Let us emphasize here that the break-down of the self-organized biosphere, which
takes place when S' crosses the threshold 
, is a clear cut first-order phase transition. Therefore hysteretic behaviour can be observed, i.e., the
state of the system depends on its history.
We want to demonstrate this by forcing our extended Daisyworld through a full hysteresis loop. So S' will be quasi-statically increased from the optimal value 1 to a supercritical value, thereby destroying all vegetation. Thereafter, S' will be decreased down to the initial value to give the biosphere a chance for renaissance. But note that the planet cannot be recolonized by life if all species have been wiped out together with their seeds.
Let us therefore introduce a uniform stochastic background process, which
represents the relentless germination of seeds protected by the soil. This can be achieved
by slightly modifying the CA growth rules. Let us assume that 
and all neighbouring cells are equally devoid of vegetation. Then instead of
applying Eq. 8, we make the following prescription:
Here 
is a very small number and 
is a random variable with uniform
distribution in the interval [0,1]. The germination process does not disturb
the original dynamics of the system.
Fig. 8 shows what happens under these conditions, when S' rises and falls again: both the evolution of the global mean temperature and of the total vegetated area are depicted. For fixed r=0.01, recolonization of the planet starts when the insolation drops to S'=1.25. This is significantly smaller than the extinction value S'=2.19! So, once the ``point of no return'' has been passed, it takes a great deal of effort to reinstall appropriate conditions for the self-organized reappearance of the biosphere.
Figure 8: Hysteresis diagram for the global mean temperature 
and the total vegetation area a in response to variation of S'.
The arrows pointing to the right indicate increasing, the arrows pointing to
the left
decreasing insolation. r=0.01, 
.