Re: Co-optation Today

Rusty Sites wrote:
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.

A tree is just a graph. That graph can be interpreted as you like. I gave an example of a tree interpreted as a non-nested hierarchy. Now it's true that any rooted tree can be interpreted as only one nested hierarchy in which its terminal nodes, but not its internal nodes, are elements, but there is no a priori reason why you have to interpret the tree that way. To put it another way, every nested hierarchy implies a tree, but a tree doesn't imply anything; it's just a topological figure.

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Relevant Pages

  • Re: Co-optation Today
    ... Every tree *can be interpreted* as a nested hierarchy. ... That's why I say that a tree is a representation of the hierarchy, ... But a nested hierarchy is best understood and defined in terms of sets, ... Now it's true that any rooted tree can be interpreted as only one nested hierarchy in which its terminal nodes, but not its internal nodes, are elements, but there is no a priori reason why you have to interpret the tree that way. ...
    (talk.origins)
  • Re: Co-optation Today
    ... Every tree *can be interpreted* as a nested hierarchy. ... but there is no a priori reason why you have to interpret the ...
    (talk.origins)
  • Re: Co-optation Today
    ... Every tree *can be interpreted* as a nested hierarchy. ... That's why I say that a tree is a representation of the hierarchy, ... But a nested hierarchy is best understood and defined in terms of sets, ... Now it's true that any rooted tree can be interpreted as only one nested hierarchy in which its terminal nodes, but not its internal nodes, are elements, but there is no a priori reason why you have to interpret the tree that way. ...
    (talk.origins)
  • Re: Co-optation Today
    ... could be interpreted as a non-nested hierarchy. ... a tree is a representation of the hierarchy, ... which is a nested hierarchy of sets. ... but there is no a priori reason why you have to interpret the ...
    (talk.origins)
  • Re: Co-optation Today
    ... hierarchy. ... That's why I say that a tree is a representation of the hierarchy, ... But a nested hierarchy is best understood and defined in terms of sets, ... of the root. ...
    (talk.origins)