Editing Cladogram (section)

==Statistics==

===Incongruence length difference test (or partition homogeneity test)===

The incongruence length difference test (ILD) is a measurement of how the combination of different datasets (e.g. morphological and molecular, plastid and nuclear genes) contributes to a longer tree. It is measured by first calculating the total tree length of each partition and summing them. Then replicates are made by making randomly assembled partitions consisting of the original partitions. The lengths are summed. A p value of 0.01 is obtained for 100 replicates if 99 replicates have longer combined tree lengths.

===Measuring homoplasy===
{{Further|Convergent evolution}}
Some measures attempt to measure the amount of homoplasy in a dataset with reference to a tree,<ref name="Archie1996">reviewed in {{cite book |doi=10.1016/B978-012618030-5/50008-3 |chapter=Measures of Homoplasy |title=Homoplasy |url=https://archive.org/details/homoplasy00sand_064 |url-access=limited |pages=[https://archive.org/details/homoplasy00sand_064/page/n179 153]–188 |year=1996 |last1=Archie |first1=James W. |editor-first=Michael J. |editor-last=Sanderson |editor-first2=Larry |editor-last2=Hufford |isbn=9780126180305}}</ref> though it is not necessarily clear precisely what property these measures aim to quantify.<ref>{{cite book|doi=10.1016/b978-012618030-5/50009-5|chapter=The Measurement of Homoplasy: A Stochastic View|title=Homoplasy|pages=189–203|year=1996|last1=Chang|first1=Joseph T.|last2=Kim|first2=Junhyong|isbn=9780126180305}}</ref>

====Consistency index====

The consistency index (CI) measures the consistency of a tree to a set of data – a measure of the minimum amount of homoplasy implied by the tree.<ref name="KLUGE, A. G 1969">{{cite journal | last1 = Kluge | first1 = A. G. | last2 = Farris | first2 = J. S. | year = 1969 | title = Quantitative Phyletics and the Evolution of Anurans | journal = Systematic Zoology | volume = 18 | issue = 1| pages = 1–32 | doi=10.2307/2412407| jstor = 2412407 }}</ref> It is calculated by counting the minimum number of changes in a dataset and dividing it by the actual number of changes needed for the cladogram.<ref name="KLUGE, A. G 1969"/>  A consistency index can also be calculated for an individual character ''i'', denoted c<sub>i</sub>.

Besides reflecting the amount of homoplasy, the metric also reflects the number of taxa in the dataset,<ref>{{cite journal | last1 = Archie | first1 = J. W. | last2 = Felsenstein | first2 = J. | year = 1993 | title = The Number of Evolutionary Steps on Random and Minimum Length Trees for Random Evolutionary Data | journal = Theoretical Population Biology | volume = 43 | pages = 52–79 | doi = 10.1006/tpbi.1993.1003 }}</ref> (to a lesser extent) the number of characters in a dataset,<ref name="ARCHIE, J. W 1989"/> the degree to which each character carries phylogenetic information,<ref name="Jennifer F p C">{{cite journal|doi=10.1111/j.1096-0031.2009.00270.x|title=A formula for maximum possible steps in multistate characters: Isolating matrix parameter effects on measures of evolutionary convergence|journal=Cladistics|volume=26|pages=98–102|year=2010|last1=Hoyal Cuthill|first1=Jennifer F.|last2=Braddy|first2=Simon J.|last3=Donoghue|first3=Philip C. J.|issue=1|pmid=34875753|s2cid=53320612|doi-access=free}}</ref> and the fashion in which additive characters are coded, rendering it unfit for purpose.<ref>{{cite journal | last1 = Sanderson | first1 = M. J. | last2 = Donoghue | first2 = M. J. | year = 1989 | title = Patterns of variations in levels of homoplasy | journal = Evolution | volume = 43 | issue = 8| pages = 1781–1795 | doi=10.2307/2409392| jstor = 2409392 | pmid = 28564338 }}</ref>

c<sub>i</sub> occupies a range from 1 to 1/[''n.taxa''/2] in binary characters with an even state distribution; its minimum value is larger when states are not evenly spread.<ref name="Jennifer F p C"/><ref name=Archie1996 /> In general, for a binary or non-binary character with <math>n.states</math>, c<sub>i</sub> occupies a range from 1 to <math>(n.states-1)/(n.taxa-\lceil n.taxa/n.states\rceil)</math>.<ref name="Jennifer F p C"/>

====Retention index====

The retention index (RI) was proposed as an improvement of the CI "for certain applications"<ref name="FARRIS, J. S 1989">{{cite journal | last1 = Farris | first1 = J. S. | year = 1989 | title = The retention index and the rescaled consistency index | journal = Cladistics | volume = 5 | issue = 4| pages = 417–419 | doi=10.1111/j.1096-0031.1989.tb00573.x| pmid = 34933481 | s2cid = 84287895 }}</ref>  This metric also purports to measure of the amount of homoplasy, but also measures how well synapomorphies explain the tree. It is calculated taking the (maximum number of changes on a tree minus the number of changes on the tree), and dividing by the (maximum number of changes on the tree minus the minimum number of changes in the dataset).

The rescaled consistency index (RC) is obtained by multiplying the CI by the RI; in effect this stretches the range of the CI such that its minimum theoretically attainable value is rescaled to 0, with its maximum remaining at 1.<ref name=Archie1996/><ref name="FARRIS, J. S 1989"/> The homoplasy index (HI) is simply 1 &minus; CI.

==== Homoplasy Excess Ratio ====

This measures the amount of homoplasy observed on a tree relative to the maximum amount of homoplasy that could theoretically be present – 1 &minus; (observed homoplasy excess) / (maximum homoplasy excess).<ref name="ARCHIE, J. W 1989">{{cite journal | last1 = Archie | first1 = J. W. | title = Homoplasy Excess Ratios: New Indices for Measuring Levels of Homoplasy in Phylogenetic Systematics and a Critique of the Consistency Index | year = 1989 | journal = Systematic Zoology | volume = 38 | issue = 3| pages = 253–269 | doi=10.2307/2992286| jstor = 2992286 }}</ref> A value of 1 indicates no homoplasy; 0 represents as much homoplasy as there would be in a fully random dataset, and negative values indicate more homoplasy still (and tend only to occur in contrived examples).<ref name="ARCHIE, J. W 1989"/>  The HER is presented as the best measure of homoplasy currently available.<ref name=Archie1996/><ref>{{cite journal|doi=10.1016/j.jtbi.2014.10.033|pmid=25451518|title=The size of the character state space affects the occurrence and detection of homoplasy: Modelling the probability of incompatibility for unordered phylogenetic characters|journal=Journal of Theoretical Biology|volume=366|pages=24–32|year=2015|last1=Hoyal Cuthill|first1=Jennifer|bibcode=2015JThBi.366...24H}}</ref>