The original Daisyworld model

  The familiar LWM is a zero-dimensional caricature of a planet, which is illuminated by the sun and which is able to support merely two different types of vegetation cover.

The surface of the ``naked'' planet, i.e., the planet without vegetation, is characterized by an overall albedo . The equilibrium temperature depends on the insolation S and the black body radiation according to
 
where is the Stephan-Boltzmann constant. The biosphere consists of two components only:

• Species 1 with albedo (``white daisies''), covering an area with temperature ;
• Species 2 with albedo (``black daisies''), covering an area with temperature .

The growth rate of species i is a unimodular function with a maximum at :
 
The dynamics of the toy biosphere is governed by a system of two coupled nonlinear differential equations:
 
Here denotes a constant mortality rate and x, the uncovered area, is trivially given by

For the sake of even more simplicity, the total area of the planet has been set equal to unity and the solar radiation is measured in ``optimal insolation'' units:

 

This feedback system has been analysed by several authors [12, 13, 14, 15] in great detail. One remarkable result is that, in contrast to the uncovered planet, the ``bioplanet'' is able to hold the global temperature relatively constant when the external ``control parameter'' S is varied within a rather wide range. This property of self-regulation is referred to as ``homeostasis''. As a matter of fact, homeostasis is achieved here by a rather simple mechanism: white (black) daisies are fitter in hot (cold) climates as their comparatively high (low) albedo tends to reduce (increase) the local temperature.

Note that by conceiving as a function of the concentration of the atmosphere, it is possible to take the greenhouse effect into account.