Worked Example: Constructing Flock Network of Golden-crowned Sparrows

3.1 Get the bird IDs:

First step, then, is to figure out all of the individuals that are in this dataset so that we can assign each of them a row. I will do this in two steps:

We can extract the columns within the dataset that contain the bird IDs. These columns all share the word “Bird” in the column name.

#get the columns that contain the bird IDs.
birdcols=grep("Bird",colnames(flockdat))
birdcols

##  [1]  4  5  6  7  8  9 10 11 12 13

With this, you can easily just get the bird ID data with this line of code (output not shown)

flockdat[,birdcols]

We can then collapse this data into one column that contains all bird IDs observed in any flock for the whole dataset. This is often called ‘long-format’ data (as opposed to the ‘wide-format’ that the data is currently in). There are different ways to do this, but here is one easy way using the gather() function from the package tidyr (output not shown).

gather(flockdat[,birdcols])

Since we can do that, all we need is to extract the unique IDs that show up in the column called ‘value’ within this long-format data. Here’s how you can do that in one line:

bird.ids=unique(gather(flockdat[,birdcols])$value)
bird.ids

##  [1] 23734 23773 23778 23732 23809 23774 23862  7615  7636  7638 23891
## [12] 23772 23777  7627  7635 23854  7632 23781 23762  7608 23815 23726
## [23] 23978  7623 23761 23770  7612  7614  7619  7640 23769 23853  7609
## [34] 23771  7633  7606 23819  7637 23831 23735  7620 23780    NA  7641
## [45] 23758  7630  7661  7617

Ok, so we have the IDs of all of the birds in this dataset. But notice that this also includes “NA”. So let’s get rid of that:

bird.ids=bird.ids[is.na(bird.ids)==F]
bird.ids

##  [1] 23734 23773 23778 23732 23809 23774 23862  7615  7636  7638 23891
## [12] 23772 23777  7627  7635 23854  7632 23781 23762  7608 23815 23726
## [23] 23978  7623 23761 23770  7612  7614  7619  7640 23769 23853  7609
## [34] 23771  7633  7606 23819  7637 23831 23735  7620 23780  7641 23758
## [45]  7630  7661  7617

3.2 Get the individual-by-group matrix using the match() function

Let’s think through how we are going to make this individual-by-group matrix now. What we need to do, then, is to go through each observed flock–i.e., each row of the original flock data–and ask whether bird A is in it, bird B is in it, etc. etc.We can do that using the apply() and match() functions.

What this line of code will do is to go through the rows of the flock data (just the columns containing the bird IDs), and ask to match the bird ID in our list with the bird IDs in that line (i.e., flock). Let’s try it (output not shown).

m1=apply(flockdat[,birdcols], 1, function(x) match(bird.ids,x))
m1

What this gives you is a matrix with 47 rows (for each bird) and 353 columns (for each flock) with a number if that bird was found in that flock, and “NA” if not. So, we can simply convert this to “0 if NA” and “1 if anything else” (result not shown):

m1[is.na(m1)]=0
m1[m1>0]=1
m1

Great, now we have our individual-by-flock matrix. Let’s name the columns and rows:

rownames(m1)=bird.ids #rows are bird ids
colnames(m1)=paste('flock', 1:ncol(m1), sep="_") #columns are flock IDs (just "flock_#")
m1

4.1 Association Indices

A quick tutorial here on how to convert group membership to edges in a social network. There are many ways to calculate an index of association between pairs of individuals. The simplest case would be to just count the number of times a pair of individuals were seen together (\(A \cap B\)). However, we would often want to account for the fact that some birds are seen often while others are seen rarely. Thus, what we really want to know might be how often a pair of birds are seen together, given the number of times they were seen at all? This is the essence of an association index. These were presented in a now-classic paper by Cairns & Schwager (1987).

Here, we will use what is called the **Simple Ratio Index*

Simple Ratio Index = \(\displaystyle \frac{|A \cap B|}{|A \cup B|}\) = \(\displaystyle \frac{|A \cap B|}{|A|+|B|-|A \cap B|}\)

where

• \(|A \cap B|\) is the number of times A and B were seen together
• \(|A|\) is the total number of times A was seen (together or separate from B)
• \(|B|\) is the total number of times B was seen (together or separate from A)

Luckily, there is a function in the asnipe package that will calculate this for every pair of individual, given the affiliation matrix. We will use the get_network() function.

Note: this function likes to take the data in the “group-by-individual” matrix format, so we need to transpose our matrix using the t() function:

adj=get_network(t(m1), data_format="GBI", association_index = "SRI") # the adjacency matrix

## Generating  47  x  47  matrix

g=graph_from_adjacency_matrix(adj, "undirected", weighted=T) #the igraph object

set.seed(2)
plot(g, edge.width=E(g)$weight*10, vertex.label="", vertex.size=5) #plot it

This is the sparrow social network!

4.1 Practical matters: Filtering the data

For the Shizuka et al. (2014) study, we employed a common method to eliminate ‘transient’ individuals that may have been seen only a few times in our observation. These individuals usually don’t affect our network structure much, but it does allow us to cut down on the noise in our data.

So, let’s try constructing the network again after removing individuals that were seen less than 3 times in our flock observations.

We can get the number of times each individual was observed simply by taking the row sums of the individual-by-flock matrix:

rowSums(m1)

## 23734 23773 23778 23732 23809 23774 23862  7615  7636  7638 23891 23772 
##    18    37    25    25    21    35    48    36     9     5    20    29 
## 23777  7627  7635 23854  7632 23781 23762  7608 23815 23726 23978  7623 
##    25    36    25    22    21     6    17    15    37    20    10     6 
## 23761 23770  7612  7614  7619  7640 23769 23853  7609 23771  7633  7606 
##     9    21    15    14     9    14    10    20    24    11     8    28 
## 23819  7637 23831 23735  7620 23780  7641 23758  7630  7661  7617 
##     3     3    24     3     1     4     1     6     3     2     1

So we can simply remove the rows of the individuals that were seen less than 3 times (or rather, just keep the rows where the sums are >2). This will remove 4 individuals. We can then re-construct the network using this reduced matrix:

m2=m1[which(rowSums(m1)>2),]
adj=get_network(t(m2), data_format="GBI","SRI")

## Generating  43  x  43  matrix

g=graph_from_adjacency_matrix(adj, "undirected", weighted=T)
set.seed(2)
plot(g, edge.width=E(g)$weight*10, vertex.label="", vertex.size=5)

4.2 Color the network based on community membership

In the study, we used the ‘fast greedy’ modularity-optimization method for identifying communities within the network and colored the nodes based on those assignments. Here is how we did that:

com=fastgreedy.community(g) #community detection method
node.colors=membership(com) #assign node color based on community membership
set.seed(2)
plot(g, edge.width=E(g)$weight*10, vertex.label="", vertex.size=5, vertex.color=node.colors)

Compare this network to the figure shown at the top of the page.