# Measures of Character Fit Measures of Character Fit

• Slides: 26

Measures of Character Fit

Measures 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.

Cladogram 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 characters wj = weight on character j lj = number of changes in character j (number of states of the character, i. e. j – 1)

Cladogram length ‘+’ is gain and ‘-’ is loss of character Cladogram length = ?

Cladogram length ‘+’ is gain and ‘-’ is loss of character Character 1 2 3 4 5 6 Cladogram length = 1 + 1 + 2 + 2 = 8

Fit 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.

Fit of Character ‘+’ is gain and ‘-’ is loss of character Which character(s) are perfect and which character(s) are not perfect?

Fit of character 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 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

Consistency index ci = m/s X A B C D E s m ci 1 2 3 Characters 4 0 0 1 1 1 0 0 0 1 1 1 1 0 1 1 1 5 6 0 1 1 0 0 1 1 1 0 0 -

Consistency index ci = m/s X A B C D E s m ci 1 2 3 Characters 4 0 0 1 1 1 0 0 1 1 1 1 1 5 6 0 1 1 0 0 1 1 1 0 0 -

Consistency index ci = m/s X A B C D E s m ci 1 2 3 0 0 1 1 1 0 0 0 1 1 1 1 Characters 4 5 6 0 1 1 1 0 0 1 1 1 0 0 -

Consistency index ci = m/s X A B C D E s m ci 1 2 3 Characters 4 0 0 1 1 1 0 0 0 1 1 1 1 0 1 1 1 1 5 6 0 1 1 0 0 1 1 1 0 0 -

Consistency index ci = m/s X A B C D E s m ci 1 2 3 Characters 4 0 0 1 1 1 0 0 0 1 1 1 1 0 1 1 1 1 5 6 0 1 1 0 0 0 2 1 0. 5 0 1 1 1 0 0 -

Consistency index ci = m/s X A B C D E s m ci 1 2 3 Characters 4 0 0 1 1 1 0 0 0 1 1 1 1 0 1 1 1 1 5 6 0 1 1 0 0 0 2 1 0. 5 0 1 1 1 0 0 2 1 05 -

Consistency index ci = m/s CI = M/S X A B C D E s m ci 1 2 3 Characters 4 0 0 1 1 1 0 0 0 1 1 1 1 0 1 1 1 1 CI = 6/8 = 0. 75 5 6 0 1 1 0 0 0 2 1 0. 5 0 1 1 1 0 0 2 1 0. 5 8 6 -

Homoplasy index (hi) explains the level of homoplasy of a character. hi = 1 - ci X A B C D E s m ci hi HI = 1 - CI 1 2 3 Characters 4 0 0 0 0 1 1 1 1 1 1 1 1 0 5 6 0 1 1 0 0 0 2 1 0. 5 0 1 1 1 0 0 2 1 0. 5 8 6 -

Problems 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 index (ri) is defined as: ri = (g – s) / (g – m) g is the fewest number of variables of a character X A B C D E s m ci hi 1 2 3 Characters 4 0 0 0 0 1 1 1 1 1 1 1 1 0 5 6 0 1 1 0 0 0 2 1 0. 5 0 1 1 1 0 0 2 1 0. 5 8 6 -

Retention index 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 2. X A B C D E s m ci hi g ri 1 2 3 Characters 4 0 0 1 1 1 0 2 1 0 0 0 1 1 1 1 0 0 1 1 1 1 0 ri = (g – s) / (g – m) 5 6 0 1 1 0 0 0 2 1 0. 5 0 1 1 1 0 0 2 1 0. 5 8 6 -

Retention index ri = (g – s) / (g – m) X A B C D E s m ci hi g ri 1 2 3 Characters 4 0 0 1 1 1 0 2 1 0 0 0 1 1 1 0 3 1 0 0 1 1 1 1 0 5 6 0 1 1 0 0 0 2 1 0. 5 0 1 1 1 0 0 2 1 0. 5 8 6 -

Retention index ri = (g – s) / (g – m) X A B C D E s m ci hi g ri 1 2 3 0 0 1 1 1 0 2 1 0 0 0 1 1 1 0 3 1 0 0 1 1 1 1 0 2 1 Characters 4 0 1 1 1 1 0 5 6 0 1 1 0 0 0 2 1 0. 5 0 1 1 1 0 0 2 1 0. 5 8 6 -

Retention index ri = (g – s) / (g – m) X A B C D E s m ci hi g ri 1 2 3 Characters 4 0 0 1 1 1 0 2 1 0 0 0 1 1 1 0 3 1 0 0 1 1 1 1 0 2 1 0 1 1 1 1 0 1 ∞ 5 6 0 1 1 0 0 0 2 1 0. 5 0 1 1 1 0 0 2 1 0. 5 8 6 -

Retention index ri = (g – s) / (g – m) X A B C D E s m ci hi g ri 1 2 3 Characters 4 0 0 1 1 1 0 2 1 0 0 0 1 1 1 0 3 1 0 0 1 1 1 1 0 2 1 0 1 1 1 1 0 1 ∞ 5 6 0 1 1 0 0 0 2 1 0. 5 2 0 0 1 1 1 0 0 2 1 0. 5 8 6 -

Retention index 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 X A B C D E s m ci hi g ri 1 2 3 Characters 4 0 0 1 1 1 0 2 1 0 0 0 1 1 1 0 3 1 0 0 1 1 1 1 0 2 1 0 1 1 1 1 0 1 ∞ 5 6 0 1 1 0 0 0 2 1 0. 5 2 0 0 1 1 1 0 0 2 1 0. 5 3 0. 5 8 6 13 -

Rescaled 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