Re: Co-optation Today

John Harshman wrote:
r norman wrote:

In other words, every tree can be interpreted to be a nested
hierarchy. You have to do the same with phylogenetic trees. The
nesting requires that a node be associated not only with the species
that occupies that node but with the clade descended from that
species.

I agree. Every tree *can be interpreted* as a nested hierarchy. Or it could be interpreted as a non-nested hierarchy. That's why I say that a tree is a representation of the hierarchy, not the hierarchy itself. This is not a big deal. But a nested hierarchy is best understood and defined in terms of sets, not trees. And of course a natural nested hierarchy is best *explained* by a tree.


Well trees can be defined in terms of sets. From Donald Knuth

A finite set T of one or more nodes such that:

1. there is one specially designated node called the root of the tree, root(T); and
2. the remaining nodes (excluding the root) are partitioned into

m >= 0 disjoint sets T1, ..., Tm, and each of these sets in

turn is a tree. The trees T1, ..., Tm are called the subtrees
of the root.

I think this is properly called a rooted tree.

A rooted tree can be represented as

{a, {b, {c, d}}, {e, f}}

which is a nested hierarchy of sets. I don't see how it could be interpreted as a non-nested hierarchy.

.

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