The Colless and Sackin indices for tree balance, as implemented in
apTreeshape, have normalizations that produce negative values.  This
is very different from the Colless normalization derived by Heard
(1992), which bounds the index between 0 and 1, but despite this step,
is still heavily sensitive to tree size and is almost meaningless
unless the trees are all contained within a very narrow size range.

So, for the normalized indices in apTreeshape, what does it mean when
a tree has a negative balance score?  Which direction is "more
balanced" or "less balanced"?
What does it say about about an evolving tree if the normalized
balance values in a time series are consistently greater or less than
zero?

NOTE:  for my purposes, I'm not really interested in determining
whether a tree is more or less balanced than a Yule/ERM expectation,
but how its balance compares to other trees in a time series.

cheers,

Gabe

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