Estimating Phylogenies from Molecular Data - Mathematical Approaches to Polymer Sequence Analysis and Related Problems - page 156

implies that if we would compare two molecular data whose nucleotide frequencies
are in equilibrium, the probability that a nucleotide i undergoes a substitution to

nucleotide j would be equal to the probability that a nucleotide j undergoes a

substitution to nucleotide . Thus, given a present-day molecular sequence and

its ancestral sequence, it would be impossible to determine which sequence is the
present and which is the ancestral one. Hence, the hypothesis of time-reversibility
removes the temporality from the evolutionary process. We shall show in the next
sections how the paradigms of phylogenetic estimation take advantage of this fact.
Below, we provide an example from [ 79 ] showing a possible application of ( 8.9 ).

i

8.2.2.1 Estimating Evolutionary Distances from Molecular Data:

A Practical Example

Consider the mitochondrial DNA sequences of human and chimpanzee showed in
Horaietal. [ 40 ]. The corresponding matrices O

.t / and ˘ are respectively

A C GT

0 1

A

0:2889 0:0012 0:0131 0:0005 A

C
G
T

@

0:0012 0:2799 0:0001 0:0266

O .t / D

0:0131 0:0001 0:1180 0:0001

0:00005 0:0266 0:0001 0:2299

and

A C GT

0
@

1
A

0:3037 0 0 0 A

C
G
T:

0 0:3079 0 0

˘ D

0 0 0:1313 0

0 0 0 0:2571

˘ 1 O

The product .t / is:

A C GT

0
@

1
A

0:9513 0:0040 0:0430 0:0017 A

C
G
T

0:0040 0:9092 0:0003 0:0865

˘ 1 O

.t / D

0:0995 0:0008 0:8989 0:0008

0:0030 0:1036 0:0004 0:8940