As sequence diverge so does the probability of there being multiple substitutions at any one site in the alignment increase. The distance will then be an underestimate of the true evolutionary distance between the sequences. Therefore, there are a number of methods for correcting the observed substitution rate for the occurence of multiple substutions.
For nucleotides, the "-position" flag allows the user to choose base positions to analyse in each codon, i.e. 123 (all bases), 12 (the first two bases), 1, 2, or 3 individual bases.
S = m/(npos + gaps*gap_penalty) (1) m - score of matches (1 for an exact match, a fraction for partial matches and 0 for no match) npos - number of positions included in m gaps - number of gaps in the sequences gap_penalty - the score given to a gapped position
D = uncorrected distance = p-distance = 1-S (2)
The score of match includes all exact matches. For nucleotides, if the flag "-ambiguous" is used then partial matches are included in the score. For example, a match of M (A or C) with A will increment m by 0.5 (0.5*1.0). Gaps are not included in the calculation unless a non zero value is given with "-gapweight". It should be noted that end gaps and internal gaps will be weighted by the same amount. So it is recommended that this be used with "-sbegin"and "-send" to specify the start and end of the region to calculate the distance from.
distance = -b ln (1-D/b) D - uncorrected distance b - constant. b= 3/4 for nucleotides and 19/20 for proteins.
Partial matches and gap positions can be taken into account in the calculation of D, by setting the "-ambiguous" and "-gapweight" flags (see "uncorrected distance" method).
Reference:
"Phylogenetic Inference", Swofford, Olsen, Waddell, and
Hillis, in Molecular Systematics, 2nd ed., Sinauer Ass., Inc., 1996, Ch. 11.
A = 1, T = 2, C = 3, G = 4 b = 0.5(1.- Sum(i=A,G)(fraction[i]^2 + D^2/h) h = Sum(i=A,C)Sum(k=T,G) (0.5 * pair_frequency[i,k]^2/(fraction[i]*fraction[k])) distance = -b ln(1.-D/b) pair_frequency[i,k] - frequency of the i and k base pair at sites in the alignement of the pair of sequences. fraction[i] - average content of the base i in both sequences
Reference:
F. Tajima and M. Nei, Mol. Biol. Evol. 1984, 1, 269.
P = transitions/npos Q = transversions/npos npos - number of positions scored distance = -0.5 ln[ (1-2P-Q)*sqrt(1-2Q)]
Reference:
M. kimura, J. Mol. Evol. 1980, 16, 111.
P = transitions/npos Q = transversions/npos npos - number of positions scored GC1 = GC fraction in sequence 1 GC2 = GC fraction in sequence 2 C = GC1 + GC2 - 2*GC1*GC2 distance = -C ln(1-P/C-Q) - 0.5(1-C) ln(1-2Q)
Reference:
K. Tamura, Mol. Biol. Evol. 1992, 9, 678.
L = average substituition = transition_rate + 2 * transversion_rate a = (average L)^2/(variance of L) P = transitions/npos Q = transversions/npos npos - number of positions scored distance = 0.5 * a ((1-2P-Q)^(-1/a) + 0.5 (1-2Q)^(-1/a) -3/2)
It is suggested [Jin et al.], in general, that the distance be calculated with an a-value of 1. However, the user can specify their own value, using the "-parametera" option, or calculate for each pair of sequence, using "-calculatea".
Reference:
L. Jin and M. Nei, Mol. Biol. Evol. 1990, 7, 82.
S = m/npos m - exact match npos - number of positions scored D = 1-S distance = -ln(1 - D - 0.2D^2)
Reference:
M. Kimura, The Neutral Theory of Molecular Evolution, Camb. Uni. Press,
Camb., 1983.
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The quality of the alignment is of paramount importance in obtaining meaningful information from this analysis.