# 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 > 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) (a~i~-b~i~)^2^ a~i~b~i~ ——- ———— ————- —————- ———- 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.