Constructing ecologies.

We synthesize the generic properties of ecologically realistic multi-trophic level models and define criteria for ecological realism. We define an "ecospace" in which all ecologically realistic dynamics are confined, and construct "resource rays" that define the resources available to each species at every point in the ecospace. Resource rays for a species are lines from a vertex of maximum resource to the opposite boundary where no resources are available. The growth functions of all biota normally decrease along their resource rays, and change sign from positive to negative. This property prescribes that each species must have a zero isosurface within the ecospace. We illustrate our conditions on a highly cited three trophic level model from population dynamics, showing how to extend this system biologically consistently to a closed ecological system. Our synthesis extends the concept of carrying capacity of population models to explicitly include exhaustion of limiting resources, and so allows for population biology models to be considered as ecologically closed systems with respect to a key limiting nutrient. This approach unifies many theoretical and applied models in a common biogeochemical framework, facilitates better understanding of the key structures of complex ecologies, and suggests strategies for efficient design of experiments. Crown