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Morisitahorn

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The morisitahorn calculator returns the Morisita-Horn index describing the dissimilarity between the structure of two communities. This calculator can be used in the summary.shared and collect.shared commands.


<math>D_{Morisita-Horn}=1-2\frac{\sum\frac{S_{A,i}}{n}\frac{S_{B,i}}{m}}{\sum \left(\frac{S_{A,i}}{n}\right)^2+\sum \left(\frac{S_{B,i}}{m}\right)^2}</math>

where,

<math> S_{A,i}</math> = the number of individuals from community A in the ith OTU

<math> S_{B,i}</math> = the number of individuals from community B in the ith OTU

<math> n</math> = the number of individuals in community A

<math> m</math> = the number of individuals in community 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 > 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 pasture XY X2 Y2
1 1 0 0 1 0
2 1 0 0 1 0
3 1 0 0 1 0
4 1 1 1 1 1
5 1 0 0 1 0
6 1 0 0 1 0
7 3 1 3 9 1
8 3 0 0 9 0
9 2 0 0 4 0
10 2 5 10 4 25
11 1 0 0 1 0
12 1 0 0 1 0
13 3 0 0 9 0
14 2 0 0 4 0
15 1 0 0 1 0
16 1 3 3 1 9
17 1 0 0 1 0
18 1 0 0 1 0
19 2 0 0 4 0
20 1 3 3 1 9
21 1 0 0 1 0
22 2 0 0 4 0
23 5 2 10 25 4
24 1 1 1 1 1
25 1 0 0 1 0
26 1 1 1 1 1
27 1 0 0 1 0
28 2 0 0 4 0
29 1 0 0 1 0
30 1 0 0 1 0
31 1 0 0 1 0
32 1 0 0 1 0
33 1 1 1 1 1
34 0 2 0 0 4
35 0 1 0 0 1
36 0 1 0 0 1
37 0 1 0 0 1
38 0 1 0 0 1
39 0 1 0 0 1
40 0 7 0 0 49
41 0 1 0 0 1
42 0 1 0 0 1
43 0 2 0 0 4
44 0 1 0 0 1
45 0 1 0 0 1
46 0 1 0 0 1
47 0 1 0 0 1
48 0 1 0 0 1
49 0 1 0 0 1
50 0 1 0 0 1
51 0 1 0 0 1
52 0 1 0 0 1
53 0 2 0 0 4
54 0 1 0 0 1
55 0 1 0 0 1
Total 49 49 33 99 131

Using these sums to evaluate D we get:


<math>D_{Morista-Horn}=1-2\frac{\frac{33}{\left(49\right)\left(49\right)}} {\frac{99}{49^2}+\frac{131}{49^2}}=0.713</math>


Running...

mothur > summary.shared(calc=morisitahorn)


...and opening 98_lt_phylip_amazon.fn.shared.summary gives:

label	comparison		MorisitaHorn
0.10	forest	pasture		0.713043

These are the same values that we found above for a cutoff of 0.10.