Evolving Complex Food Webs

McKane's model seeks to simulate the evolution of many species over time in a given ecosystem. Species represent nodes in a digraph, and directed edges between nodes represent a prey-to-predator relationship.

Species are characterized by their unique list of attributes, which are a subset of a larger list. McKane specifically in his model defines species arbitrarily as a set of 10 attributes that are randomly selected from a possible collection of 500.  Although he does not make an attempt to base these attributes off of any real characteristic, it would be feasible to use adjectives from a zoological encyclopedia to do so.

McKane goes on to model each species potential as a predator against every other species, with this potential being quantified as a score, which itself is a summation on the scores of the individual attributes scores against each other. This score is used later in his population dynamics equation.

McKane's population dynamics equation is what makes his model unique. Whereas previous models statically defined the extent to which a given species would predate on another, McKane takes into account the population of the predator, the prey, alternative prey, and competing predators to predict the preference a given predator has for a given prey, and uses population dynamics and these inter-species preferences to calculate fluctuations in a population.

In addition to modeling population fluctuations, McKane simulates evolution in his model by randomly changing a single attribute of a single species to create a new child species, and then introducing that species into the model, to see how its attributes affect the ecological success of itself, and the other species in the ecosystem. 

The results of McKane's model found that the single most important factor in determining the number of species in an ecosystem were the available initial resources. Most prior studies predicted that as the number of species present in an ecosystem grew, so too would the relative instability of the ecosystem (defined by extinction events per time step.) McKane's model found that the number of species was not an accurate predictor of ecological stability.