Additive tree distances are object dissimilarities $d$ satisfying
the so-called additive tree conditions, also known as
four-point conditions $d_{ij} + d_{kl} \le \max(d_{ik} +
d_{jl}, d_{il} + d_{jk})$ for all quadruples $i, j, k, l$.
Equivalently, for each such quadruple, the largest two values of the
sums $d_{ij} + d_{kl}$, $d_{ik} + d_{jl}$, and $d_{il} +
d_{jk}$ must be equal.
Centroid distances are additive tree distances where the inequalities
in the four-point conditions are strengthened to equalities (such that
all three sums are equal), and can be represented as $d_{ij} = g_i
+ g_j$, i.e., as sums of distances from a centroid.
See, e.g., Barthélémy and Guénoche (1991) for more details on additive
tree distances. as.cl_addtree is a generic function. Its default method can
handle objects representing ultrametric distances and raw additive
distance matrices. In addition, there is a method for coercing
objects of class "phylo" from package
ape.
Functions ls_fit_addtree and
ls_fit_centroid can be used to find the additive tree
distance or centroid distance minimizing least squares distance
(Euclidean dissimilarity) to a given dissimilarity object.
There is a plot method for additive tree distances.