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Jabund
The jabund calculator returns the abundance-based Jaccard dissimilarity index describing the fraction of individuals that don't belong to shared OTUs. This calculator can be used in the summary.shared and collect.shared commands.
Note that this approach attempts to incorporate the effect of unseen shared species. For a reference and background, see:
Chao A, Chazdon RL, Colwell RK and Shen T-J. 2005. A new statistical approach for assessing similarity of species composition with incidence and abundance data. Ecology Letters 8: 148-159. DOI: 10.1111/j.1461-0248.2004.00707.x
<math>D_{J_{abund}} = 1-\frac{U_{est}V_{est}}{U_{est} + V_{est} - U_{est}V_{est}}</math>
where,
<math>U_{est} = \sum_{i=1}^{S_{12}}{\frac{A_i}{n_{total}} + \frac{m_{total}-1}{m_{total}} \frac{f_{+1}}{2f_{+2}}} \sum_{i=1}^{S_{12}}{\frac{A_i}{n_{total}}I\left(B_i = 1\right)}</math>
<math>V_{est} = \sum_{i=1}^{S_{12}}{\frac{B_i}{m_{total}} + \frac{n_{total}-1}{n_{total}} \frac{f_{1+}}{2f_{2+}}} \sum_{i=1}^{S_{12}}{\frac{B_i}{m_{total}}I\left(A_i = 1\right)}</math>
<math>S_{12}</math> = the number of shared OTUs between groups A and B
<math>A_i</math> = the number of individuals in OTU i of group A
<math>B_i</math> = the number of individuals in OTU i of group B
<math>m_{total}</math> = total number of individuals sampled from group A
<math>m_{total}</math> = total number of individuals sampled from group B
<math>f_{1+}\mbox{, }f_{2+}</math> = number of shared OTUs with one or two individuals observed in A
<math>f_{+1}\mbox{, }f_{+2}</math> = number of shared OTUs with one or two individuals observed in B
I(•) = if the argument, •, is true then I(•) is 1; otherwise it is 0.
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 > read.otu(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 (A) | pasture (B) | shared | f_{1+} | f_{+1} | f_{2+} | f_{+2} |
---|---|---|---|---|---|---|---|
1 | 1 | 0 | |||||
2 | 1 | 0 | |||||
3 | 1 | 0 | |||||
4 | 1 | 1 | X | 1 | 1 | ||
5 | 1 | 0 | |||||
6 | 1 | 0 | |||||
7 | 3 | 1 | X | 1 | |||
8 | 3 | 0 | |||||
9 | 2 | 0 | |||||
10 | 2 | 5 | X | 1 | |||
11 | 1 | 0 | |||||
12 | 1 | 0 | |||||
13 | 3 | 0 | |||||
14 | 2 | 0 | |||||
15 | 1 | 0 | |||||
16 | 1 | 3 | X | 1 | |||
17 | 1 | 0 | |||||
18 | 1 | 0 | |||||
19 | 2 | 0 | |||||
20 | 1 | 3 | X | 1 | |||
21 | 1 | 0 | |||||
22 | 2 | 0 | |||||
23 | 5 | 2 | X | 1 | |||
24 | 1 | 1 | X | 1 | 1 | ||
25 | 1 | 0 | |||||
26 | 1 | 1 | X | 1 | 1 | ||
27 | 1 | 0 | |||||
28 | 2 | 0 | |||||
29 | 1 | 0 | |||||
30 | 1 | 0 | |||||
31 | 1 | 0 | |||||
32 | 1 | 0 | |||||
33 | 1 | 1 | X | 1 | 1 | ||
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 | 49 | 49 | 9 | 6 | 5 | 1 | 1 |
Using these sums to evaluate C we first need to calculate U and V:
<math>U_{est} = \frac{16}{49} + \left(\frac{48}{49}\right)\left(\frac{5}{2\left(1\right)}\right)\left(\frac{1+3+1+1+1}{49}\right) = 0.6764</math>
<math>V_{est} = \frac{18}{49} + \left(\frac{48}{49}\right)\left(\frac{6}{2\left(1\right)}\right)\left(\frac{1+3+3+1+1+1}{49}\right) = 0.9671</math>
<math>C_{J_{abund}} = 1-\frac{\left(0.6764\right)\left(0.9671\right)}{0.6764 + 0.9671 - 0.6541}=0.3388</math>
Running...
mothur > summary.shared(calc=jabund)
...and opening 98_lt_phylip_amazon.fn.shared.summary gives:
label comparison JAbund 0.10 forest pasture 0.33883
These are the same values that we found above for a cutoff of 0.10.