Hamming
The hamming calculator returns the Hamming distance between two communities. This calculator can be used in the summary.shared, collect.shared, and dist.shared commands.
\[D_{Hamming} = S_{A} + S_{B} - 2S_{AB}\]where,
\(S_A\) is the number of nonzero OTUs in A.
\(S_B\) is the number of nonzero OTUs in B.
\(S_{AB}\) is the number of OTU’s shared by A and B.
Open the file 98_lt_phylip_amazon.fn.sabund generated using the Amazonian dataset with the following commands:
mothur > read.dist(phylip=98_lt_phylip_amazon.dist, cutoff=0.10)
mothur > cluster()
mothur > make.shared(list=98_lt_phylip_amazon.fn.list, group=amazon.groups, label=0.10)
The 98_lt_phylip_amazon.fn.shared file will contain the following two lines:
0.10 forest 55 1 1 1 1 1 1 3 3 2 2 1 1 3 2 1 1 1 1 2 1 1 2 5 1 1 1 1 2 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0.10 pasture 55 0 0 0 1 1 0 1 0 0 5 0 0 0 0 0 2 0 0 0 3 0 0 2 1 0 1 0 0 0 0 0 0 1 2 1 1 1 1 1 7 1 1 2 1 1 1 1 1 1 1 1 1 2 1 1
This indicates that the label for the OTU definition was 0.10. The first line is from the forest sample and the second is from the pasture sample. There are a total of 55 OTUs between the two communities. Writing the data in a more presentable manner we see:
index forest pasture shared
——- ——– ——— ——–
1 1 0
2 1 0
3 1 0
4 1 1 X
5 1 0
6 1 0
7 3 1 X
8 3 0
9 2 0
10 2 5 X
11 1 0
12 1 0
13 3 0
14 2 0
15 1 0
16 1 3 X
17 1 0
18 1 0
19 2 0
20 1 3 X
21 1 0
22 2 0
23 5 2 X
24 1 1 X
25 1 0
26 1 1 X
27 1 0
28 2 0
29 1 0
30 1 0
31 1 0
32 1 0
33 1 1 X
34 0 2
35 0 1
36 0 1
37 0 1
38 0 1
39 0 1
40 0 7
41 0 1
42 0 1
43 0 2
44 0 1
45 0 1
46 0 1
47 0 1
48 0 1
49 0 1
50 0 1
51 0 1
52 0 1
53 0 2
54 0 1
55 0 1
Total 33 31 9
Using these sums to evaluate D we get:
\[D_{Hamming} = 33 + 31 - 2 \left(9\right)=46\]Running...
mothur > summary.shared(shared=amazon.fn.shared, calc=hamming)
...and opening 98_lt_phylip_amazon.fn.shared.summary gives:
label comparison hamming 0.10 forest pasture 46.00000
These are the same values that we found above for a cutoff of 0.10.