Consistency() calculates the consistency "index" and retention index
(Farris 1989)
for each character in a dataset, given a bifurcating tree.
Although there is not a straightforward interpretation of these indices,
they are sometimes taken as an indicator of the fit of a character to a
tree.
Values correlate with the number of species sampled and the
distribution of taxa between character states, so are not strictly comparable
between characters in which these factors differ; and values cannot be
compared between datasets (Speed and Arbuckle 2017)
.
Arguments
- dataset
A phylogenetic data matrix of phangorn class
phyDat, whose names correspond to the labels of any accompanying tree. Perhaps load into R usingReadAsPhyDat(). Additive (ordered) characters can be handled usingDecompose().- tree
A tree of class
phylo.- nRelabel
Integer specifying how many times to relabel leaves when estimating null tree length for RHI calculation. Steell et al. (2025) recommend 1000, but suggest that 100 may suffice. If zero (the default), the RHI is not calculated.
- compress
Logical specifying whether to retain the compression of a
phyDatobject or to return a vector specifying to each individual character, decompressed using the dataset'sindexattribute.
Value
Consistency() returns a matrix with named columns specifying the
consistency index (ci),
retention index (ri),
rescaled consistency index (rc) and
relative homoplasy index (rhi).
Details
The consistency "index" (Kluge and Farris 1969) is defined as the number of steps observed in the most parsimonious mapping of a character to a tree, divided by the number of steps observed on the shortest possible tree for that character. A value of one indicates that a character's fit to the tree is optimal. Note that as the possible values of the consistency index do not range from zero to one, it is not an index in the mathematical sense of the term. Shortcomings of this measure are widely documented (Archie 1989-09; Brooks et al. 1986; Steell et al. 2025) .
The maximum length of a character (see MaximumLength()) is the
number of steps in a parsimonious reconstruction on the longest possible tree
for a character.
The retention index is the maximum length of a character minus the number
of steps observed on a given tree; divided by the maximum length minus the
minimum length. It is interpreted as the ratio between the observed
homoplasy, and the maximum observed homoplasy, and scales from zero
(worst fit that can be reconstructed under parsimony) to one (perfect fit).
The rescaled consistency index is the product of the consistency and retention indices; it rescales the consistency index such that its range of possible values runs from zero (least consistent) to one (perfectly consistent).
The relative homoplasy index (Steell et al. 2025) is the ratio of the observed excess tree length to the excess tree length due to chance, taken as the median score of a character when the leaves of the given tree are randomly shuffled.
The lengths of characters including inapplicable tokens are calculated
following Brazeau et al. (2019)
, matching their
default treatment in TreeLength().
References
Archie JW (1989-09).
“Homoplasy Excess Ratios: New Indices for Measuring Levels of Homoplasy in Phylogenetic Systematics and a Critique of the Consistency Index.”
Systematic Zoology, 38(3), 253.
doi:10.2307/2992286
.
Brazeau MD, Guillerme T, Smith MR (2019).
“An algorithm for morphological phylogenetic analysis with inapplicable data.”
Systematic Biology, 68(4), 619–631.
doi:10.1093/sysbio/syy083
.
Brooks DR, O'Grady RT, Wiley EO (1986).
“A Measure of the Information Content of Phylogenetic Trees, and Its Use as an Optimality Criterion.”
Systematic Biology, 35(4), 571–581.
doi:10.2307/2413116
.
Farris JS (1989).
“The Retention Index and the Rescaled Consistency Index.”
Cladistics, 5(4), 417–419.
doi:10.1111/j.1096-0031.1989.tb00573.x
.
Kluge AG, Farris JS (1969).
“Quantitative Phyletics and the Evolution of Anurans.”
Systematic Zoology, 18(1), 1–32.
doi:10.1093/sysbio/18.1.1
.
Speed MP, Arbuckle K (2017).
“Quantification Provides a Conceptual Basis for Convergent Evolution.”
Biological Reviews, 92(2), 815–829.
doi:10.1111/brv.12257
.
Steell EM, Hsiang AY, Field DJ (2025).
“Revealing Patterns of Homoplasy in Discrete Phylogenetic Datasets with a Cross-Comparable Index.”
Zoological Journal of the Linnean Society, 204(1), zlaf024.
doi:10.1093/zoolinnean/zlaf024
.
Examples
data(inapplicable.datasets)
dataset <- inapplicable.phyData[[4]]
head(Consistency(dataset, TreeTools::NJTree(dataset), nRelabel = 10))
#> ci ri rc rhi
#> [1,] 0.2500000 0.6250000 0.1562500 0.6000000
#> [2,] 0.3333333 0.3333333 0.1111111 0.6666667
#> [3,] 0.3333333 0.6000000 0.2000000 0.5000000
#> [4,] 0.2500000 0.2500000 0.0625000 1.0000000
#> [5,] 0.5000000 0.8333333 0.4166667 0.2000000
#> [6,] 0.2500000 0.2500000 0.0625000 0.7500000