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of the impoundment to the other is short in comparison to the time it needs to
cross a dam. This will be appropriate in situations where fish passage is low,i.e.
if dams have low fish permeabilities and certainly regarding salmon migration on
the river Moselle for example. If more details in modelling are necessary,as one
advantage,many habitat modelling approaches or ecomorphological assessment
procedures can be easily connected to our model [7,8,9].
Generally the benefits of individual based models is that they are easy to
formulate and variables and rules can be interpreted directly in biological terms.
There are few discrete freshwater fish models known from literature and in their
review on habitat modelling Parasiewicz and Dunbar [11] also discuss discrete
models. Another example is the work of Jager et al. [6] who study effects of
river fragmentation on sturgeon populations with an individual based model
- they investigate also the effect of fragmentation on fish migration. However
one drawback of individual based models is that often no analytic results are
available and we are have to rely on simulations.
A continuous description corresponding to our approach would be a system
of coupled ordinary differential equations. Such models are known for metapop-
ulations or optimal vaccination strategies for example. Each equation would
describe one impoundment. For some of these formulations analytic solutions
can be obtained. And like in discrete models,if the time fish spend
in
the im-
poundment is important,this can be incorporated with using delay equations,
or even a system of reaction-diffusion equations. Related to our model is the
work of Zabel and Anderson [14]: With a partial differential equation formula-
tion they investigate the migration of juvenile salmon through segments of the
Columbia and Snake Rivers. Their model is connected with the CPiSP project
and program [15] to predict downstream migration and survival of juvenile fish
at the tributaries and dams of the Columbia and Snake rivers. Yet,as often,the
differential equations can not be solved analytically. Solutions are approximated
using numerical methods. It has been argued that then it would be better to
formulate the model in an discrete,individual based view from the beginning.
An individual based migration model is very flexible and different dam im-
provement strategies can be tested easily and fast. Using analytical methods
from optimisation theory however can lead to more general results. Here,results
from established models may be translated to fish migration,even if such an
interpretation is not near at hand. An example is a age-structured model for
optimisation of vaccination strategies [10]: age classes correspond to impound-
ments,individuals to fish,investing resources in vaccinations at a certain age
class is equivalent to improving the permeability of a dam.
The formulation and investigation of different models - optimisation models
and individual based models - will show us different aspects of fish migration. It
ensures that the results obtained are not artefacts of the modelling techniques
but solely derived from the specified assumptions. Therefore our work will pro-
ceed in two directions: adapting the model to the situation of river Moselle
situation in very detail with estimating permeability and cost-effect function for
each dam. On the other hand we are working on analytic results.
