Fast Algorithms for Minimum Evolution. Richard Desper, NCBI Olivier Gascuel, LIRMM. Overview. Statement of phylogeny reconstruction problem and various approaches to solving it. Tree length formula as a function of average distances. Greedy algorithms for tree building and tree swapping.
Richard Desper, NCBI
Olivier Gascuel, LIRMM
If sij= 1 for alliandj, this is called the ordinary least-squaresmethod.
Given TgT’ the tree swap in prior slide, lthe edge length function:
wherel and l’ are constants depending on
Thus, if we require p swaps, the total complexity of
FASTNNI is O(n2 + pn).
The average complexity, when performing p swaps, is
O(n2 + pn diam(T)).
We have NNI algorithms for OLS and balanced branch lengths. But what if we have no initial topology for NNIs?
(Use Equation (3) on the next slide.)
GME runs in O(n2)running time
Same as GME,except:
BME runs in O(n2 diam(T)) running time.
all input trees
is large with fast rates
and high numbers of taxa
NNI trees are close to the
best possible for BME
The quality of the
NNI tree is (mostly)
of starting point
Computations done on Sun Enterprise E4500/E5500 running Solaris 8
on 10 400-Mhz processors with 7 Gb memory.
We see that the average number of NNIs is
considerably lower than the number of taxa.
Why does the balanced approach work so well?
Where pT(i,j) is the length of the (i,j) path in T.
Distantly related taxa see their importance
l(T) > l(S).
Proof structure modeled after OLS/ME proof (Rzhetsky and Nei, 1993).
Recall that the length of an edge is described by
We do not perform the switch because