VNRLQQNIVSL____________EVDHKVANYKPQVEPFGHGPIFMATALVPGLYLGVPWF VNRLQQSIVSLRDAFNDGTKLLEELDHRVLNYKPQANPFGNGPIFMVTAIVPGLHLGAPWFUnassociated positions are called

- a)
- that the two sequences are
independent of each other,
and hence an arbitrary position with amino acid
*i*aligned to another arbitrary position with amino acid*j*has the probability equal to the product of the individual frequencies

- b)
- that the two sequences have evolved
from some common ancestral sequence
after
*t*units of evolution.

We use
as a shorthand for
,
that is
a sum over all symbols of the alphabet.
The entries of the Dayhoff matrix are the logarithm
of the quotient of these two probabilities.

Since DP maximizes the sum of the similarity measure, DP maximizes the sum of the logarithms or maximizes the product of these quotients of probabilities. As a conclusion, DP finds the alignment which maximizes the probability of having evolved from a common ancestor (a maximum likelihood alignment) against the null hypothesis of being independent. This makes aligning sequences using Dayhoff matrices a soundly based algorithm.