# Thetayc

The thetayc calculator returns the Yue & Clayton measure of dissimilarity between the structures of two communities. This calculator can be used in the summary.shared and collect.shared commands.

$D_{\Theta_{YC}}=1-\frac{\sum_{i=1}^{S_T} a_i b_i }{\sum_{i=1}^{S_T} \left(a_i-b_i\right)^2+\sum_{i=1}^{S_T} a_i b_i}$

where,

$S_{T}$ = the total number of OTUs in communities A and B

$a_i$ = the relative abundance of OTU i in community A

$b_i$ = the relative abundance of OTU i 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()


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) (ai-bi)2 aibi
1 1 0 0.0004 0.0000
2 1 0 0.0004 0.0000
3 1 0 0.0004 0.0000
4 1 1 0.0000 0.0004
5 1 0 0.0004 0.0000
6 1 0 0.0004 0.0000
7 3 1 0.0017 0.0012
8 3 0 0.0037 0.0000
9 2 0 0.0017 0.0000
10 2 5 0.0037 0.0042
11 1 0 0.0004 0.0000
12 1 0 0.0004 0.0000
13 3 0 0.0037 0.0000
14 2 0 0.0017 0.0000
15 1 0 0.0004 0.0000
16 1 3 0.0017 0.0012
17 1 0 0.0004 0.0000
18 1 0 0.0004 0.0000
19 2 0 0.0017 0.0000
20 1 3 0.0017 0.0012
21 1 0 0.0004 0.0000
22 2 0 0.0017 0.0000
23 5 2 0.0037 0.0042
24 1 1 0.0000 0.0004
25 1 0 0.0004 0.0000
26 1 1 0.0000 0.0004
27 1 0 0.0004 0.0000
28 2 0 0.0017 0.0000
29 1 0 0.0004 0.0000
30 1 0 0.0004 0.0000
31 1 0 0.0004 0.0000
32 1 0 0.0004 0.0000
33 1 1 0.0000 0.0004
34 0 2 0.0017 0.0000
35 0 1 0.0004 0.0000
36 0 1 0.0004 0.0000
37 0 1 0.0004 0.0000
38 0 1 0.0004 0.0000
39 0 1 0.0004 0.0000
40 0 7 0.0204 0.0000
41 0 1 0.0004 0.0000
42 0 1 0.0004 0.0000
43 0 2 0.0017 0.0000
44 0 1 0.0004 0.0000
45 0 1 0.0004 0.0000
46 0 1 0.0004 0.0000
47 0 1 0.0004 0.0000
48 0 1 0.0004 0.0000
49 0 1 0.0004 0.0000
50 0 1 0.0004 0.0000
51 0 1 0.0004 0.0000
52 0 1 0.0004 0.0000
53 0 2 0.0017 0.0000
54 0 1 0.0004 0.0000
55 0 1 0.0004 0.0000
Total 49 49 0.0683 0.0137

Using these sums to evaluate D we get:

$D_{\Theta_{YC}}=1-\frac{0.0137 }{0.0683+0.0137}=0.833$

Running...

mothur > summary.shared(calc=thetayc)


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

label	comparison		thetayc		thetayc_lci	thetayc_hci
0.10	forest	pasture		0.832487	0.026986	0.308039


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