Red Queen Simulator

Scaling of Population Energy-Use

      Let us ask how much energy, per unit area, the local population of a species uses. We could calculate this by taking the number of individuals of that species (the population density, D) and multiplying by the rate at which each individual uses energy (call it B). We know from a large body of work that B also tends to follow an allometric relationship with body mass, but with an exponent of approximately +0.75. So,

Since in multiplication, exponents are added, the two exponents cancel, with the result that population energy use is not related to body size. Not every species uses the same amount of energy (there is variation at all body sizes), but if you plot log energy-use versus log body mass of many species you get a plot with a slope of approximately 0, meaning that energy use doesn't change in any particular way when body size changes. Remarkably, since population density and individual energy requirements scale approximately reciprocally, no species has an advantage in energy control by virtue of its size alone. This is known as "energetic equivalence."

      For present purposes, the important point is: when the slope of the plot of log density vs. log body mass is –0.75, population energy-use is independent of body size.

     It has been difficult to envision specific ecological or evolutionary processes responsible for the origin and maintenance of the energy equivalence relationship. The Red Queen Simulator illustrates one possible process that might do this.

What the Red Queen Simulator does

      The Red Queen Simulator simulates evolutionary interactions among species in a local community. In each time step, a number of randomly chosen species make an "evolutionary advance" and evolve such that each of their individuals can obtain more (food) energy from the environment than before. Since the total amount of energy in the environment is assumed to be fixed, this means that for each such advance some other (randomly chosen) species must lose the equivalent amount of energy. Once these exchanges

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