# Bootstrap

The bootstrap calculator returns the bootstrap richness estimate for an OTU definition. This calculator can be used in the summary.single, collect.single, and rarefaction.single commands. The calculations for the bootstrap richness estimator are implemented as described by Smith and Van Belle for a single "quadrant".

$S_{bootstrap} = S_{obs} + \sum_{i=1}^{S_{obs}} \left ( 1 - \frac {S_i}{N}\right )^N$

where,

$N$ = the number of individuals sampled

$S_{i}$ = the number of sequences in the ith OTU

$S_{obs}$ = the observed number of species

Open the file 98_lt_phylip_amazon.fn.sabund generated using the Amazonian dataset with the following commands:

mothur > cluster(phylip=98_lt_phylip_amazon.dist, cutoff=0.10)
mothur > summary.single(calc=boostrap)


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 ACE estimator is then calculated using the values found in the subsequent columns. For demonstration we will calculate the bootstrap estimator for an OTU definition of 0.03:

$S_{bootstrap} = 84 + 75 \left( 1 - \frac {1}{98}\right )^{98} + 6 \left( 1 - \frac {2}{98}\right )^{98} + 1 \left( 1 - \frac {3}{98}\right )^{98} + 2 \left( 1 - \frac {4}{98}\right )^{98} = 112.33$

This ACE richness estimate is the same value that is found in 98_lt_phylip_amazon.fn.summary:

label	Bootstrap
unique	130.668609
0.00	129.069184
0.01	125.870334
0.02	120.120520
0.03	112.326160 <---
0.04	107.527884
0.05	95.029232
0.06	87.586010
0.07	84.387159
0.08	74.246203
0.09	71.860150
0.10	69.345451