1. Heuristic search heuristic search attempts to find the best tree, without looking at all possible trees

2. heuristic search methods tend to be greedy

4. local optimum global optimum heuristic search methods may fail to find the best solution

5. Moving through the trees 1.Nearest-neighbour interchanges b a c e d nearest neighbour interchanges ‘swap’ adjacent branches to find alternative trees

6. Moving through the trees 1.Nearest-neighbour interchanges b a c e d nearest neighbour interchanges starts by erasing an internal branch

7. Moving through the forest 1.Nearest-neighbour interchanges b a c e d and then erases the two braches connected to it at each end

8. Moving through the forest 1.Nearest-neighbour interchanges b a c e d b e a c d the four subtrees are now hooked together in all possible ways ((a+c) + e) + (b+d)

9. Moving through the forest 1.Nearest-neighbour interchanges b a c e d b e a c d b c a e d ((a+e) + c) + (b+d)

10. Moving through the forest 1.Nearest-neighbour interchanges b a c e d b e a c d b c a e d b a c e d now a second internal branch is erased and the procedure is repeated

11. Moving through the forest 1.Nearest-neighbour interchanges b a c e d b e a c d b c a e d b a c e d a b c e d b d c e a

12. Moving through the forest 1.Nearest-neighbour interchanges b a c e d b e a c d b c a e d b a c e d a b c e d b d c e a

13. b d c e a a b c e d b c e a d a d b c e b a c e d a e b d c a b d e c a d b e c a c b e d a e b c d a e c d b c a b e d a b c d e d a b c e a c d e b

14. Characters Species 123456 Alpha (a)100110 Beta (b)001000 Gamma (c)110000 Delta (d)110111 Epsilon (e)001110

15. b d c e a a b c e d b c e a d a d b c e b a c e d a e b d c a b d e c a d b e c a c b e d a e b c d a e c d b c a b e d a b c d e d a b c e a c d e b [11] [9] [10] [9] [8] [9]

16. b d c e a a b c e d b c e a d a d b c e b a c e d a e b d c a b d e c a d b e c a c b e d a e b c d a e c d b c a b e d a b c d e d a b c e a c d e b [11] [9] [10] [9] [8] [11] [9]

17. b d c e a a b c e d b c e a d a d b c e b a c e d a e b d c a b d e c a d b e c a c b e d a e b c d a e c d b c a b e d a b c d e d a b c e a c d e b [11] [9] [10] [9] [8] [11] [9]

18. b d c e a a b c e d b c e a d a d b c e b a c e d a e b d c a b d e c a d b e c a c b e d a e b c d a e c d b c a b e d a b c d e d a b c e a c d e b [11] [9] [10] [9] [8] [11] [9]

19. b d c e a a b c e d b c e a d a d b c e b a c e d a e b d c a b d e c a d b e c a c b e d a e b c d a e c d b c a b e d a b c d e d a b c e a c d e b [11] [9] [10] [9] [8] [11] [9]

20. Moving through the forest 1.Nearest-neighbour interchanges 2.Subtree pruning and regrafting (SPR) g c a d f b i h j k e in SPR, a branch with a subtree is removed…

21. Moving through the forest 1.Nearest-neighbour interchanges 2.Subtree pruning and regrafting g c a d f b i h j k e … and reinserted in all possible places.

22. Moving through the forest 1.Nearest-neighbour interchanges 2.Subtree pruning and regrafting g c a d f b i h j k e

23. Moving through the forest 1.Nearest-neighbour interchanges 2.Subtree pruning and regrafting g c a d f b i h j k e

24. Moving through the forest 1.Nearest-neighbour interchanges 2.Subtree pruning and regrafting (SPR) 3.Tree bisection and reconnection (TBR) g c a d f b i h j k e in TBR, the tree is first bisected …

25. Moving through the forest 1.Nearest-neighbour interchanges 2.Subtree pruning and regrafting 3.Tree bisection and reconnection g c a d f b i h j k e and then all possible connections are made between a branch of one subtree and a branch of the other

26. Moving through the forest 1.Nearest-neighbour interchanges 2.Subtree pruning and regrafting 3.Tree bisection and reconnection g c a d k e f b i h j

27. Moving through the forest 1.Nearest-neighbour interchanges 2.Subtree pruning and regrafting 3.Tree bisection and reconnection 4.… many more rearrangement methods exist and new ones are being developed

28. Sequential addition a b c the sequential addition strategy starts with a simple tree and adds species one by one

29. 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,...

30. 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 e c b [9] [11] [9] [7] [8] … and the most promising path is taken

31. Star decomposition a bc d e f a bc d e f a bc d 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