<s>
WPGMA	B-Algorithm
(	O
Weighted	O
Pair	O
Group	O
Method	O
with	O
Arithmetic	O
Mean	O
)	O
is	O
a	O
simple	O
agglomerative	O
(	O
bottom-up	O
)	O
hierarchical	B-Algorithm
clustering	I-Algorithm
method	O
,	O
generally	O
attributed	O
to	O
Sokal	O
and	O
Michener	O
.	O
</s>
<s>
The	O
WPGMA	B-Algorithm
method	O
is	O
similar	O
to	O
its	O
unweighted	O
variant	O
,	O
the	O
UPGMA	B-Algorithm
method	O
.	O
</s>
<s>
The	O
WPGMA	B-Algorithm
algorithm	O
constructs	O
a	O
rooted	O
tree	O
(	O
dendrogram	B-Application
)	O
that	O
reflects	O
the	O
structure	O
present	O
in	O
a	O
pairwise	O
distance	O
matrix	O
(	O
or	O
a	O
similarity	O
matrix	O
)	O
.	O
</s>
<s>
The	O
WPGMA	B-Algorithm
algorithm	O
produces	O
rooted	O
dendrograms	B-Application
and	O
requires	O
a	O
constant-rate	O
assumption	O
:	O
it	O
produces	O
an	O
ultrametric	B-Algorithm
tree	O
in	O
which	O
the	O
distances	O
from	O
the	O
root	O
to	O
every	O
branch	O
tip	O
are	O
equal	O
.	O
</s>
<s>
This	O
ultrametricity	B-Algorithm
assumption	O
is	O
called	O
the	O
molecular	O
clock	O
when	O
the	O
tips	O
involve	O
DNA	O
,	O
RNA	O
and	O
protein	O
data	O
.	O
</s>
<s>
This	O
corresponds	O
to	O
the	O
expectation	O
of	O
the	O
ultrametricity	B-Algorithm
hypothesis	O
.	O
</s>
<s>
Because	O
of	O
the	O
ultrametricity	B-Algorithm
constraint	O
,	O
the	O
branches	O
joining	O
or	O
to	O
,	O
and	O
to	O
are	O
equal	O
and	O
have	O
the	O
following	O
length	O
:	O
</s>
<s>
The	O
dendrogram	B-Application
is	O
now	O
complete	O
.	O
</s>
<s>
It	O
is	O
ultrametric	B-Algorithm
because	O
all	O
tips	O
(	O
to	O
)	O
are	O
equidistant	O
from	O
:	O
</s>
<s>
The	O
dendrogram	B-Application
is	O
therefore	O
rooted	O
by	O
,	O
its	O
deepest	O
node	O
.	O
</s>
<s>
Alternative	O
linkage	O
schemes	O
include	O
single	B-Algorithm
linkage	I-Algorithm
clustering	I-Algorithm
,	O
complete	B-Algorithm
linkage	I-Algorithm
clustering	I-Algorithm
,	O
and	O
UPGMA	B-Algorithm
average	I-Algorithm
linkage	I-Algorithm
clustering	I-Algorithm
.	O
</s>
<s>
Complete	B-Algorithm
linkage	I-Algorithm
clustering	I-Algorithm
avoids	O
a	O
drawback	O
of	O
the	O
alternative	O
single	B-Algorithm
linkage	I-Algorithm
clustering	I-Algorithm
method	O
-	O
the	O
so-called	O
chaining	O
phenomenon	O
,	O
where	O
clusters	O
formed	O
via	O
single	B-Algorithm
linkage	I-Algorithm
clustering	I-Algorithm
may	O
be	O
forced	O
together	O
due	O
to	O
single	O
elements	O
being	O
close	O
to	O
each	O
other	O
,	O
even	O
though	O
many	O
of	O
the	O
elements	O
in	O
each	O
cluster	O
may	O
be	O
very	O
distant	O
to	O
each	O
other	O
.	O
</s>
<s>
+	O
Comparison	O
of	O
dendrograms	B-Application
obtained	O
under	O
different	O
clustering	O
methods	O
from	O
the	O
same	O
distance	O
matrix	O
.	O
</s>
<s>
Average	O
linkage	O
clustering	O
:	O
WPGMA	B-Algorithm
.	O
</s>
