It isn't readily measured for one species, let alone a whole foodweb's worth of species. So, that's how a population grows, "all else being equal." But K, the carrying capacity, is not a constant here. It's set by what's available to eat. The crux of this simulator is repeatedly finding K for each species. In each timestep, the simulator does:
There are a few more parameters used in the simulator than appear in the discrete logistic growth equation. Specifically:
Two species in the Chaparral (Cat and Coyote) are "sponsored". This means that although they eat here, their numbers are independent of the K-setting dynamics, and their R is unused. For Cats, this is because their food and reproduction are more-or-less controlled by humans. For Coyotes, the problem is range. Typical Coyote ranges are huge compared to any suburban land fragment. Seeds should be made by the plants, that submodel wasn't implemented here. Seeds are treated more-or-less like another kind of Space. They are increased or decreased by the cards, not by how the plants are doing. Seeds are kept separate because eating seeds is not equivalent to eating plants--it does the plants no harm. Although the Chaparral isn't a bad model, I won't defend it as science. I have very little basis for setting the parameters. The reality check used to parameterize the foodweb was a comment in the paper describing this system (Crooks & Soule, 1999) giving proportions and implied numbers of the lizards, birds, and rodents the cats drag home. The paper also indicated the cat and mesopredator densities, the rare-visitor role of the coyote, and listed the bird species. The Chaparral model gets the numbers and proportions pretty close to what the paper implied. The paper didn't provide all the detail needed to structure this foodweb. That was fleshed out by surfing the net to find out what species to put in a chaparral, and what they generally eat. Then I pared my cartoon down to what seemed a minimum, omitting details like roadrunners eating snakes, etc., but leaving all the bird species because they formed the core of the story. What a gnatcatcher eats was supplied only by its name.
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