Measures of Character Fit Measures of Character Fit.

Measures of Character Fit Measures of Character Fit

Measures of Character FitMeasures of Character Fit

Parsimony programme utilizes a number of different statistics to assess the ‘quality’ of cladograms. Standard measures are cladogram length, the consistency index and the retention index.

ClaCladogram lengthdogram length

The cladogram length is the minimum number of steps (changes) needed in building the cladogram for the given data. Therefore, the larger the dataset (number of characters) the longer the cladogram length.

The possible minimum length of a cladogram (L) is given below:

C = total number of characterswj = weight on character jlj = number of changes in character j (number of states of the character, i.e. j – 1)


‘‘+’ is gain and ‘-’ +’ is gain and ‘-’ is loss of is loss of charactercharacter

Cladogram length = ?Cladogram length = ?


‘‘+’ is gain and ‘-’ +’ is gain and ‘-’ is loss of is loss of charactercharacter

Cladogram length = 1 + 1 + 1 + 1 + 2 + 2 = 8Cladogram length = 1 + 1 + 1 + 1 + 2 + 2 = 8

1 2 3 4 5 61 2 3 4 5 6CharacterCharacter

Fit of CharacterFit of Character

• The fit of a character depends on the occurrence of the character on the cladogram.• When a character fits a cladogram perfectly (for binary character, to one node with one step), it can be considered 100% consistent with that particular cladogram.•When a character does not fit a cladogram perfectly (to more than one node with more than one step), it is less than 100% consistent. Such character exhibits homoplasy.

‘‘+’ is gain and ‘-’ is +’ is gain and ‘-’ is loss of characterloss of character

Which character(s) are perfect and which character(s) are not perfect?

Fit of CharacterFit of Character

Fit of chaFit of characterracter

Homoplasy is discordance with a particular cladogram and can be measured by various indices:

consistency index (ci)homoplasy index (hi)retention index (ri)rescaled consistency (rc)

Consistency indexConsistency index

Character consistency (ci) is defined as:

ci = m/s

m is the minimum number of steps of a character can show on a cladogram

s is the minimum number of steps of a character shows on a cladogram


Characters1 2 3 4 5 6

X 0 0 0 0 0 0 -A 0 0 0 1 1 1 -B 0 0 1 1 1 1 -C 0 1 1 1 0 1 -D 1 1 1 1 0 0 -E 1 1 1 1 0 0 -s 1m 1ci 1

ci = m/s



X 0 0 0 0 0 0 -A 0 0 0 1 1 1 -B 0 0 1 1 1 1 -C 0 1 1 1 0 1 -D 1 1 1 1 0 0 -E 1 1 1 1 0 0 -s 1 1m 1 1ci 1 1

ci = m/s



X 0 0 0 0 0 0 -A 0 0 0 1 1 1 -B 0 0 1 1 1 1 -C 0 1 1 1 0 1 -D 1 1 1 1 0 0 -E 1 1 1 1 0 0 -s 1 1 1m 1 1 1ci 1 1 1

ci = m/s



X 0 0 0 0 0 0 -A 0 0 0 1 1 1 -B 0 0 1 1 1 1 -C 0 1 1 1 0 1 -D 1 1 1 1 0 0 -E 1 1 1 1 0 0 -s 1 1 1 1m 1 1 1 1ci 1 1 1 1

ci = m/s



X 0 0 0 0 0 0 -A 0 0 0 1 1 1 -B 0 0 1 1 1 1 -C 0 1 1 1 0 1 -D 1 1 1 1 0 0 -E 1 1 1 1 0 0 -s 1 1 1 1 2m 1 1 1 1 1ci 1 1 1 1 0.5

ci = m/s



X 0 0 0 0 0 0 -A 0 0 0 1 1 1 -B 0 0 1 1 1 1 -C 0 1 1 1 0 1 -D 1 1 1 1 0 0 -E 1 1 1 1 0 0 -s 1 1 1 1 2 2m 1 1 1 1 1 1ci 1 1 1 1 0.5 05

ci = m/s



X 0 0 0 0 0 0 -A 0 0 0 1 1 1 -B 0 0 1 1 1 1 -C 0 1 1 1 0 1 -D 1 1 1 1 0 0 -E 1 1 1 1 0 0 -s 1 1 1 1 2 2 8m 1 1 1 1 1 1 6ci 1 1 1 1 0.5 0.5 -

ci = m/s

CI = M/S CI = 6/8 = 0.75

Homoplasy indexHomoplasy index


X 0 0 0 0 0 0 -A 0 0 0 1 1 1 -B 0 0 1 1 1 1 -C 0 1 1 1 0 1 -D 1 1 1 1 0 0 -E 1 1 1 1 0 0 -s 1 1 1 1 2 2 8m 1 1 1 1 1 1 6ci 1 1 1 1 0.5 0.5 -

Homoplasy index (hi) explains the level of homoplasy of a character.

hi = 1 - ci HI = 1 - CI

hi 0 0 0 0 0.5 0.5 -

Problems with CI or HIProblems with CI or HI

•The inclusion of uninformative characters (autapomorphies) in calculation will inflate CI values.• As the number of taxa increases, value of CI are observed to decrease.• CI values can never reach zero.

Retention indexRetention index


X 0 0 0 0 0 0 -A 0 0 0 1 1 1 -B 0 0 1 1 1 1 -C 0 1 1 1 0 1 -D 1 1 1 1 0 0 -E 1 1 1 1 0 0 -s 1 1 1 1 2 2 8m 1 1 1 1 1 1 6ci 1 1 1 1 0.5 0.5 -

Retention index (ri) is defined as:

ri = (g – s) / (g – m)

g is the fewest number of variables of a character

hi 0 0 0 0 0.5 0.5 -



X 0 0 0 0 0 0 -A 0 0 0 1 1 1 -B 0 0 1 1 1 1 -C 0 1 1 1 0 1 -D 1 1 1 1 0 0 -E 1 1 1 1 0 0 -s 1 1 1 1 2 2 8m 1 1 1 1 1 1 6ci 1 1 1 1 0.5 0.5 -

ri = (g – s) / (g – m)

hi 0 0 0 0 0.5 0.5 -g 2ri 1

e.g. character 1 has two variables which are “1” and “0”. Variable “1” appears two times and variable “0” appears 4 times. Therefore, the g value for character 1 is 22.



X 0 0 0 0 0 0 -A 0 0 0 1 1 1 -B 0 0 1 1 1 1 -C 0 1 1 1 0 1 -D 1 1 1 1 0 0 -E 1 1 1 1 0 0 -s 1 1 1 1 2 2 8m 1 1 1 1 1 1 6ci 1 1 1 1 0.5 0.5 -

ri = (g – s) / (g – m)

hi 0 0 0 0 0.5 0.5 -g 2 3ri 1 1



X 0 0 0 0 0 0 -A 0 0 0 1 1 1 -B 0 0 1 1 1 1 -C 0 1 1 1 0 1 -D 1 1 1 1 0 0 -E 1 1 1 1 0 0 -s 1 1 1 1 2 2 8m 1 1 1 1 1 1 6ci 1 1 1 1 0.5 0.5 -

ri = (g – s) / (g – m)

hi 0 0 0 0 0.5 0.5 -g 2 3 2ri 1 1 1



X 0 0 0 0 0 0 -A 0 0 0 1 1 1 -B 0 0 1 1 1 1 -C 0 1 1 1 0 1 -D 1 1 1 1 0 0 -E 1 1 1 1 0 0 -s 1 1 1 1 2 2 8m 1 1 1 1 1 1 6ci 1 1 1 1 0.5 0.5 -

ri = (g – s) / (g – m)

hi 0 0 0 0 0.5 0.5 -g 2 3 2 1ri 1 1 1 ∞



X 0 0 0 0 0 0 -A 0 0 0 1 1 1 -B 0 0 1 1 1 1 -C 0 1 1 1 0 1 -D 1 1 1 1 0 0 -E 1 1 1 1 0 0 -s 1 1 1 1 2 2 8m 1 1 1 1 1 1 6ci 1 1 1 1 0.5 0.5 -

ri = (g – s) / (g – m)

hi 0 0 0 0 0.5 0.5 -g 2 3 2 1 2ri 1 1 1 ∞ 0



X 0 0 0 0 0 0 -A 0 0 0 1 1 1 -B 0 0 1 1 1 1 -C 0 1 1 1 0 1 -D 1 1 1 1 0 0 -E 1 1 1 1 0 0 -s 1 1 1 1 2 2 8m 1 1 1 1 1 1 6ci 1 1 1 1 0.5 0.5 -

ri = (g – s) / (g – m)

RI = (G – S) / (G – M) = (13 – 8) / (13 – 6) = 5/7 = 0.71

CI = S/M = 8/6 = 0.75

hi 0 0 0 0 0.5 0.5 -g 2 3 2 1 2 3 13ri 1 1 1 ∞ 0 0.5 -

Rescaled Consistency IndexRescaled Consistency Index

In rescaled consistency index (RC), RI value is used to rescaled CI value.

RC = CI x RI = 0.75 x 0.71 = 0.53

Measures of Character Fit Measures of Character Fit.

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