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In order to reflect fundamental ecosystems dynamics based on trophic
interactions as well, we extend the 2D model even further and add herbivores to
our toy planet (see also, e.g., Harding and Lovelock [15]).
These vegetarian ``lattice animals'' move on the grid as
random walkers. As in reality, the herbivores are capable of reproduction,
but the latter capacity depends heavily on their nutritional state.
Formally, the herbivore dynamics can be conveniently described by an occupation
map
,
defined on a second lattice layer parallel to the daisy lattice, and a small
set of non-deterministic behavioural rules. If the site is
occupied by an animal at time , i.e., ,
then those rules allow for four different events:
- Death:
- The herbivore deceases with a probability , thus
.
- Ingestion:
- If the herbivore survives and if the cell is covered
by a daisy, i.e. , then the animal consumes the plant. The
number of ingestion acts that have been performed by the herbivore considered
so far is stored as a state variable N. Thus
in this case. Evidently, we also have and .
- Reproduction:
- The herbivore in question may give birth to a ``lattice
child'' at a randomly chosen next-neighbour cell with probability
The temperature-dependent factor is chosen similar to the one
which governs the growth of daisies, while is assumed to
behave like a discrete Heaviside function, i.e.,
The latter assumption reflects the conception that only ``grown-up'' lattice
animals will be capable of replication. Clearly, the ingestive status of
the new-born herbivore is zero.
- Move:
- The herbivore may also walk to a randomly chosen next-neighbour
cell if this cell is not already occupied by another herbivore.
As a matter of fact, consistent combinations of all those events may occur according
to the probabilistic set-up. Note that the presence of herbivores is not
assumed to change the local albedo. So it is only the act of daisy
consumption that affects the radiative properties of our virtual environment.
Note that the interaction between plants and animals is realized by mainly two
processes, namely (i) temperature-dependent reproduction of herbivores and (ii)
ingestion of daisies. Note also that our herbivores are rather dumb as their
dietary strategy consists in random walking only.
Next: The impacts of fragmentation
Up: Modelling the geosphere-biosphere feedback
Previous: Introducing spatial dependencecompetition,
Werner von Bloh (Data & Computation)
Thu Jul 13 14:36:30 MEST 2000