# Morisitahorn

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.

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

where,

$$S_{A,i}$$ = the number of individuals from community A in the ith OTU

$$S_{B,i}$$ = the number of individuals from community B in the ith OTU

$$n$$ = the number of individuals in community A

$$m$$ = 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()


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 X^2^ Y^2^ ——- ——– ——— —- —— —— 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:

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

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.