Heuristic searchheuristic search attempts to find the best tree, without looking at all possible trees
Moving through the trees
1. Nearest-neighbour interchanges
ba c
ed
nearest neighbour interchanges ‘swap’ adjacent branches to find alternative trees
Moving through the trees
1. Nearest-neighbour interchanges
ba c
ed
nearest neighbour interchanges starts by erasing an internal branch
Moving through the forest
1. Nearest-neighbour interchanges
ba c
ed
and then erases the two braches connected to it at each end
Moving through the forest
1. Nearest-neighbour interchanges
ba c
edb
e a
cd
the four subtrees are now hooked together in all possible ways
((a+c) + e) + (b+d)
Moving through the forest
1. Nearest-neighbour interchanges
ba c
edb
e a
cd
bc a
ed
((a+e) + c) + (b+d)
Moving through the forest
1. Nearest-neighbour interchanges
ba c
edb
e a
cd
bc a
ed
ba c
ed
now a second internal branch is erased and the procedure is repeated
Moving through the forest
1. Nearest-neighbour interchanges
ba c
edb
e a
cd
bc a
ed
ba c
eda
b c
ed
bd c
ea
Moving through the forest
1. Nearest-neighbour interchanges
ba c
edb
e a
cd
bc a
ed
ba c
eda
b c
ed
bd c
ea
b d c
ea
a b c
ed
b c e
ad
a d b
ce
b a c
eda e b
dc
a b d
eca d b
ec
a c b
ed
a e b
cd
a e c
dbc a b
ed
a b c
de
d a b
ce
a c d
eb
Characters
Species 1 2 3 4 5 6
Alpha (a) 1 0 0 1 1 0
Beta (b) 0 0 1 0 0 0
Gamma (c) 1 1 0 0 0 0
Delta (d) 1 1 0 1 1 1
Epsilon (e) 0 0 1 1 1 0
b d c
ea
a b c
ed
b c e
ad
a d b
ce
b a c
eda e b
dc
a b d
eca d b
ec
a c b
ed
a e b
cd
a e c
dbc a b
ed
a b c
de
d a b
ce
a c d
eb
[11]
[11][11]
[11] [11]
[11]
[11][9]
[10] [10]
[9]
[9] [9]
[8]
[9]
b d c
ea
a b c
ed
b c e
ad
a d b
ce
b a c
eda e b
dc
a b d
eca d b
ec
a c b
ed
a e b
cd
a e c
dbc a b
ed
a b c
de
d a b
ce
a c d
eb
[11]
[11][11]
[11] [11]
[11]
[11][9]
[10] [10]
[9]
[9] [9]
[8]
[11]
[9]
b d c
ea
a b c
ed
b c e
ad
a d b
ce
b a c
eda e b
dc
a b d
eca d b
ec
a c b
ed
a e b
cd
a e c
dbc a b
ed
a b c
de
d a b
ce
a c d
eb
[11]
[11][11]
[11] [11]
[11]
[11][9]
[10] [10]
[9]
[9] [9]
[8]
[11]
[9]
b d c
ea
a b c
ed
b c e
ad
a d b
ce
b a c
eda e b
dc
a b d
eca d b
ec
a c b
ed
a e b
cd
a e c
dbc a b
ed
a b c
de
d a b
ce
a c d
eb
[11]
[11][11]
[11] [11]
[11]
[11][9]
[10] [10]
[9]
[9] [9]
[8]
[11]
[9]
b d c
ea
a b c
ed
b c e
ad
a d b
ce
b a c
eda e b
dc
a b d
eca d b
ec
a c b
ed
a e b
cd
a e c
dbc a b
ed
a b c
de
d a b
ce
a c d
eb
[11]
[11][11]
[11] [11]
[11]
[11][9]
[10] [10]
[9]
[9] [9]
[8]
[11]
[9]
Moving through the forest
1. Nearest-neighbour interchanges2. Subtree pruning and regrafting (SPR)
g c
a
df
b
i
hj
k
e
in SPR, a branch with a subtree is removed…
Moving through the forest
1. Nearest-neighbour interchanges2. Subtree pruning and regrafting
g c
a
d
f
b
i
hj
k
e
… and reinserted in all possible places.
Moving through the forest
1. Nearest-neighbour interchanges2. Subtree pruning and regrafting
g c
a
d
f
b
i
hj
k
e
Moving through the forest
1. Nearest-neighbour interchanges2. Subtree pruning and regrafting
g c
ad
f
b
i
hj
k
e
Moving through the forest
1. Nearest-neighbour interchanges2. Subtree pruning and regrafting (SPR)3. Tree bisection and reconnection (TBR)
g c
a
df
b
i
hj
k
e
in TBR, the tree is first bisected …
Moving through the forest
1. Nearest-neighbour interchanges2. Subtree pruning and regrafting3. Tree bisection and reconnection
g c
a
df
b
i
hj
k
e
and then all possible connections are made between a branch of one subtree and a branch of the other
Moving through the forest
1. Nearest-neighbour interchanges2. Subtree pruning and regrafting3. Tree bisection and reconnection
g
c
a d
k
e
f
bi h
j
Moving through the forest
1. Nearest-neighbour interchanges2. Subtree pruning and regrafting3. Tree bisection and reconnection4. …
many more rearrangement methods exist and new ones are being developed
Sequential addition
a
b
c
the sequential addition strategy starts with a simple tree and adds species one by one
Sequential addition
a
b
c
a
b
c
d
a
d
b
c
a
c
b
d[9][7][8]
every new tree is evaluated on the way,...
Sequential addition
a
b
c
a
b
c
d
a
d
b
c
a
c
b
d
a
d
b
c
a
d
b
e
a
d
c
e
a
e
b
c
e
d
b
c
a
d
ec
b
[9]
[9]
[9]
[9]
[11]
[9][7][8]
… and the most promising path is taken