# Sharedchao

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 $S_{A,B Chao}$ (11) estimator is calculated as:

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

where,

$f_{11}$ = number of shared OTUs with one observed individual in A and B

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

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

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

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

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