2.3.4. Reserves with central area and buffer zone
We end this section on spatial considerations by discussing the
selection of nature reserves with central area and buffer zone (see
e.g., Williams and ReVelle, 1998; Clemens et al., 1999; Hamaide
et al., 2009). In this case, there are two types of species to be protected,
endangered and common species, and two types of protected
areas, central areas and buffer zones that protect the
central area of nuisances caused by human activities outside the
reserve. To be protected, an endangered species must be present
in a central area and a common species must be present either in
a central area or in a buffer zone. It is considered that a selected
parcel is part of a central area if all the parcels that surround it
are also selected to be either in the central area or in the buffer
zone (Fig. 2). The decision maker can define a buffer zone more
or less important. Consider the Boolean variable zi that is equal
to 1 iff the parcel si is selected to be part of the central area and
the Boolean variable xi that is equal to 1 iff the parcel si is selected
to be part of the buffer zone or of the central area. Denote by
NC # N the set of indices of the parcels candidates for the central
area and by Ni # N the set formed by the index i and the set of
indices of the parcels surrounding the parcel si and that must be se
2.3.4. Reserves with central area and buffer zone
We end this section on spatial considerations by discussing the
selection of nature reserves with central area and buffer zone (see
e.g., Williams and ReVelle, 1998; Clemens et al., 1999; Hamaide
et al., 2009). In this case, there are two types of species to be protected,
endangered and common species, and two types of protected
areas, central areas and buffer zones that protect the
central area of nuisances caused by human activities outside the
reserve. To be protected, an endangered species must be present
in a central area and a common species must be present either in
a central area or in a buffer zone. It is considered that a selected
parcel is part of a central area if all the parcels that surround it
are also selected to be either in the central area or in the buffer
zone (Fig. 2). The decision maker can define a buffer zone more
or less important. Consider the Boolean variable zi that is equal
to 1 iff the parcel si is selected to be part of the central area and
the Boolean variable xi that is equal to 1 iff the parcel si is selected
to be part of the buffer zone or of the central area. Denote by
NC # N the set of indices of the parcels candidates for the central
area and by Ni # N the set formed by the index i and the set of
indices of the parcels surrounding the parcel si and that must be se
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