Qstat
The qstat calculator returns the Q statistic for an OTU definition. This calculator can be used in the summary.single, collect.single, and rarefaction.single commands.
\[Q=\frac{\frac{1}{2}n_{R1} + \sum n_r + \frac{1}{2}n_{R2}}{\ln\left(\frac{R_2}{R_1}\right)}\]where,
\(R_1\) = the number of individuals in an OTU when at least 25% of the least abundance OTUs are sampled
\(R_2\) = the number of individuals in an OTU when at least 75% of the least abundance OTUs are sampled
\(n_{R1}\) = the number of OTUs that belong to the OTU where the 25% cutoff is found
\(n_{R2}\) = the number of OTUs that belong to the OTU where the 75% cutoff is found
\(\sum n_r\) = the total number of OTUs that lie between the 25% and 75% cutoffs
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.sabund file is also outputted to the terminal window when the cluster() command is executed:
unique 2 94 2
0.00 2 92 3
0.01 2 88 5
0.02 4 84 2 2 1
0.03 4 75 6 1 2
0.04 4 69 9 1 2
0.05 4 55 13 3 2
0.06 4 48 14 2 4
0.07 4 44 16 2 4
0.08 7 35 17 3 2 1 0 1
0.09 7 35 14 3 3 0 0 2
0.10 7 34 13 3 2 0 0 3
The first column is the label for the OTU definition and the second column is an integer indicating the number of sequences in the dominant OTU. The Q statistic is then calculated using the values found in the subsequent columns. For demonstration we will calculate the Q statistic for an OTU definition of 0.10. There are 55 OTUs so the 25% cutoff would occur at 13.75 and the 75% cutoff at 41.25:
Abundance Number of OTUs Cum. Num. of OTUs Quartile
———– —————- ——————- ———-
1 34 34 <-- R1
2 13 47 <-- R2
3 3 50
4 2 52
5 0 52
6 0 52
7 3 55
Therefore we have \(n_{R1}\) and \(n_{R2}\) equalling 34 and 13, respectively and R1 and R2 are 1 and 2, respectively. Finally, \(\sum n_r\) equals zero.
\[Q=\frac{\frac{34}{2} + 0 + \frac{13}{2}}{\ln\left(\frac{2}{1}\right)}=33.90\]Running...
mothur > summary.single(calc=qstat)
...and opening 98_lt_phylip_amazon.fn.summary gives:
label qstat
unique 69.249362
0.00 68.528014
0.01 67.085319
0.02 62.035887
0.03 58.429149
0.04 56.265107
0.05 49.051631
0.06 44.723546
0.07 43.280851
0.08 37.510071
0.09 35.346029
0.10 33.903333 <---
These are the same values that we found above for a cutoff of 0.10.