# Individual patch connectivity

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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)

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))

And that’s all.

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