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3.3. Evolutionary Time
3.3.1. Evolutionary distance and the course of time
As said earlier, phylogenetics is a matter not only of cladogenesis, but
also of anagenesis, which involves inter alia the fundamental problem
of estimating some sort of evolutionary distance between nodes
in a tree.
Generally, this represents either a straight pairwise measurement of dif-
ferences between the homologous characters of an ancestor and those of a
descendant (a dissimilarity), or the accumulated number of mutations which
have occurred along the lineage from this ancestor to a present-day form.
When applied to present-day forms, it is either their pairwise dissimilarity or
the sum of the accumulated number of mutations from the cenancestor to
each of the present-day forms.
These two different estimators of evolutionary distances have
very different properties. A pairwise dissimilarity between two
sequences, which is incremented by one unit when two homologous
nucleotides are different, cannot be additive. j Statistically, it is
a monotonically increasing function of time, but definitely not a
linear function of time, if only because a character can mutate more
than once in a lineage and of course return to an ancestral state while
so doing. k
On the other hand, an estimate of a counter which is incremented by
one unit every time a nucleotide is transformed to any one of the three
others can be additive, and should be. This kind of mutational distance
between two nodes can more appropriately be treated as proportional to
the time distance between them.
A dendrogram in which each branch length is proportional to an
estimate of evolutionary distance between the two interconnected nodes,
whether additive or not, is often called a phylogram.
j If distance d is additive, C being the cenancestor of terminal nodes A and B, then
d [ A , B ] = d [ A , C ] + d [ B , C ].
k With nonadditive metric dissimilarity D , D ( A , B ) can only be said to be smaller or
equal to D ( A, C ) + D ( B , C ).
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