Self-sustained temperature oscillations on Daisyworld

Abstract

The daisyworld model of Watson and Lovelock demonstrated that a simple biological feedback system involving coupling between black and white daisies and their physical environment can stabilize planetary temperature over a wide range of solar luminosity. Here, we show that the addition of a differential equation for temperature to the original daisyworld model leads to periodic oscillations in temperature about a homeostatic mean. These oscillations, in which the model alternates between dominance by either black or white daisies, arise from the internal dynamics of the system rather than from external forcing. An important criterion for the oscillations to occur is that solar luminosity be within the range in which both daisy species are viable. A second important criterion is that the ratio of the timescales for daisy population turnover and climate system thermal response be bounded. While internally driven oscillations are well known in predator’prey biological models and in coupled ocean energy balance— cryosphere models, the present study shows that such oscillations also can arise in a model of the biosphere coupled to its physical environment. The potential significance of this result to planet Earth and the science of geophysiology is discussed.