Environmental Engineering Reference
In-Depth Information
as a spatially explicit, individual-based implementation of a Lotka-Volterra
predator-prey interaction with one prey and one predator species (Breckling et al.
2000). The Lotka-Volterra model is a frequently considered topic in differential
equation based population modelling (see Chaps. 6 and 7). It is used here to
demonstrate the change of perspective, when an individual-based point of view is
adopted. Both simulated species have a limited activity repertoire consisting of
feeding, growing, reproduction and movement. All activities are kept at a low level
of complexity, thus serving as prototypes, however, illustrating the potential for
further development.
The total numbers of both prey and predators are limited to a few thousand
objects, which corresponds to the processing capacity of the environment to facili-
tate reasonably fast computation. The potential “movement” algorithms are the
same for both species. They consist either of a Brownian (random) movement (for
each movement step the new direction is chosen stochastically) or a directed walk
(for the next step, the old direction and speed is maintained and a small random
component is added). This leads to a higher autocorrelation of the overall move-
ment direction. The choice of the movement algorithm (random vs. directed) has to
be made for all organisms of one class by setting a specific value for a switch in a
parameter file (“InFile”). It then applies to the whole simulation run. The length of
each movement step is calculated in relation to the biomass of the respective
organism.
Feeding and energy physiology differ between the simulated prey and predators.
The prey grow independently from any external influence. This simulates unlimited
resources. However, the predators search a specified radius around their current
location during each time step and feed on the prey which they find within this
radius. Then, the biomass of the identified accessible prey (multiplied with a
conversion factor between 0 and 1) is added to the current biomass of the predator
individual. The predator loses biomass according to a biomass dependent respira-
tion function which leads to starvation below a certain threshold, if no prey
individuals are met.
Reproduction for both, prey and predators, is biomass dependent and implemen-
ted as a fission-like process. If an individual reaches a specified biomass threshold,
new objects of the same species are instantiated at the same location, and adult
biomass is then distributed between juveniles and the adult.
The environment for the simulation run is established as a homogeneous area,
with each edge being connected to the opposite site and thus leading to torus
boundary conditions (see Fig. 8.3 in Chap. 8). These conditions minimize boundary
side effects (Jopp 2003).
In the beginning of each simulation run, a specified number of prey and predator
individuals are distributed randomly across the simulation area. Generally, all relevant
parameters describing the behaviour of prey and predator as well as other parameters
of the specific simulation (e.g. duration, size of area, etc.) are set in a parameter file.
Though individual actions do not include any directional preference, and only
random components change the movement paths, we obtain emerging large-scale
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