1. Bootstrapping (non-parametric)
Bootstrapping is a modern statistical technique that uses computer intensive random resampling of data to determine sampling error or confidence intervals for some estimated parameter

2. Bootstrapping (non-parametric)
Characters are resampled with replacement to create many bootstrap replicate data sets
Each bootstrap replicate data set is analysed (e.g. with parsimony, distance, ML)
Agreement among the resulting trees is summarized with a majority-rule consensus tree
Frequency of occurrence of groups, bootstrap proportions (BPs), is a measure of support for those groups
Additional information is given in partition tables

3. Bootstrapping
Original data matrix
Resampled data matrix
Characters
Characters
Taxa
Taxa
Summarise the results of multiple analyses with a majority-rule consensus tree
Bootstrap proportions (BPs) are the frequencies with which groups are encountered in analyses of replicate data sets
A R R Y Y Y Y Y Y
A R R R Y Y Y Y Y
B R R Y Y Y Y Y Y
B R R R Y Y Y Y Y
C Y Y Y Y Y R R R
C Y Y Y Y Y R R R
D Y Y R R R R R R
D Y Y Y R R R R R
Outgp R R R R R R R R
Outgp R R R R R R R R
Randomly resample characters from the original data with
replacement to build many bootstrap replicate data sets of the
same size as the original - analyse each replicate data set A B C D A B C D A B C D 1 5 2 1 5
96% 8 2 7 8 2 6 6
66% 6 2 5 4 1 3
Outgroup
Outgroup
Outgroup

4. Bootstrapping - an example
Partition Table
Ciliate SSUrDNA - parsimony bootstrap
Ochromonas (1)
Freq
.**
...**
.....**
...****
...****** **
...****.*
...*****
.*******
.**....*
.**.....*
Symbiodinium (2)
100
Prorocentrum (3)
Euplotes (8) 84
Tetrahymena (9) 96
Loxodes (4)
100
Tracheloraphis (5)
100
Spirostomum (6)
100
Gruberia (7)
Majority-rule consensus

5. Bootstrapping - random data
Partition Table
Randomly permuted data - parsimony bootstrap
Freq
.*****.**
..**
....*..*
.*......*
.***.*.**
...*...*
.*..**.**
.....*..*
.*...*..*
.***....*
....**.**
....**.*
..*...*
.**..*..*
.*...*
.....*.**
.***
Majority-rule consensus (with minority components)

6. Bootstrap - interpretation
Bootstrapping was introduced as a way of establishing confidence intervals for phylogenies
This interpretation of bootstrap proportions (BPs) depends on the assumption that the original data is a random sample from a much larger set of independent and identically distributed data
However, several things complicate this interpretation
Perhhaps the assumptions are unreasonable - making any statistical interpretation of BPs invalid
Some theoretical work indicates that BPs are very conservative, and may underestimate confidence intervals - problem increases with numbers of taxa
BPs can be high for incongruent relationships in separate analyses - and can therefore be misleading (misleading data -> misleading BPs)
with parsimony it may be highly affected by inclusion or exclusion of only a few characters

7. Bootstrap - interpretation
Bootstrapping is a very valuable and widely used technique - it (or some suitable) alternative is demanded by some journals, but it may require a pragmatic interpretation:
BPs depend on two aspects of the support for a group - the numbers of characters supporting a group and the level of support for incongruent groups
BPs thus provides an index of the relative support for groups provided by a set of data under whatever interpretation of the data (method of analysis) is used