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    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.

 
Sergei L. Kosakovsky Pond and Spencer V. Muse, 1997-2002