The role of herbivores in a fragmented landscape

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:

1. : The herbivores rapidly die back and the remaining biosphere controls the global temperature until the percolation threshold for the growth space is reached.
2. : The homeostatic power of the co-existing daisy-herbivore community is similar to the one exhibited by the daisy community alone. The concentration of herbivores increases with decreasing mortality
3. : In this parameter domain the overall system's behaviour attains a new quality. When the fragmentation degree p grows beyond the approximate value 0.2, an intermediate homeostatic situation emerges, where and plants and animals co-exist at rather low population densities. Even more interesting is the finding that in the moderate fragmentation regime the herbivore concentration is higher for higher values of the mortality parameter! This is in marked contrast to what one would expect and what indeed happens in the homogeneous landscape.

   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.

4. : Plants and animals die back rapidly with increasing p, and our model world behaves like a desert planet for small values of the fragmentation parameter. Thus the unchecked vitality of the herbivores destroys the ecological balance completely.

  
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.