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# Sharedchao

Validate output by making calculations by hand

**Example Calculations**

***.sharedChao**

Example calculations below will be performed using data from the Eckburg 70.stool_compare files with an OTU definition of 0.03.

Estimating the richness of shared OTUs between two communities. A Non-parametric richness estimator of the number of shared OTUs between two communities has been developed that is analogous to the Chao1 (6) single community richness estimator. The <math>S_{A,B Chao}</math> (11) estimator is calculated as:

<math>S_{A,B Chao} = S_{12 \left ( Obs \right )} + f_{11} \frac {f_{1+}f_{+1}}{4f_{2+}f_{+2}} + \frac{f_{1+}^{2}}{2f_{2+}} + \frac{f_{+1}^{2}}{2f_{+2}}</math>,

where,

<math>f_{11}</math> = number of shared OTUs with one observed individual in A and B

<math>f_{1+}, f_{2+}</math> = number of shared OTUs with one or two individuals observed in A

<math>f_{+1}, f_{+2}</math> = number of shared OTUs with one or two individuals observed in B

<math>S_{12\left(obs\right)}</math> = number of shared OTUs in A and B.

Calculation of the <math>S_{A,B Chao}</math> requires the number of OTUs where only one sequence was observed from each library, <math>f_{11}</math>. For our example case, <math>f_{11}</math> is 2. Plugging the f-values and <math>S_{12\left( obs \right )}\mbox{into } S_{A,B Chao}</math> yields a value of 76.7, which matches the value in <math>S_{A,B Chao}</math> of the table above.

**File Samples on the Eckburg 70.stool_compare Dataset**

- .shared

This file contains the frequency of sequences from each group found in each OTU. Each row consists of the distance being considered, group name, number of OTUS, and the abundance information separated by tabs. Note: only the line for distance0.03 are shown below. The abundance information is as follows. Each subsequent number represents a different OTU so that the number indicates the number of sequences in that group that clustered within that OTU. Note that OTU frequencies can only be compared within a distance definition.

0.03 stool 110 174 27 5 127 7 1 46 10 25 39 23 57 12 9 4 36 48 48 75 29 23 45 10 5 5 2 3 11 6 1 2 11 12 1 2 11 1 2 2 7 1 4 6 14 1 4 4 2 1 1 6 1 6 2 2 2 1 1 2 1 3 4 3 3 1 1 2 2 1 1 1 1 2 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 0 0 0 0 0 0 0.03 tissue 110 1135 91 2 6 4 4 129 0 21 137 4 51 8 92 0 29 25 10 248 63 410 42 26 31 1 3 9 25 0 0 1 0 6 10 0 8 12 1 36 9 0 3 18 30 0 24 0 0 34 0 6 11 42 0 55 0 0 26 2 4 8 3 0 0 0 0 2 25 29 13 7 0 15 1 0 5 3 1 0 32 4 5 2 11 3 51 43 22 1 1 4 1 1 1 1 2 7 1 1 1 7 1 3 1 1 1 2 63 1 1