Heuristic searchheuristic search attempts to find the best tree, without looking at all possible trees

heuristic search methods tend to be greedy

local optimumglobal optimum

heuristic search methods may fail to find the best solution

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

Star decomposition

a

b c

d

e f

a

b c

d

e f

a

b cd

e f

a

b c

d

e f

star decomposition starts out with an unresolved tree and sequentially pairs species: e.g. UPGMA and neighbour-joining techniques