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Next: Introducing spatial dependencecompetition, Up: Self-stabilization of the biosphere Previous: Introduction

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 tex2html_wrap_inline1079. The equilibrium temperature tex2html_wrap_inline1081 depends on the insolation S and the black body radiation according to
 equation28
where tex2html_wrap_inline1085 is the Stephan-Boltzmann constant. The biosphere consists of two components only:

The growth rate tex2html_wrap_inline1099 of species i is a unimodular function with a maximum at tex2html_wrap_inline1103:
 equation34
The dynamics of the toy biosphere is governed by a system of two coupled nonlinear differential equations:
 eqnarray43
Here tex2html_wrap_inline1105 denotes a constant mortality rate and x, the uncovered area, is trivially given by
equation48
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:


 equation50

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 tex2html_wrap_inline1085 as a function of the tex2html_wrap_inline1113 concentration of the atmosphere, it is possible to take the greenhouse effect into account.


next up previous
Next: Introducing spatial dependencecompetition, Up: Self-stabilization of the biosphere Previous: Introduction

Werner von Bloh (Data & Computation)
Thu Jul 13 13:46:37 MEST 2000