Lennon
The lennon calculator returns the Lennon index describing the dissimilarity between two communities. This calculator can be used in the summary.shared and collect.shared commands.
\[D_{Lennon}=1-\frac{S_{AB}}{S_{AB}+min\left(S_A-S_{AB}\mbox{, } S_B-S_{AB}\right)}\]where,
\(S_{AB}\) = the number of shared OTUs between communities A and B
\(S_{A}\) = the number of OTUs in community A
\(S_{B}\) = the number of OTUs 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   shared
  ——- ——– ——— ——–
  1       1        0       
  2       1        0       
  3       1        0       
  4       1        1         X
  5       1        0       
  6       1        0       
  7       3        1         X
  8       3        0       
  9       2        0       
  10      2        5         X
  11      1        0       
  12      1        0       
  13      3        0       
  14      2        0       
  15      1        0       
  16      1        3         X
  17      1        0       
  18      1        0       
  19      2        0       
  20      1        3         X
  21      1        0       
  22      2        0       
  23      5        2         X
  24      1        1         X
  25      1        0       
  26      1        1         X
  27      1        0       
  28      2        0       
  29      1        0       
  30      1        0       
  31      1        0       
  32      1        0       
  33      1        1         X
  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   33       31        9
Using these sums to evaluate D we get:
\[D_{Lennon}=1-\frac{9}{9+min\left(33-9\mbox{, } 31-9\right)}=0.290\]Running...
mothur > summary.shared(calc=lennon)
...and opening 98_lt_phylip_amazon.fn.shared.summary gives:
label  comparison      Lennon
0.10   forest  pasture     0.290323
These are the same values that we found above for a cutoff of 0.10.