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Self-stabilization of global temperature without herbivores

First, we test the decay of self-stabilizing power with increasing patchiness in the 2D Daisyworld without animals.

Fig. 2 summarizes our findings regarding the relation between global mean temperature tex2html_wrap_inline643 and the percolation parameter tex2html_wrap_inline645. It can be observed that even the fragmented biosphere is able to stabilize the planetary temperature near the optimal value, unless p exceeds a value of approximately 0.4.

  figure160
Figure: Convergence of numerical results for p-tex2html_wrap_inline643-relationship for increasing lattice size ranging from tex2html_wrap_inline655 (wiggliest line) to tex2html_wrap_inline657 (smoothest line). S has been fixed to a value that generates a geophysical planetary temperature tex2html_wrap_inline661.

The numerical results are robust. As a matter of fact, Fig. 2 shows for a series of extensive calculations with increasing lattice dimensions that finite-size effects can be neglected. It actually turns out that the above-mentioned threshold value for patchiness has universal character. The adaptive power of Daisyworld clearly breaks down when p approaches the value tex2html_wrap_inline665.

The explanation for this phenomenon is simple but illuminating: for tex2html_wrap_inline667 the growth space has lost its connectivity and is broken up into many isolated domains. Our toy model hence provides us with clear-cut evidence that the ecological performance of a system directly depends on its connectivity! For detailed results concerning, for example, the corresponding change in the species spectrum see again von Bloh[5].


next up previous
Next: The role of herbivores Up: The impacts of fragmentation Previous: The impacts of fragmentation

Werner von Bloh (Data & Computation)
Thu Jul 13 14:36:30 MEST 2000