The two methods of calculation produce the expected uncertainty of *n*sample bases, *E*(*H*_{nb}):

When

That is, the uncertainty of the pattern is increased because there is only a small sample. Substituting equations (17) and (18) into (5) gives equation (6).

The curve for *E*(*H*_{nb}) as a function of the number of example sites, *n*,
(Fig. 5)
has several important general properties. As the number of example
sites increases, *E*(*H*_{nb}) approaches *H*_{g}(= 2 bits/base in the figures) since the
error *e*(*n*) becomes smaller. As the number of examples drops, *E*(*H*_{nb}) also
drops (the error increases), until at only one example *E*(*H*_{nb}) is zero. With
only one example, the uncertainty of what the sequence is, *Hs*(*L*), is also
zero. At this point,
*R*_{sequence} is forced to zero (from equation 6): one
cannot measure an information content from only one example.

The sampling error correction results in an interesting effect. If
*R*_{sequence} could be measured for an infinite number of
*Hin*cII sites (this would
look something like
Fig. 1a),
the two *peaks*
would be 2 bits/base. When the
correction is made for a small sample, the peaks are less than 2 bits/base
(Figs. 1b and 1c).
This appears odd if we *know exactly* what
*Hin*cII
recognizes. However, given only six examples, we would not be so sure what
the "real" pattern is. The sampling error correction prevents us from
assuming that we have more knowledge than can be obtained from the
sequences alone.
That is, the value *e*(*n*) represents our uncertainty of the pattern,
owing to a small sample size.
In the extreme case of one sequence,
we have no knowledge of what the pattern at the site is,
even though we see a sequence. Because of the correction,
*R*_{sequence} will be underestimated at truly conserved positions
when only a few sites are known.
*R*_{sequence} for six *Hin*cII
sites in
Fig. 1c
is
estimated to be 8 bits even though we "know" (by looking at more than six
examples) that *Hin*cII recognizes 10 bits.

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