Individual patch connectivity

February 27, 2019
By

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Answering questions from users is actually a good way to find potentially interesting things to post…

With the obvious advantage that other people might find it useful too!

So… let’s start… This MetaLandSim user wanted a way to derive the contribution of each individual patch to overall landscape connectivity. Here I used the method presented in the paper by Saura & Pascual-Hortal (2007) “A new habitat availability index to integrate connectivity in landscape conservation planning: Comparison with existing indices and application to a case study“, using his Integral Index of Connectivity (IIC) and equation 1 to derive each patch relevance to overall connectivity.

As allways, start by loading the package:

library(MetaLandSim)

Now, we create a new landscape graph (rl1), which will be plotted if we set plotG to TRUE:

set.seed(123)

rl1 <- rland.graph(mapsize=500, dist_m=50, areaM=0.1, 
    areaSD=0.02, Npatch=50,
    disp=70, plotG=TRUE)

fig1

This landscape has 50 patches, and we eant to know each individual dIIC, or their individual contribution to connectivity.

If we are following eq. 1 on Saura’s paper we have to start by computing the IIC of the full landscape, with all the patches (full.IIC):

#as.numeric is just to guarantee the output is just a number
full.IIC <- as.numeric(metrics.graph (rl=rl1, metric="IIC"))

Now we extract the data frame with the information on the patches:

patches <- rl1$nodes.characteristics

#Here are the top 6 rows:
head(patches)
##           x        y      areas   radius cluster    colour nneighbour ID
## 1 143.78876 394.1526 0.08410288 16.36178       1 #FF0000FF   64.01614  1
## 2 132.51637 282.2952 0.07285381 15.22829       1 #FF0000FF   51.84446  2
## 3 338.78532 286.3167 0.12808067 20.19142       1 #FF0000FF   67.61306  3
## 4  12.30684 238.8980 0.08026654 15.98425       1 #FF0000FF   67.02337  4
## 5 275.71751 228.3074 0.13367483 20.62766       1 #FF0000FF   50.44706  5
## 6  71.40001 207.2732 0.08448427 16.39883       1 #FF0000FF   51.92737  6

Then we create a vector to insert the values of the partial IIC (dIIC). I had to modify the function removepoints, which I had originally in the package. The original version removes a number of patches randomly. This adapted version removes one specific patch (by ID), it’s called removepoints.byID.

dIIC <- rep(NA, 50)

#the new version of the function:
removepoints.byID <-
function (rl, nr=1, ID)
  {
if (class(rl)!="landscape") 
  {
    stop(paste(rl, " should be an object of class class 'landscape'.", sep=""), call. = FALSE)
  } 
    mapsize2 <- rl$mapsize
    dist_m2 <- rl$minimum.distance
    areaM2 <- rl$mean.area
    areaSD2 <- rl$SD.area
    Npatch2 <- rl$number.patches
    disp2 <- rl$dispersal
    rl_0 <- rl$nodes.characteristics
    ID2 <- rl_0$ID
    nr_select <- nrow(rl_0)-nr
    rl_1 <- rl_0[-ID, ]
    rl_2 <- rl_1[sort.list(as.numeric(rownames(rl_1))), ]
    names(rl_2)[names(rl_2) == "ID2"] <- "ID"
    rl_3 <- list(mapsize=mapsize2, minimum.distance=dist_m2,
                 mean.area=mean(rl_2$areas), SD.area=sd(rl_2$areas),
                 number.patches=nrow(rl_2), dispersal=disp2,
                 nodes.characteristics=rl_2)
    class(rl_3) <- "landscape"
    rl_4 <- cluster.id(rl_3)
    rownames(rl_4$nodes.characteristics) <- 1:nrow(rl_4$nodes.characteristics)
    class(rl_4) <- "landscape"
    return(rl_4)
  }

Finally… compute the dIIC (partial connectivity) to each patch:

#Set up the loop to do the calculations
for (i in 1:50){

rl2 <- rl1 #This is just no to change rl1

rl3 <- removepoints.byID(rl1,ID=i)#removing patch i

partial.IIC <- as.numeric(metrics.graph (rl=rl3, metric="IIC"))

dIIC[i] <- 100*((full.IIC-partial.IIC)/full.IIC)#send the result to the vector

}

#And here's the result:

dIIC

##  [1]  3.4090909 14.7727273  7.9545455  2.8409091 13.0681818  5.1136364
##  [7]  2.8409091  7.9545455  7.3863636  6.8181818 11.3636364  3.9772727
## [13]  3.4090909 10.7954545  3.4090909 13.6363636 15.9090909  2.2727273
## [19]  3.9772727  2.2727273  1.7045455  0.5681818  1.7045455  1.7045455
## [25]  3.4090909  2.8409091  1.1363636  4.5454545  2.2727273 10.2272727
## [31]  5.6818182  2.8409091  6.8181818  3.9772727  6.2500000  7.3863636
## [37]  3.4090909  1.1363636  2.2727273  2.2727273  0.5681818  1.7045455
## [43]  2.8409091  4.5454545  2.2727273  1.7045455  2.8409091  3.9772727
## [49]  1.1363636  2.2727273

Let’s plot it:

plot_graph(rl=rl1, species=FALSE, links=TRUE)

#The individual connectivity patches
text(x = patches[,'x'],y = patches[,'y'], pos = 3, 
offset = 0.2, labels = round(dIIC,2))

fig2.jpg

And that’s all.

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