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Add constraints to a problem
to ensure that each feature is
represented in a contiguous unit of dispersible habitat. These constraints
are a more advanced version of those implemented in the
add_contiguity_constraints
function, because they ensure that
each feature is represented in a contiguous unit and not that the entire
solution should form a contiguous unit. Additionally, this function
can use data showing the distribution of dispersible habitat for each
feature to ensure that all features can disperse through out the areas
designated for their conservation.
# S4 method for ConservationProblem,ANY,Matrix
add_feature_contiguity_constraints(x, zones, data)# S4 method for ConservationProblem,ANY,data.frame
add_feature_contiguity_constraints(x, zones, data)
# S4 method for ConservationProblem,ANY,matrix
add_feature_contiguity_constraints(x, zones, data)
# S4 method for ConservationProblem,ANY,ANY
add_feature_contiguity_constraints(x, zones, data)
ConservationProblem-class
object.
matrix
, Matrix
or list
object describing
the connection scheme for different zones. For matrix
or
and Matrix
arguments, each row and column corresponds
to a different zone in the argument to x
, and cell values must
contain binary numeric
values (i.e. one or zero) that indicate
if connected planning units (as specified in the argument to
data
) should be still considered connected if they are allocated to
different zones. The cell values along the diagonal
of the matrix indicate if planning units should be subject to
contiguity constraints when they are allocated to a given zone. Note
arguments to zones
must be symmetric, and that a row or column has
a value of one then the diagonal element for that row or column must also
have a value of one. If the connection scheme between different zones
should differ among the features, then the argument to zones
should
be a list
of matrix
or Matrix
objects that shows the
specific scheme for each feature using the conventions described above.
The default argument to zones
is an identity
matrix (i.e. a matrix with ones along the matrix diagonal and zeros
elsewhere), so that planning units are only considered connected if they
are both allocated to the same zone.
NULL
, matrix
, Matrix
, data.frame
or list
of matrix
, Matrix
, or data.frame
objects. The argument to data shows which planning units should be treated
as being connected when implementing constraints to ensure that features
are represented in contiguous units. If different features have
different dispersal capabilities, then it may be desirable to specify
which sets of planning units should be treated as being connected
for which features using a list
of objects. The default argument
is NULL
which means that the connection data is calculated
automatically using the connected_matrix
function and so
all adjacent planning units are treated as being connected for all
features. See the Details section for more information.
ConservationProblem-class
object with the constraints
added to it.
This function uses connection data to identify solutions that
represent features in contiguous units of dispersible habitat. In earlier
versions of the prioritizr package, it was known as the
add_corridor_constraints
function but has since been renamed for
clarity. It was inspired by the mathematical formulations detailed in
\"Onal and Briers (2006) and Cardeira et al. 2010. For an
example that has used these constraints, see Hanson, Fuller,
and Rhodes (2018). Please note
that these constraints require the expanded formulation and therefore
cannot be used with feature data that have negative vales.
Please note that adding these constraints to a problem will
drastically increase the amount of time required to solve it.
The argument to data
can be specified in several ways:
NULL
connection data should be calculated automatically
using the connected_matrix
function. This is the default
argument and means that all adjacent planning units are treated
as potentially dispersible for all features.
Note that the connection data must be manually defined
using one of the other formats below when the planning unit data
in the argument to x
is not spatially referenced (e.g.
in data.frame
or numeric
format).
matrix
, Matrix
where rows and columns represent
different planning units and the value of each cell indicates if the
two planning units are connected or not. Cell values should be binary
numeric
values (i.e. one or zero). Cells that occur along the
matrix diagonal have no effect on the solution at all because each
planning unit cannot be a connected with itself. Note that pairs
of connected planning units are treated as being potentially dispersible
for all features.
data.frame
containing the fields (columns)
"id1"
, "id2"
, and "boundary"
. Here, each row
denotes the connectivity between two planning units following the
Marxan format. The field boundary
should contain
binary numeric
values that indicate if the two planning units
specified in the fields "id1"
and "id2"
are connected
or not. This data can be used to describe symmetric or
asymmetric relationships between planning units. By default,
input data is assumed to be symmetric unless asymmetric data is
also included (e.g. if data is present for planning units 2 and 3, then
the same amount of connectivity is expected for planning units 3 and 2,
unless connectivity data is also provided for planning units 3 and 2).
Note that pairs of connected planning units are treated as being
potentially dispersible for all features.
list
containing matrix
, Matrix
, or
data.frame
objects showing which planning units
should be treated as connected for each feature. Each element in the
list
should correspond to a different feature (specifically,
a different target in the problem), and should contain a matrix
,
Matrix
, or data.frame
object that follows the conventions
detailed above.
\"Onal H and Briers RA (2006) Optimal selection of a connected reserve network. Operations Research, 54: 379--388.
Cardeira JO, Pinto LS, Cabeza M and Gaston KJ (2010) Species specific connectivity in reserve-network design using graphs. Biological Conservation, 2: 408--415.
Hanson JO, Fuller RA, & Rhodes JR (2018) Conventional methods for enhancing connectivity in conservation planning do not always maintain gene flow. Journal of Applied Ecology, In press: https://doi.org/10.1111/1365-2664.13315.
# NOT RUN {
# load data
data(sim_pu_raster, sim_pu_zones_stack, sim_features, sim_features_zones)
# create minimal problem
p1 <- problem(sim_pu_raster, sim_features) %>%
add_min_set_objective() %>%
add_relative_targets(0.3)
# create problem with contiguity constraints
p2 <- p1 %>% add_contiguity_constraints()
# create problem with constraints to represent features in contiguous
# units
p3 <- p1 %>% add_feature_contiguity_constraints()
# create problem with constraints to represent features in contiguous
# units that contain highly suitable habitat values
# (specifically in the top 1.5th percentile)
cm4 <- lapply(seq_len(nlayers(sim_features)), function(i) {
# create connectivity matrix using the i'th feature's habitat data
m <- connectivity_matrix(sim_pu_raster, sim_features[[i]])
# convert matrix to TRUE/FALSE values in top 20th percentile
m <- m > quantile(as.vector(m), 1 - 0.015, names = FALSE)
# convert matrix from TRUE/FALSE to sparse matrix with 0/1s
m <- as(m, "dgCMatrix")
# remove 0s from the sparse matrix
m <- Matrix::drop0(m)
# return matrix
m
})
p4 <- p1 %>% add_feature_contiguity_constraints(data = cm4)
# }
# NOT RUN {
# solve problems
s1 <- stack(solve(p1), solve(p2), solve(p3), solve(p4))
# plot solutions
plot(s1, axes = FALSE, box = FALSE,
main = c("basic solution", "contiguity constraints",
"feature contiguity constraints",
"feature contiguity constraints with data"))
# }
# NOT RUN {
# create minimal problem with multiple zones, and limit the solver to
# 30 seconds to obtain solutions in a feasible period of time
p5 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
add_min_set_objective() %>%
add_relative_targets(matrix(0.1, ncol = 3, nrow = 5)) %>%
add_default_solver(time_limit = 30) %>%
add_binary_decisions()
# create problem with contiguity constraints that specify that the
# planning units used to conserve each feature in different management
# zones must form separate contiguous units
p6 <- p5 %>% add_feature_contiguity_constraints(diag(3))
# create problem with contiguity constraints that specify that the
# planning units used to conserve each feature must form a single
# contiguous unit if the planning units are allocated to zones 1 and 2
# and do not need to form a single contiguous unit if they are allocated
# to zone 3
zm7 <- matrix(0, ncol = 3, nrow = 3)
zm7[seq_len(2), seq_len(2)] <- 1
print(zm7)
p7 <- p5 %>% add_feature_contiguity_constraints(zm7)
# create problem with contiguity constraints that specify that all of
# the planning units in all three of the zones must conserve first feature
# in a single contiguous unit but the planning units used to conserve the
# remaining features do not need to be contiguous in any way
zm8 <- lapply(seq_len(number_of_features(sim_features_zones)), function(i)
matrix(ifelse(i == 1, 1, 0), ncol = 3, nrow = 3))
print(zm8)
p8 <- p5 %>% add_feature_contiguity_constraints(zm8)
# }
# NOT RUN {
# solve problems
s2 <- lapply(list(p5, p6, p7, p8), solve)
s2 <- stack(lapply(s2, category_layer))
# plot solutions
plot(s2, main = c("p5", "p6", "p7", "p8"), axes = FALSE, box = FALSE)
# }
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