Molecular Clock is a standard hypothesis of whether the
total "amount" evolution varies from lineage to lineage in a tree. A subtree of a tree is
under molecular clock on model parameter "x", if the sum of the values of "x" along the path
from any internal node, to a descendant leaf, is the same for every leaf. Molecular clock
on all model parameters implies that the same is true of the expected amount of substituitions
for every lineage in that subtree. Global clock is in effect if every
subtree of the entire tree obeys the clock.
The way HyPhy implements molecular clock is to define a
set of additive constraints. For example, here are the constraints needed
to define global clock on a 5 species tree, assuming that the model parameter is 'a':
Chimpanzee.a := Human.a;
Gibbon.a := Human.a+Node2.a+Node1.a;
Orangutan.a := Human.a+Node2.a+Node1.a;
Gorilla.a := Human.a+Node2.a;
It is worth noting, that for reversible models of
evolution, the placement of the root is arbitrary, and we could place it
on any of the three branches which are children of the "root" of the
unrooted tree (an unrooted binary tree can be represented as a rooted tree,
whose root has 3 children, and all other nodes - at most two; the picture above
is an example). This is precisely
the meaning of molecular clock for unrooted trees: the "rooted"
version of the tree, i.e. the one where the root has three children, obeys
the clock.
If a rooting is specified, there is one less constraint:
Chimpanzee.a := Human.a;
Gibbon.a := Orangutan.a;
Gorilla.a := Human.a+Node2.a;
In this setting, the clock means that there is a way
to slide the placement of the root along the two top-level branches which will
enforce the clock (in the example above, the branch above Node6 can be divided
in a way to enforce the clock).
Again, this ambiguity is due to the fact that reversible models can't resolve root placement.
Local clocks are obtained by constraining only a subtree of the
given tree, e.g.:
Chimpanzee.a := Human.a;
Gorilla.a := Human.a+Node2.a;
Only the subtree with (Human, Chimpanzee, Gorilla)
is subject to molecular clock.
|