Create a matrix showing the connectivity between planning units. Connectivity is calculated as the average conductance of two planning units multiplied by the amount of shared boundary between the two planning units. Thus planning units that each have higher a conductance and share a greater boundary are associated with greater connectivity.
connectivity_matrix(x, y, ...) # S4 method for Spatial,Raster connectivity_matrix(x, y, ...) # S4 method for Spatial,character connectivity_matrix(x, y, ...) # S4 method for sf,character connectivity_matrix(x, y, ...) # S4 method for sf,Raster connectivity_matrix(x, y, ...) # S4 method for Raster,Raster connectivity_matrix(x, y, ...)
x 


y 

...  additional arguments passed to 
dsCMatrix
symmetric sparse matrix object.
Each row and column represents a planning unit.
Cells values indicate the connectivity between different pairs of planning
units.
To reduce computational burden, cells among the matrix diagonal are
set to zero. Furthermore, if the argument to x
is a
Raster
object, then cells with NA
values are set to zero too.
Shared boundary calculations are performed using
boundary_matrix()
.
# load data data(sim_pu_raster, sim_pu_sf, sim_features) # create connectivity matrix using raster planning unit data using # the raster cost values to represent conductance ## extract 9 planning units r < crop(sim_pu_raster, c(0, 0.3, 0, 0.3)) ## extract conductance data for the 9 planning units cd < crop(sim_features, r) ## make connectivity matrix using the habitat suitability data for the ## second feature to represent the planning unit conductance data cm_raster < connectivity_matrix(r, cd[[2]]) ## plot data and matrix # \dontrun{ par(mfrow = c(1,3)) plot(r, main = "planning units (raster)", axes = FALSE, box = FALSE) plot(cd[[2]], main = "conductivity", axes = FALSE, box = FALSE) plot(clamp(raster(as.matrix(cm_raster)), lower = 1e5, useValues = FALSE), main = "connectivity", axes = FALSE, box = FALSE)# } # create connectivity matrix using polygon planning unit data using # the habitat suitability data for the second feature to represent # planning unit conductances ## subset data to 9 polygons ply < sim_pu_sf[c(1:2, 10:12, 20:22), ] ## make connectivity matrix cm_ply < connectivity_matrix(ply, sim_features[[2]]) ## plot data and matrix # \dontrun{ par(mfrow = c(1, 2)) plot(st_geometry(ply), main = "planning units (sf)") plot(clamp(raster(as.matrix(cm_ply)), lower = 1e5, useValues = FALSE), main = "connectivity", axes = FALSE, box = FALSE)# } # create connectivity matrix using habitat suitability data for each feature, # this could be useful if prioritisations should spatially clump # together adjacent planning units that have suitable habitat # for the same species (e.g. to maintain functional connectivity) ## let's use the raster data for this example, and we can generate the ## connectivity matrix that we would use in the prioritization by ## (1) generating a connectivity matrix for each feature separately, and ## and then (2) then summing the values together cm_sum < lapply(as.list(cd), connectivity_matrix, x = r) # make matrices cm_sum < Reduce("+", cm_sum) # sum matrices together ## plot data and matrix # \dontrun{ par(mfrow = c(1, 2)) plot(r, main = "planning units (raster)", axes = FALSE, box = FALSE) plot(clamp(raster(as.matrix(cm_sum)), lower = 1e5, useValues = FALSE), main = "connectivity", axes = FALSE, box = FALSE)# } ## we could take this example one step further, and use weights to indicate ## relative importance of maintaining functional connectivity ## for each feature (i.e. use the weighted sum instead of the sum) ## let's pretend that the first feature is 20 times more important ## than all the other species weights < c(20, 1, 1, 1, 1) ## calculate connectivity matrix using weighted sum cm_wsum < lapply(as.list(cd), connectivity_matrix, x = r) # make matrices cm_wsum < Map("*", cm_wsum, weights) # multiply by weights cm_wsum < Reduce("+", cm_wsum) # sum matrices together ## plot data and matrix # \dontrun{ par(mfrow = c(1, 2)) plot(r, main = "planning units (raster)", axes = FALSE, box = FALSE) plot(clamp(raster(as.matrix(cm_wsum)), lower = 1e5, useValues = FALSE), main = "connectivity", axes = FALSE, box = FALSE)# } ## since the statistical distribution of the connectivity values ## for each feature (e.g. the mean and standard deviation of the ## connectivity values) are different, it might make sense  depending ## on the goal of the conservation planning exercise and the underlying ## data  to first normalize the conductance values before applying the ## weights and summing the data for feature together ## one approach would be to linearly rescale the values between 0.01 and 1 ## note that we wouldn't want to rescale them between 0 and 1 since ## a value of zero means that there is no connectivity at all (and ## and not a relatively small amount of connectivity) # \dontrun{ ### define helper function library(scales) # load scales library for rescale rescale_matrix < function(x) {x@x < rescale(x@x, c(0.01, 1)); x} ### calculate functional connectivity matrix using the weighted sum of ### connectivity values that have been normalized by linearly rescaling ### values cm_lwsum < lapply(as.list(cd), connectivity_matrix, x = r) # make matrices cm_lwsum < lapply(cm_lwsum, rescale_matrix) # rescale matrices to [0.01, 1] cm_lwsum < Map("*", cm_lwsum, weights) # multiply by weights cm_lwsum < Reduce("+", cm_lwsum) # sum matrices together # } ## plot data and matrix # \dontrun{ par(mfrow = c(1, 2)) plot(r, main = "planning units (raster)", axes = FALSE, box = FALSE) plot(clamp(raster(as.matrix(cm_lwsum)), lower = 1e5, useValues = FALSE), main = "connectivity", axes = FALSE, box = FALSE)# } ## another approach for normalizing the data could be using zscores ## note that after normalizing the data we would need to add a constant ## value so that none of the connectivity values are negative ### define helper functions zscore < function(x) {x@x < (x@x  mean(x@x)) / sd(x@x); x} min_non_zero_value < function(x) min(x@x) add_non_zero_value < function(x, y) {x@x < x@x + y; x} ### calculate functional connectivity matrix using the weighted sum of ### connectivity values that have been normalized using zscores, ### and transformed to account for negative values cm_zwsum < lapply(as.list(cd), connectivity_matrix, x = r) # make matrices cm_zwsum < lapply(cm_zwsum, zscore) # normalize using zscores min_value < min(sapply(cm_zwsum, min_non_zero_value)) # find min value min_value < abs(min_value) + 0.01 # prepare constant for adding to matrices cm_zwsum < lapply(cm_zwsum, add_non_zero_value, min_value) # add constant cm_zwsum < Map("*", cm_zwsum, weights) # multiply by weights cm_zwsum < Reduce("+", cm_zwsum) # sum matrices together ## plot data and matrix # \dontrun{ par(mfrow = c(1, 2)) plot(r, main = "planning units (raster)", axes = FALSE, box = FALSE) plot(clamp(raster(as.matrix(cm_zwsum)), lower = 1e5, useValues = FALSE), main = "connectivity", axes = FALSE, box = FALSE)# }