Tables for Approximation of Bootstrap and Decay Index to Confidence Intervals
Richard H. Zander
March 20, 2006

Res Botanica, a Missouri Botanical Garden Web Site

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The Bayesian posterior probability (BPP)  can be used directly from the molecularly based literature, with recognition that it may be too high given the numerous 1.00 values for data sets generating rather low bootstrap proportions (BPs), but can be taken as equivalent to a probability of branch arrangement (PBA). Table 1 gives 4-taxon PBA equivalents for BPs at various branch lengths, obtained by calculation with small contrived data sets as described by Zander (2004). Proportions below 0.50 are not dealt with because these are seldom cited in published works and are possibly stochastic artifacts. For intermediate branch lengths and BP values, interpolate for the appropriate PBA. These values may be used by researchers to help determine PBAs and IRCIs for published cladograms with BP values. Except for the very shortest branch lengths, the BP closely approximates the jackknife proportion.

 

Table 1. Approximate maximum assignable fail-safe 4-taxon binomial (chi-squared with one degree of freedom) probability of branch arrangements (PBAs) calculated from the nonparametric bootstrap proportion (BP) for various branch lengths. Interpolate for intermediate values; extrapolate for longer branch lengths.

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                                                                        PBA

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BP                   5 steps             10 steps           15 steps           20 steps           25 steps

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1.00                 0.99                 0.99                 0.99                 0.99                 0.99

0.95                 0.95                 0.97                 0.98                 0.98                 0.98

0.90                 0.93                 0.95                 0.95                 0.95                 0.95

0.85                 0.90                 0.90                 0.92                 0.92                 0.93

0.80                 0.85                 0.88                 0.90                 0.90                 0.90

0.75                 0.83                 0.83                 0.85                 0.86                 0.87

0.70                 0.79                 0.78                 0.81                 0.80                 0.82

0.65                 0.70                 0.75                 0.78                 0.77                 0.78

0.60                 0.66                 0.70                 0.74                 0.75                 0.76

0.55                 0.62                 0.64                 0.65                 0.71                 0.72

0.50                 0.57                 0.60                 0.61                 0.64                 0.65

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The 4-taxon PBA equivalent of the Decay Index (DI or Bremer Support) is easily calculated, but Table 2 is given for convenience. This is the “local DI”, with no provision for collapse of a clade due to influence of well-nested totally different contrary phylogenetic signal, but that is an np-hard problem with no approximate solution at present. The PBA here is equal to the chance of AB or greater out of AB + AC + BC trials where AC and BC are equal (as possible), and AC and BC are each set equal to AB minus the DI in number of steps. Thus, for a branch length of 10 steps and a DI of 6, AB = 10 and AC and BC are both equal to 4.


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Table 2. Approximate maximum assignable fail-safe 4-taxon PBAs calculated from the DI for various branch lengths.

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                                                            PBA

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DI        3 steps    4 steps       5 steps    10 steps     15 steps  20 steps     25 steps

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1          0.57        0.56           0.52        0.54           0.53        0.53           0.52

2          0.79        0.74           0.71        0.64           0.62        0.60           0.59

3          0.96        0.95           0.85        0.75           0.70        0.67           0.65

4          -              0.99           0.95        0.84           0.78        0.74           0.72

5          -              -                 0.99        0.91           0.85        0.80           0.78

6          -              -                 -              0.96           0.90        0.86           0.83

7          -              -                 -              0.98           0.94        0.90           0.87

8          -              -                 -              0.99           0.97        0.94           0.91

9          -              -                 -              0.99           0.99        0.96           0.94

10        -              -                 -              0.99           0.99        0.98           0.96

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Reference:

Zander, R. H. 2004. Minimal values for reliability of bootstrap and jackknife proportions, decay index, and Bayesian posterior probability. Phyloinformatics 2: 1--13.

 

A suggested citation fro the present Web paper is:

Zander, R. H. 2006. Tables for Approximation of Bootstrap and Decay Index to Confidence Intervals. Missouri Botanical Garden Web site, Res Botanica. http://www.mobot.org/plantscience/resbot/Phyl/BPandDItables.htm. (Put date you actually read this paper here.)