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near Koblenz [4]. There are fish ladders associated with the weirs in river Moselle
but up to now no adult salmon migrating upstream through the fish ladders has
been observed [5]. Some few adult individuals,found in fact in river Moselle,
probably passed through the sluices. An improvement of the fish passage sys-
tems to reintroduce salmon in this area is an important objective. The question
arises how to invest the given financial resources yielding the best effect. Our
concept is to optimise not a single fish passage system but migration on the
whole river,from estuary to headwater.
On first view this task seems straightforward and even solvable analytically.
However the aim is not to bring most fish to the river's source. Salmon for
example needs suitable gravel beds to lay spawn. These can be found in tributary
rivers and will have different capacities. To meet these demands we develop a
simulation tool that can be adjusted to the specific habitat setting. It allows to
test different strategies of fish passage improvement.
We will first discuss the optimisation problem. Then the basic model is in-
troduced and a simulation example of migrating salmon through river Moselle
is shown. Finally we discuss further applications and extensions of the model.
1.1 Optimisation of Fish Migration
Most models on optimisation of fish migration known from literature are quite
technically oriented. They aim for example on the improvement of fish ladders
for upstream migration [1] or optimisation of a certain turbine type for down-
stream migration (for a review see [2]). In our setting however the problem is
how achieve best fish migration on the whole river system. Often optimisation
problems investigate how to get a certain effect with minimal resources. In our
case the resources are more or less fixed. Therefore it is more appropriate to ask
how to invest the given resources for maximal effect. So basically we have a num-
ber of river dams and a certain amount of money. The question is how the given
money should be distributed on the dams. To describe solutions a 'permeability'
coe @ cient is given to each dam. It characterises how well fish can migrate. The
value is interpreted as the probability that one fish migrates successfully over
the respective dam in one try. A solution for the whole river can be formulated
by a vector or tuple of such permeability coe @ cients.
For this optimisation problem quite general analytic solutions can be ob-
tained [13]. Consider for example a river without tributaries and a finite number
of dams. Fish migrate upstream from the estuary,i.e. we aim for most fish arriv-
ing at the river's source. Assume that effort depends at least linearly on effect,
i.e. if we want to double the permeability,at least the double amount of resources
have to be invested. Then it can be shown that the best strategy is to invest
such that all dams have equal permeability.
In real applications however the setting will be more complex. Suitable
spawning habitats for anadromous fish for example will be found to a differ-
ent extent in the tributaries of the flow regulated river. Since habitat suitability
of the spawning sites depends also on the density of individuals it may be ad-
vantageous for one population not to be concentrated at one optimal spawning
 
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