Mutation of albedo and growth response produces oscillations in a spatial Daisyworld

Details Mutation of albedo and growth response produces oscillations in a spatial Daisyworld Mutation of albedo and growth response produces oscillations in a spatial Daisyworld

Dec 2005

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2005agufmng23a0088w&link_type=abstract

American Geophysical Union, Fall Meeting 2005, abstract #NG23A-0088

Physics

0426 Biosphere/Atmosphere Interactions (0315), 0510 Agent-Based Models

Scientific paper

We present an extension of a 2-dimensional cellular automata (CA) Daisyworld to include mutation of optimum growth temperature as well as mutation of albedo. It is well established for the latter case such models exhibit homeostasis of the environment -- temperature in this case. In our model the organisms (daisies) can adapt to prevailing environmental conditions or evolve to alter their environment. This setup allows us to examine whether or not the former inhibits or even destroys the homeostatic effect. We find the resulting system to be capable of regulation on average but that it oscillates with a period of hundreds of daisy generations. The ability of the daisies to alter their optimal growing temperature leads initially to a planet which is less able to sustain itself, but the planet becomes steadily more stable (on average) for greater rates of genetic drift in this characteristic. Weaker and less regular oscillations have already been predicted in Daisyworlds before but in this model they become stronger and more regular as the mutation rate of the optimum growth temperature is increased. The oscillation itself is non-trivial and is composed by a series of well defined stages: when the population is maximal, a local region of daisies may lower (raise) the local temperature and adapt to it offering them a competitive advantage. The thermal time delay means that their newly adapted offspring are more successful, spiraling the daisies away from the optimal temperature. Once the population fragments, growth occurs primarily at boundaries between daisy patches and the bare earth - so warm (cold) adapted daisies are more successful, the direction of heating changes and the cycle reverses. We have analysed in detail the dependency of the period of oscillation on the various external parameters. It is found to decrease with increasing death rate, and to increase separately with increasing heat diffusion and heat capacity. The dependence of the period is supportive of the idea that the mathematical origin of this oscillation is a Hopf bifurcation, previously predicted in a zero dimensional system, induced by the time delay between the thermal and evolutionary timescales. This demonstrates that long period oscillations can be generated internally by even highly simplified earth models. Here a new timescale is induced by including evolutionary dynamics, an effect not normally included in such models.

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