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# Difference between revisions of "Sharedchao"

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− | 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} | + | 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: |

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

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

## Revision as of 17:23, 14 January 2009

**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.