In STS content mapping, the clone overlaps are inferred
by shared STSs, so the apparent islands are those clones
anchored by common STSs. We call them anchored islands.
In this scenario, we have a random library
of N clones of length 
with mean L
for a genome of size G, and a random library of M STSs.
Since the size an STS (100-700 bp) 
, we can model the
STSs (and call them anchors) as points on the line.
Suppose the left ends of the clones are a homogeneous Poisson process
with rate 
, and the anchors are an independent Poisson
process with rate 
. We can carry out the above thinning
process argument, and have similar results:
The number of anchored clones:
So 
a random clone is not anchored 
, and the process of anchored clones is a thinned
process of the original clone process with intensity
. So the expected number of anchored clones is just
.
The number of anchored islands:
Thin the clone process by removing all clones that are not the first
clone in an anchored island. Note that a clone is the left end of an
anchored island whenever it has an anchor, and no clones starting to
its left has the same anchor. Denote the probability of this event be
. Let
the probability that an interval of length x (wlog, 
)
is not covered by a single clone}. Thin the clone process by
retaining a clone at t
whenever L+t>x. Then 
is not covered by a common clone iff no
clones remain in 
:
Also, let V denote the location of the first anchor after 0. Then
So the anchored island process has the intensity 
, and
the expected number of anchored islands is 
.
Total coverage of anchored islands = 
For the details and more results, see [2], [5], [11].