Red Queen Simulator

of energy levels are determined, the population densities of the affected species are adjusted accordingly. Some species may lose all of their energy in this process and become extinct. (New species with average characteristics are periodically added to the community, as if they migrated from elsewhere, which allows the simulation to run for long periods of time.)

This process of population changes and extinctions can alter the slope of the relationship between log density and log mass. The Red Queen Simulator allows one to follow the trajectory of changes in slope for one or more communities over time. As you will see, the slopes tend to converge on a region near -0.75.

Why does the simulation act this way?

     I think that the mechanism is extremely simple. "When slopes are substantially more negative than –0.75, it is some of the larger species that currently exhibit the lowest absolute energy use values. Hence these species are now those most likely to become locally extinct if they become the victims of an evolutionary advance by another species. Their extinction will tend to cause the slope of the entire fauna to become less negative. Likewise, if the slope is substantially more positive than –0.75, a number of small species are currently the ones with the lowest energy-use, and their more likely extinction will tend to make the slope more negative. When slopes are near –0.75, species of the lowest and highest energy-use are distributed over all body sizes, so their differential extinction causes only relatively small, random changes in slope. It is thus differential local extinction of species-populations of relatively low energy-use that drives the process to a dynamic equilibrium and keeps it there." (Damuth 2007)

This roughly 6-second animation is a cartoon depicting species exchanging energy over timesteps, and illustrating the above mechanism. The animation loops endlessly, and the word "start" flashes to tell you when the loop is restarting. For reference, the gray region has a slope of –0.75. When the line becomes very shallow it is a number of unusually rare, small species (depicted in red when this condition occurs) that are pulling the line "down" (or, if you like, rotating it counter clockwise). When these species go extinct, the line returns to a steeper slope. Similarly, when the line becomes very steeply negative there are some unusually rare, large species (again depicted in red) that are most responsible for this behavior (and most likely to go extinct). Their subsequent extinction now returns the slope to the shallower region near –0.75 and thus near to energy equivalence.