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fusco.test: Imbalance statistics using Fusco and Cronk's method.

Description

Fusco and Cronk (1995) described a method for testing the imbalance of phylogenetic trees based on looking at the distribution of I. I is calculated using the number of tips descending from each side of a bifurcating node using the formula I = (B-m)/(M-m) and is bounded between 0 (a perfectly balanced node) and 1 (maximum imbalance). B is the larger number of tips descending from each branch, M is the maximum size of this larger group (i.e. a 1 : (S-1) split, where S is the total number of descendent tips), and m is the minimum size of the larger group (ceiling of S/2). The method can cope with small proportions of polytomies in the phylogeny and these are not used in calculating balance statistics. It can also incorporate information about species richness at the tips of the phylogeny and can therefore be used to distinguish between an unbalanced topology and the unbalanced distribution of diversity at the tips of a phylogeny.

Purvis et al. (2002) demonstrated that I is not independent of the node size S, resulting in a bias to the expected median of 0.5. They proposed a modification (I') that corrects this to give a statistic with an expected median of 0.5 regardless of node size. The defaults in this function perform testing of imbalance using I', but it is also possible to use the original measure proposed by Fusco and Cronk (1995).

Usage

fusco.test(phy, data , names.col, rich, tipsAsSpecies=FALSE, randomise.Iprime=TRUE,  reps=1000, conf.int=0.95)
## S3 method for class 'fusco':
print(x, ...)
## S3 method for class 'fusco':
summary(object, ...)
## S3 method for class 'fusco':
plot(x, correction=TRUE, nBins=10, right=FALSE, I.prime=TRUE, plot=TRUE, ...)

Arguments

phy
An object of class 'comparative.data' or of class 'phylo'.
data
A data frame containing species richness values. Not required if phy is a 'comparative.data' object.
names.col
A variable in data identifying tip labels. Not required if phy is a 'comparative.data' object.
rich
A variable identifying species richness.
tipsAsSpecies
A logical value. If TRUE, a species richness column need not be specified and the tips will be treated as species.
randomise.Iprime
Use a randomization test on calculated I' to generate confidence intervals.
reps
Number of replicates to use in simulation or randomization.
conf.int
Width of confidence intervals required.
x, object
An object of class 'fusco'.
correction
Apply the correction described in Appendix A of Fusco and Cronk (1995) to the histogram of nodal imbalance.
nBins
The number of bins to be used in the histogram of nodal imbalance.
right
Use right or left open intervals in plotting the distribution and calculating the correction
I.prime
Plot distribution of I' or I.
plot
If changed to FALSE, then the plot method does not plot the frequency histogram. Because the method invisibly returns a table of histogram bins along with the observed and corrected frequencies, this isn't as dim an option as it sounds.
...
Further arguments to generic methods

Value

  • The function fusco.test produces an object of class 'fusco' containing:
  • observedA data frame of informative nodes showing nodal imbalance statistics.
  • medianThe median value of I.
  • qdThe quartile deviation of I.
  • tipsAsSpeciesA logical indicating whether the tips of the trees were treated as species or higher taxa.
  • nInformativeThe number of informative nodes.
  • nSpeciesThe number of species distributed across the tips.
  • nTipsThe number of tips.
  • repsThe number of replicates used in randomization.
  • conf.intThe confidence levels used in randomization.
  • If randomise.Iprime is TRUE, or the user calls fusco.randomize on a 'fusco' object, then the following are also present.
  • randomisedA data frame of mean I' from the randomized observed values.
  • rand.meanA vector of length 2 giving confidence intervals in mean I'.

Details

I is calculated only at bifurcating nodes giving rise to more than 3 tips (or more than 3 species at the tips): nodes with three or fewer descendants have no variation in I and are not informative in assessing imbalance. The expected distribution of the nodal imbalance values between 0 and 1 is theoretically uniform under a Markov null model. However, the range of possible I values at a node is constrained by the number of descendent species. For example, for a node with 8 species, only the values 0, 0.33, 0.66, 1 are possible, corresponding to 4:4, 5:3, 6:2 and 7:1 splits (Fusco and Cronk, 1995). As node size increases, this departure from a uniform distribution decreases. The plot method incorporates a correction, described by Fusco and Cronk (1995), that uses the distribution of all possible splits at each node to characterize and correct for the departure from uniformity.

The randomization option generates confidence intervals around the mean I'.

References

Fusco, G. & Cronk, Q.C.B. (1995) A New Method for Evaluating the Shape of Large Phylogenies. J. theor. Biol. 175, 235-243

Purvis A., Katzourakis A. & Agapow, P-M (2002) Evaluating Phylogenetic Tree Shape: Two Modifications to Fusco & Cronk's Method. J. theor. Biol. 214, 93-103.

Examples

Run this code
data(syrphidae)
syrphidae <- comparative.data(phy=syrphidaeTree, dat=syrphidaeRich, names.col=genus)
summary(fusco.test(syrphidae, rich=nSpp))
summary(fusco.test(syrphidae, tipsAsSpecies=TRUE))
plot(fusco.test(syrphidae, rich=nSpp))

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