One of the main features of real-world ecological communities is their trophic complexity as defined by the food-web structure [16]. By introducing herbivores into our 2D Daisyworld, we are able to study the most simple non-trivial community case, namely a classical prey-predator situation. The well-known Lotka-Volterra theory does not apply here, however, as the community strongly interacts with a heterogeneous environment.
The co-dynamics of plants and animals within our model world has been described
in Sect. 2.3 above. If we now ``switch on'' habitat fragmentation, both
daisies and herbivores are affected as more and more cells become inaccessible
to growth and grazing, respectively. For the sake of clarity, we keep the
insolation S again constant and study exclusively the impacts of
denaturalization. Extensive numerical calculations reveal that the crucial
parameter is the herbivores' mortality rate . This is demonstrated
in Fig. 3 and 4 where the relationships between global mean temperature
and fragmentation p and between herbivore concentration and
p are depicted for different
values.
Four distinct ``vitality regimes'' can be identified:
Our interpretation is as follows: In a complex environment, the more vital herbivores turn to ``overgraze'' their substrate. This behaviour produces additional negative effects by raising the ambient temperature to uncomfortable values.
When the fragmentation approaches the first percolation threshold ,
the herbivores become extinct while the daisies still survive in reduced
numbers. Then the system's behaviour is similar to the one of Daisyworld
without predators.
Figure 3: Dependence of global mean temperature on fragmentation
parameter p for distinct herbivore mortality rates
.
Figure 4: Dependence of herbivore concentration on
p for the same values as in Fig. 3.
Our general finding is that our herbivores can exist in a heterogeneous
landscape with albedo feedback only in a rather small regime of the mortality
parameter . While daisies are able to survive in a fragmented
growth space even above the first percolation threshold, the ``lattice
animals'' definitely cease to exist there. This reflects an observation
encountered again and again in our studies: predators are more vulnerable
to habitat fragmentation than their preys as the former depend heavily
on mobility.