# 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.