Chapter 4 . Applications of Evolutionary Computation
51
variable. This equation can then be used to predict the future states of the system
given present knowledge. These models are often formulated as a combination of
deterministic factors combined with a term or terms that capture the intrinsic
stochastic nature of the system and the errors associated with measurement and
observation. Of course, although these models are typically expressed in linear
terms, they describe a system that is generally replete with nonlinear interactions
and temporal variation.
Extensions to these basic linear functions are often formulated as differential
equations (when time is continuous) or difference equations (when time is taken
in discrete intervals). Difference equations rely on an interpretation of nonlinear
systems and their resolution in the form of a singular equation, and have been
applied to individuals and population dynamics (Hassei and Comins 1976). With
this approach, it may not be possible to encapsulate all of the correct variables into
the equation or might incorrectly set the importance (weights) for each term in the
equation. There are also a number of simplifying assumptions required when
formulating difference or differential equations that can make the resulting models
difficult to interpret when applying them to real ecosystems. Coupled equations
have been used to understand and explore plant-herbivore, host-parasite, hostpathogen and other competition interactions. Extensions to these models have
allowed intraspecies competition to be represented (for example, (Watkinson
1987)), however all these equations have constants that must be set to represent
the corresponding modelIed system. As these equations become more complex the
issue of parameter selection, based on measured data, has become an issue due to
the nonlinear behaviour of the model as a whole.
The dynamics of communities are interested in the interactions between
species, and how the communities as a whole res pond to changes in exogenous
factors, and the introduction or removal of species in the community pool. These
models are often constructed as a matrix of interactions, and expressed as partial
differential equations. The dynamics of communities are often very complex and
are difficult to model in any complete sense. Once again, the tuning of parameters
and the selection of other constants in the model relies on mate hing the measured
dynamics of the community and the model.
The previously described models have focused on the time dynamics of
systems, and have assumed that the spatial interactions can be ignored, are at the
same scale, or are homogeneous. However, since most ecological systems have
spatial extent, and are limited in their interactions by location, the inclusion of
space is often fundamental for exploring ecological systems. Extending the
previous non-spatial models to a regular grid often involves extending the
complexity of the model to include not only local interactions (at a single grid
cell) but the influence of neighbouring cells and the species found at these
locations. These models, often termed cellular automata (CA), have been widely
used in studying plant and animal interactions (Comins et al. 1992; Silverton et al.
1992; Colasanti and Grime 1993). Spatial models often display long-term
population persistence and dynamics that cannot be captured using a spatial
51
variable. This equation can then be used to predict the future states of the system
given present knowledge. These models are often formulated as a combination of
deterministic factors combined with a term or terms that capture the intrinsic
stochastic nature of the system and the errors associated with measurement and
observation. Of course, although these models are typically expressed in linear
terms, they describe a system that is generally replete with nonlinear interactions
and temporal variation.
Extensions to these basic linear functions are often formulated as differential
equations (when time is continuous) or difference equations (when time is taken
in discrete intervals). Difference equations rely on an interpretation of nonlinear
systems and their resolution in the form of a singular equation, and have been
applied to individuals and population dynamics (Hassei and Comins 1976). With
this approach, it may not be possible to encapsulate all of the correct variables into
the equation or might incorrectly set the importance (weights) for each term in the
equation. There are also a number of simplifying assumptions required when
formulating difference or differential equations that can make the resulting models
difficult to interpret when applying them to real ecosystems. Coupled equations
have been used to understand and explore plant-herbivore, host-parasite, hostpathogen and other competition interactions. Extensions to these models have
allowed intraspecies competition to be represented (for example, (Watkinson
1987)), however all these equations have constants that must be set to represent
the corresponding modelIed system. As these equations become more complex the
issue of parameter selection, based on measured data, has become an issue due to
the nonlinear behaviour of the model as a whole.
The dynamics of communities are interested in the interactions between
species, and how the communities as a whole res pond to changes in exogenous
factors, and the introduction or removal of species in the community pool. These
models are often constructed as a matrix of interactions, and expressed as partial
differential equations. The dynamics of communities are often very complex and
are difficult to model in any complete sense. Once again, the tuning of parameters
and the selection of other constants in the model relies on mate hing the measured
dynamics of the community and the model.
The previously described models have focused on the time dynamics of
systems, and have assumed that the spatial interactions can be ignored, are at the
same scale, or are homogeneous. However, since most ecological systems have
spatial extent, and are limited in their interactions by location, the inclusion of
space is often fundamental for exploring ecological systems. Extending the
previous non-spatial models to a regular grid often involves extending the
complexity of the model to include not only local interactions (at a single grid
cell) but the influence of neighbouring cells and the species found at these
locations. These models, often termed cellular automata (CA), have been widely
used in studying plant and animal interactions (Comins et al. 1992; Silverton et al.
1992; Colasanti and Grime 1993). Spatial models often display long-term
population persistence and dynamics that cannot be captured using a spatial