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■♥tr♦❞✉❝t✐♦♥ t♦ ♣❤②❧♦❣❡♥❡t✐❝s

❚❤✐❜❛✉t ❏♦♠❜❛rt ✶✺ ❉❡❝❡♠❜❡r ✷✵✶✼

▼❘❈ ❈❡♥tr❡ ❢♦r ❖✉t❜r❡❛❦ ❆♥❛❧②s✐s ❛♥❞ ▼♦❞❡❧❧✐♥❣ ■♠♣❡r✐❛❧ ❈♦❧❧❡❣❡ ▲♦♥❞♦♥

❖✉t❧✐♥❡

P❤②❧♦❣❡♥✐❡s✳✳✳ ❉✐st❛♥❝❡ tr❡❡s P❛rs✐♠♦♥② ▲✐❦❡❧✐❤♦♦❞✴❇❛②❡s✐❛♥ ❯♥❝❡rt❛✐♥t② P✐t❢❛❧❧s ✫ ❜❡st ♣r❛❝t✐❝❡s ❆♥❞ ♠♦r❡✳✳✳

✶

P❤②❧♦❣❡♥❡t✐❝s✿ ❢r♦♠ t❤❡ ♦r✐❣✐♥s✳✳✳

❈✳ ❉❛r✇✐♥✱ ◆♦t❡❜♦♦❦✱ ✶✽✸✼✳ ✬❋r♦♠ t❤❡ ✜rst ❣r♦✇t❤ ♦❢ t❤❡ tr❡❡✱ ♠❛♥② ❛ ❧✐♠❜ ❛♥❞ ❜r❛♥❝❤ ❤❛s ❞❡❝❛②❡❞ ❛♥❞ ❞r♦♣♣❡❞ ♦✛❀ ❛♥❞ t❤❡s❡ ❢❛❧❧❡♥ ❜r❛♥❝❤❡s ♦❢ ✈❛r✐♦✉s s✐③❡s ♠❛② r❡♣r❡s❡♥t t❤♦s❡ ✇❤♦❧❡ ♦r❞❡rs✱ ❢❛♠✐❧✐❡s✱ ❛♥❞ ❣❡♥❡r❛ ✇❤✐❝❤ ❤❛✈❡ ♥♦✇ ♥♦ ❧✐✈✐♥❣ r❡♣r❡s❡♥t❛t✐✈❡s✱ ❛♥❞ ✇❤✐❝❤ ❛r❡ ❦♥♦✇♥ t♦ ✉s ♦♥❧② ✐♥ ❛ ❢♦ss✐❧ st❛t❡✳✬

✷

P❤②❧♦❣❡♥❡t✐❝s✿ ✳✳✳t♦ t❤❡ ♣r❡s❡♥t

❇✐♥✐♥❞❛✲❊♠♦♥❞s ❡t ❛❧✳✱ ✷✵✵✼✱ ◆❛t✉r❡✳

• ♣❤②❧♦❣❡♥❡t✐❝ tr❡❡s ❛r❡ ♣❛rt ♦❢ t❤❡

st❛♥❞❛r❞ t♦♦❧❜♦① ♦❢ ❣❡♥❡t✐❝ ❞❛t❛ ❛♥❛❧②s✐s

• r❡♣r❡s❡♥t t❤❡ ❡✈♦❧✉t✐♦♥❛r② ❤✐st♦r② ♦❢

❛ s❡t ♦❢ ✭s❛♠♣❧❡❞✮ t❛①❛

✸

❆♥❞ t❤❡ ♠❛✐♥ ❞✐✛❡r❡♥❝❡ ✐s✳✳✳

❈✉rr❡♥t tr❡❡s ❧♦♦❦ ❜❡tt❡r✦ ✭❛♥❞ s♦♠❡ ♦t❤❡r ♠✐♥♦r ❞✐✛❡r❡♥❝❡s✮

✹

❆♥❞ t❤❡ ♠❛✐♥ ❞✐✛❡r❡♥❝❡ ✐s✳✳✳

❈✉rr❡♥t tr❡❡s ❧♦♦❦ ❜❡tt❡r✦ ✭❛♥❞ s♦♠❡ ♦t❤❡r ♠✐♥♦r ❞✐✛❡r❡♥❝❡s✮

✹

❆♥❞ t❤❡ ♠❛✐♥ ❞✐✛❡r❡♥❝❡ ✐s✳✳✳

❈✉rr❡♥t tr❡❡s ❧♦♦❦ ❜❡tt❡r✦ ✭❛♥❞ s♦♠❡ ♦t❤❡r ♠✐♥♦r ❞✐✛❡r❡♥❝❡s✮

✹

❆❜♦✉t t❤❡ ♠✐♥♦r ❞✐✛❡r❡♥❝❡s✳✳✳

• ❉◆❆ s❡q✉❡♥❝✐♥❣ r❡✈♦❧✉t✐♦♥
• ❤✉❣❡ ❞❛t❛ ❜❛♥❦s ❢r❡❡❧② ❛✈❛✐❧❛❜❧❡

✭❡✳❣✳ ●❡♥❇❛♥❦✮

• ❡❛s✐❡r✱ ❝❤❡❛♣❡r✱ ❢❛st❡r t♦ ♦❜t❛✐♥

❉◆❆ s❡q✉❡♥❝❡s

• ✐♥❝r❡❛s✐♥❣ ♥✉♠❜❡r ♦❢ ❢✉❧❧ ❣❡♥♦♠❡s

❛✈❛✐❧❛❜❧❡ ❉✐✛❡r❡♥t ✇❛②s t♦ ❡①♣❧♦✐t t❤✐s ✐♥❢♦r♠❛t✐♦♥✳

✺

❆❜♦✉t t❤❡ ♠✐♥♦r ❞✐✛❡r❡♥❝❡s✳✳✳

• ❉◆❆ s❡q✉❡♥❝✐♥❣ r❡✈♦❧✉t✐♦♥
• ❤✉❣❡ ❞❛t❛ ❜❛♥❦s ❢r❡❡❧② ❛✈❛✐❧❛❜❧❡

✭❡✳❣✳ ●❡♥❇❛♥❦✮

• ❡❛s✐❡r✱ ❝❤❡❛♣❡r✱ ❢❛st❡r t♦ ♦❜t❛✐♥

❉◆❆ s❡q✉❡♥❝❡s

• ✐♥❝r❡❛s✐♥❣ ♥✉♠❜❡r ♦❢ ❢✉❧❧ ❣❡♥♦♠❡s

❛✈❛✐❧❛❜❧❡ ❉✐✛❡r❡♥t ✇❛②s t♦ ❡①♣❧♦✐t t❤✐s ✐♥❢♦r♠❛t✐♦♥✳

✺

❖✉t❧✐♥❡

P❤②❧♦❣❡♥✐❡s✳✳✳ ❉✐st❛♥❝❡ tr❡❡s P❛rs✐♠♦♥② ▲✐❦❡❧✐❤♦♦❞✴❇❛②❡s✐❛♥ ❯♥❝❡rt❛✐♥t② P✐t❢❛❧❧s ✫ ❜❡st ♣r❛❝t✐❝❡s ❆♥❞ ♠♦r❡✳✳✳

✻

• ❡♥❡t✐❝ ❝❤❛♥❣❡s ✭s✉❜st✐t✉t✐♦♥✮ ❛❝❝✉♠✉❧❛t❡ ♦✈❡r t✐♠❡

❙✉❜st✐t✉t✐♦♥✿ r❡♣❧❛❝❡♠❡♥t ♦❢ ❛ ♥✉❝❧❡♦t✐❞❡ ✭❡✳❣✳ ❛ → t✮

...attgtacgtaggatctagg... ...attgaacgtaggatctagg... ...attgtacgtaccatctagg... ...atcgtacgtaccatctggg... ...attgaacgtagttgctagg...

Time

❙✉❜st✐t✉t✐♦♥ ♣❛tt❡r♥s r❡✢❡❝t t❤❡ ❡✈♦❧✉t✐♦♥❛r② ❤✐st♦r②

✼

• ❡♥❡t✐❝ ❝❤❛♥❣❡s ✭s✉❜st✐t✉t✐♦♥✮ ❛❝❝✉♠✉❧❛t❡ ♦✈❡r t✐♠❡

❙✉❜st✐t✉t✐♦♥✿ r❡♣❧❛❝❡♠❡♥t ♦❢ ❛ ♥✉❝❧❡♦t✐❞❡ ✭❡✳❣✳ ❛ → t✮

...attgaacgtagttgctagg... ...atcgtacgtaccatctggg... ...attgaacgtaggatctagg... ...attgtacgtaccatctagg...

Time

...attgtacgtaggatctagg...

❙✉❜st✐t✉t✐♦♥ ♣❛tt❡r♥s r❡✢❡❝t t❤❡ ❡✈♦❧✉t✐♦♥❛r② ❤✐st♦r②

✼

• ❡♥❡t✐❝ ❝❤❛♥❣❡s ✭s✉❜st✐t✉t✐♦♥✮ ❛❝❝✉♠✉❧❛t❡ ♦✈❡r t✐♠❡

❙✉❜st✐t✉t✐♦♥✿ r❡♣❧❛❝❡♠❡♥t ♦❢ ❛ ♥✉❝❧❡♦t✐❞❡ ✭❡✳❣✳ ❛ → t✮

...attgaacgtagttgctagg... ...atcgtacgtaccatctggg...

Time

...attgtacgtaggatctagg... ...attgaacgtaggatctagg... ...attgtacgtaccatctagg...

❙✉❜st✐t✉t✐♦♥ ♣❛tt❡r♥s r❡✢❡❝t t❤❡ ❡✈♦❧✉t✐♦♥❛r② ❤✐st♦r②

✼

• ❡♥❡t✐❝ ❝❤❛♥❣❡s ✭s✉❜st✐t✉t✐♦♥✮ ❛❝❝✉♠✉❧❛t❡ ♦✈❡r t✐♠❡

❙✉❜st✐t✉t✐♦♥✿ r❡♣❧❛❝❡♠❡♥t ♦❢ ❛ ♥✉❝❧❡♦t✐❞❡ ✭❡✳❣✳ ❛ → t✮

Time

...attgtacgtaggatctagg... ...attgaacgtaggatctagg... ...attgtacgtaccatctagg... ...atcgtacgtaccatctggg... ...attgaacgtagttgctagg...

❙✉❜st✐t✉t✐♦♥ ♣❛tt❡r♥s r❡✢❡❝t t❤❡ ❡✈♦❧✉t✐♦♥❛r② ❤✐st♦r②

✼

• ❡♥❡t✐❝ ❝❤❛♥❣❡s ✭s✉❜st✐t✉t✐♦♥✮ ❛❝❝✉♠✉❧❛t❡ ♦✈❡r t✐♠❡

❙✉❜st✐t✉t✐♦♥✿ r❡♣❧❛❝❡♠❡♥t ♦❢ ❛ ♥✉❝❧❡♦t✐❞❡ ✭❡✳❣✳ ❛ → t✮

Time

...attgtacgtaggatctagg... ...attgaacgtaggatctagg... ...attgtacgtaccatctagg... ...atcgtacgtaccatctggg... ...attgaacgtagttgctagg...

❙✉❜st✐t✉t✐♦♥ ♣❛tt❡r♥s r❡✢❡❝t t❤❡ ❡✈♦❧✉t✐♦♥❛r② ❤✐st♦r②

✼

• ❡♥❡t✐❝ ❝❤❛♥❣❡s ✭s✉❜st✐t✉t✐♦♥✮ ❛❝❝✉♠✉❧❛t❡ ♦✈❡r t✐♠❡

❙✉❜st✐t✉t✐♦♥✿ r❡♣❧❛❝❡♠❡♥t ♦❢ ❛ ♥✉❝❧❡♦t✐❞❡ ✭❡✳❣✳ ❛ → t✮

Time

...attgtacgtaggatctagg... ...attgaacgtaggatctagg... ...attgtacgtaccatctagg... ...atcgtacgtaccatctggg... ...attgaacgtagttgctagg...

❙✉❜st✐t✉t✐♦♥ ♣❛tt❡r♥s r❡✢❡❝t t❤❡ ❡✈♦❧✉t✐♦♥❛r② ❤✐st♦r②

✼

❯s✐♥❣ s✉❜st✐t✉t✐♦♥ ♣❛tt❡r♥s t♦ r❡❝♦♥str✉❝t t❤❡ ❡✈♦❧✉t✐♦♥❛r② ❤✐st♦r②

Reconstructed phylogeny

...attaaacgtaggatctagg... ...attaaacgtaggatctagg... ...attcatacgtaggatcagg... ...attgtacgtaggatctttt... ...attgtacgtaggatctttt... ...attgcatgtaggatctttt...

P❤②❧♦❣❡♥❡t✐❝s ❛✐♠ t♦ r❡❝♦♥str✉❝t ❡✈♦❧✉t✐♦♥❛r② tr❡❡s ✭♣❤②❧♦❣❡♥✐❡s✮ ❢r♦♠ ❣❡♥❡t✐❝ s❡q✉❡♥❝❡ ❞❛t❛✳

✽

❯s✐♥❣ s✉❜st✐t✉t✐♦♥ ♣❛tt❡r♥s t♦ r❡❝♦♥str✉❝t t❤❡ ❡✈♦❧✉t✐♦♥❛r② ❤✐st♦r②

...attaaacgtaggatctagg... ...attaaacgtaggatctagg... ...attcatacgtaggatcagg... ...attgtacgtaggatctttt... ...attgtacgtaggatctttt... ...attgcatgtaggatctttt...

Reconstructed phylogeny

P❤②❧♦❣❡♥❡t✐❝s ❛✐♠ t♦ r❡❝♦♥str✉❝t ❡✈♦❧✉t✐♦♥❛r② tr❡❡s ✭♣❤②❧♦❣❡♥✐❡s✮ ❢r♦♠ ❣❡♥❡t✐❝ s❡q✉❡♥❝❡ ❞❛t❛✳

✽

❯s✐♥❣ s✉❜st✐t✉t✐♦♥ ♣❛tt❡r♥s t♦ r❡❝♦♥str✉❝t t❤❡ ❡✈♦❧✉t✐♦♥❛r② ❤✐st♦r②

...attaaacgtaggatctagg... ...attaaacgtaggatctagg... ...attcatacgtaggatcagg... ...attgtacgtaggatctttt... ...attgtacgtaggatctttt... ...attgcatgtaggatctttt...

Reconstructed phylogeny

P❤②❧♦❣❡♥❡t✐❝s ❛✐♠ t♦ r❡❝♦♥str✉❝t ❡✈♦❧✉t✐♦♥❛r② tr❡❡s ✭♣❤②❧♦❣❡♥✐❡s✮ ❢r♦♠ ❣❡♥❡t✐❝ s❡q✉❡♥❝❡ ❞❛t❛✳

✽

❯s✐♥❣ tr❡❡s t♦ r❡♣r❡s❡♥t t❤❡ ❡✈♦❧✉t✐♦♥❛r② ❤✐st♦r②

❍♦✇ t♦ ✇❡ ❜✉✐❧❞ t❤❡♠❄

✾

❯s✐♥❣ tr❡❡s t♦ r❡♣r❡s❡♥t t❤❡ ❡✈♦❧✉t✐♦♥❛r② ❤✐st♦r②

• "taxa"
• "tips"
• "leaves"
• "Operational Taxonomic

Units (OTUs)"

❍♦✇ t♦ ✇❡ ❜✉✐❧❞ t❤❡♠❄

✾

❯s✐♥❣ tr❡❡s t♦ r❡♣r❡s❡♥t t❤❡ ❡✈♦❧✉t✐♦♥❛r② ❤✐st♦r②

Most Recent Common Ancestors (MRCA)

• "nodes"
• "Hypothetical Taxonomic

Units (HTUs)"

❍♦✇ t♦ ✇❡ ❜✉✐❧❞ t❤❡♠❄

✾

❯s✐♥❣ tr❡❡s t♦ r❡♣r❡s❡♥t t❤❡ ❡✈♦❧✉t✐♦♥❛r② ❤✐st♦r②

• "edge"
• length = amount of evolution (not time, as a rule)
• length is optional

branch

❍♦✇ t♦ ✇❡ ❜✉✐❧❞ t❤❡♠❄

✾

❯s✐♥❣ tr❡❡s t♦ r❡♣r❡s❡♥t t❤❡ ❡✈♦❧✉t✐♦♥❛r② ❤✐st♦r②

• "patristic" distance: sum of branch lengths
• other measures of distance/dissimilarity
• vertical axis meaningless

distances between tips

❍♦✇ t♦ ✇❡ ❜✉✐❧❞ t❤❡♠❄

✾

❯s✐♥❣ tr❡❡s t♦ r❡♣r❡s❡♥t t❤❡ ❡✈♦❧✉t✐♦♥❛r② ❤✐st♦r②

Root

• oldest part of the tree
• defined using an outgroup
• optional

❍♦✇ t♦ ✇❡ ❜✉✐❧❞ t❤❡♠❄

✾

❯s✐♥❣ tr❡❡s t♦ r❡♣r❡s❡♥t t❤❡ ❡✈♦❧✉t✐♦♥❛r② ❤✐st♦r②

Root

• oldest part of the tree
• defined using an outgroup
• optional

❍♦✇ t♦ ✇❡ ❜✉✐❧❞ t❤❡♠❄

✾

❲♦r❦✢♦✇

Pr❡♣❛r❡ ❞❛t❛

• ❛❧✐❣♥ s❡q✉❡♥❝❡s✿ ❛❧✐❣♥♠❡♥t s♦❢t✇❛r❡ ✰ ♠❛♥✉❛❧ r❡✜♥❡♠❡♥t

❇✉✐❧❞ t❤❡ tr❡❡

❞✐st❛♥❝❡✲❜❛s❡❞ ♠❡t❤♦❞s ♠❛①✐♠✉♠ ♣❛rs✐♠♦♥② ❧✐❦❡❧✐❤♦♦❞✲❜❛s❡❞ ♠❡t❤♦❞s ✭▼▲✱ ❇❛②❡s✐❛♥✮

❆♥❛❧②s❡ t❤❡ tr❡❡

❛ss❡ss ✉♥❝❡rt❛✐♥t② t❡st ♣❤②❧♦❣❡♥❡t✐❝ s✐❣♥❛❧ ♠♦❞❡❧ tr❛✐t ❡✈♦❧✉t✐♦♥ ✳✳✳

✶✵

❲♦r❦✢♦✇

Pr❡♣❛r❡ ❞❛t❛

• ❛❧✐❣♥ s❡q✉❡♥❝❡s✿ ❛❧✐❣♥♠❡♥t s♦❢t✇❛r❡ ✰ ♠❛♥✉❛❧ r❡✜♥❡♠❡♥t

❇✉✐❧❞ t❤❡ tr❡❡

• ❞✐st❛♥❝❡✲❜❛s❡❞ ♠❡t❤♦❞s
• ♠❛①✐♠✉♠ ♣❛rs✐♠♦♥②
• ❧✐❦❡❧✐❤♦♦❞✲❜❛s❡❞ ♠❡t❤♦❞s ✭▼▲✱ ❇❛②❡s✐❛♥✮

❆♥❛❧②s❡ t❤❡ tr❡❡

❛ss❡ss ✉♥❝❡rt❛✐♥t② t❡st ♣❤②❧♦❣❡♥❡t✐❝ s✐❣♥❛❧ ♠♦❞❡❧ tr❛✐t ❡✈♦❧✉t✐♦♥ ✳✳✳

✶✵

❲♦r❦✢♦✇

Pr❡♣❛r❡ ❞❛t❛

• ❛❧✐❣♥ s❡q✉❡♥❝❡s✿ ❛❧✐❣♥♠❡♥t s♦❢t✇❛r❡ ✰ ♠❛♥✉❛❧ r❡✜♥❡♠❡♥t

❇✉✐❧❞ t❤❡ tr❡❡

• ❞✐st❛♥❝❡✲❜❛s❡❞ ♠❡t❤♦❞s
• ♠❛①✐♠✉♠ ♣❛rs✐♠♦♥②
• ❧✐❦❡❧✐❤♦♦❞✲❜❛s❡❞ ♠❡t❤♦❞s ✭▼▲✱ ❇❛②❡s✐❛♥✮

❆♥❛❧②s❡ t❤❡ tr❡❡

• ❛ss❡ss ✉♥❝❡rt❛✐♥t②
• t❡st ♣❤②❧♦❣❡♥❡t✐❝ s✐❣♥❛❧
• ♠♦❞❡❧ tr❛✐t ❡✈♦❧✉t✐♦♥
• ✳✳✳

✶✵

❲♦r❦✢♦✇

Pr❡♣❛r❡ ❞❛t❛

• ❛❧✐❣♥ s❡q✉❡♥❝❡s✿ ❛❧✐❣♥♠❡♥t s♦❢t✇❛r❡ ✰ ♠❛♥✉❛❧ r❡✜♥❡♠❡♥t

❇✉✐❧❞ t❤❡ tr❡❡

• ❞✐st❛♥❝❡✲❜❛s❡❞ ♠❡t❤♦❞s
• ♠❛①✐♠✉♠ ♣❛rs✐♠♦♥②
• ❧✐❦❡❧✐❤♦♦❞✲❜❛s❡❞ ♠❡t❤♦❞s ✭▼▲✱ ❇❛②❡s✐❛♥✮

❆♥❛❧②s❡ t❤❡ tr❡❡

• ❛ss❡ss ✉♥❝❡rt❛✐♥t②
• t❡st ♣❤②❧♦❣❡♥❡t✐❝ s✐❣♥❛❧
• ♠♦❞❡❧ tr❛✐t ❡✈♦❧✉t✐♦♥
• ✳✳✳

✶✵

❖✉t❧✐♥❡

P❤②❧♦❣❡♥✐❡s✳✳✳ ❉✐st❛♥❝❡ tr❡❡s P❛rs✐♠♦♥② ▲✐❦❡❧✐❤♦♦❞✴❇❛②❡s✐❛♥ ❯♥❝❡rt❛✐♥t② P✐t❢❛❧❧s ✫ ❜❡st ♣r❛❝t✐❝❡s ❆♥❞ ♠♦r❡✳✳✳

✶✶

❉✐st❛♥❝❡✲❜❛s❡❞ ♣❤②❧♦❣❡♥❡t✐❝ r❡❝♦♥str✉❝t✐♦♥

❆♣♣r♦❛❝❤❡s r❡❧②✐♥❣ ♦♥ ❛❣❣❧♦♠❡r❛t✐✈❡ ❝❧✉st❡r✐♥❣ ❛❧❣♦r✐t❤♠s ✭❡✳❣✳ ❙✐♥❣❧❡ ❧✐♥❦❛❣❡✱ ❯P●▼❆✱ ◆❡✐❣❤❜♦r✲❏♦✐♥✐♥❣✮ ❘❛t✐♦♥❛❧❡ ✶✳ ❝♦♠♣✉t❡ ♣❛✐r✇✐s❡ ❣❡♥❡t✐❝ ❞✐st❛♥❝❡s D ✷✳ ❣r♦✉♣ ❝❧♦s❡st s❡q✉❡♥❝❡s ✸✳ ✉♣❞❛t❡ D ✹✳ ❣♦ ❜❛❝❦ t♦ ✷✮ ✉♥t✐❧ ❛❧❧ s❡q✉❡♥❝❡s ❛r❡ ❣r♦✉♣❡❞

✶✷

❉✐st❛♥❝❡✲❜❛s❡❞ ♣❤②❧♦❣❡♥❡t✐❝ r❡❝♦♥str✉❝t✐♦♥

✶✸

❉✐st❛♥❝❡✲❜❛s❡❞ ♣❤②❧♦❣❡♥❡t✐❝ r❡❝♦♥str✉❝t✐♦♥

✶✸

❉✐st❛♥❝❡✲❜❛s❡❞ ♣❤②❧♦❣❡♥❡t✐❝ r❡❝♦♥str✉❝t✐♦♥

✶✸

❉✐st❛♥❝❡✲❜❛s❡❞ ♣❤②❧♦❣❡♥❡t✐❝ r❡❝♦♥str✉❝t✐♦♥

✶✸

❉✐st❛♥❝❡✲❜❛s❡❞ ♣❤②❧♦❣❡♥❡t✐❝ r❡❝♦♥str✉❝t✐♦♥

✶✸

❉✐st❛♥❝❡✲❜❛s❡❞ ♣❤②❧♦❣❡♥❡t✐❝ r❡❝♦♥str✉❝t✐♦♥

✶✸

❲❤❛t ✐s t❤❡ ❞✐st❛♥❝❡ ❜❡t✇❡❡♥ ❛ ♥♦❞❡ ❛♥❞ t✐♣s❄

❍✐❡r❛r❝❤✐❝❛❧ ❝❧✉st❡r✐♥❣✿

k i j

Di,j

g

D =...

k,g

s✐♥❣❧❡ ❧✐♥❦❛❣❡✿ ♠✐♥ ❝♦♠♣❧❡t❡ ❧✐♥❦❛❣❡✿ ♠❛① ❯P●▼❆✿ ◆❡✐❣❤❜♦r ❥♦✐♥✐♥❣✿ ❚r❛♥s❢♦r♠s ♦r✐❣✐♥❛❧ ❞✐st❛♥❝❡s t♦ ❛❝❝♦✉♥t ❢♦r ❤❡t❡r♦❣❡♥❡♦✉s r❛t❡s ♦❢ ❡✈♦❧✉t✐♦♥✳

✶✹

❲❤❛t ✐s t❤❡ ❞✐st❛♥❝❡ ❜❡t✇❡❡♥ ❛ ♥♦❞❡ ❛♥❞ t✐♣s❄

❍✐❡r❛r❝❤✐❝❛❧ ❝❧✉st❡r✐♥❣✿

k i j

Di,j

g

D =...

k,g

• s✐♥❣❧❡ ❧✐♥❦❛❣❡✿ Dk,g = ♠✐♥(Dk,i, Dk,j)

❝♦♠♣❧❡t❡ ❧✐♥❦❛❣❡✿ ♠❛① ❯P●▼❆✿ ◆❡✐❣❤❜♦r ❥♦✐♥✐♥❣✿ ❚r❛♥s❢♦r♠s ♦r✐❣✐♥❛❧ ❞✐st❛♥❝❡s t♦ ❛❝❝♦✉♥t ❢♦r ❤❡t❡r♦❣❡♥❡♦✉s r❛t❡s ♦❢ ❡✈♦❧✉t✐♦♥✳

✶✹

❲❤❛t ✐s t❤❡ ❞✐st❛♥❝❡ ❜❡t✇❡❡♥ ❛ ♥♦❞❡ ❛♥❞ t✐♣s❄

❍✐❡r❛r❝❤✐❝❛❧ ❝❧✉st❡r✐♥❣✿

k i j

Di,j

g

D =...

k,g

• s✐♥❣❧❡ ❧✐♥❦❛❣❡✿ Dk,g = ♠✐♥(Dk,i, Dk,j)
• ❝♦♠♣❧❡t❡ ❧✐♥❦❛❣❡✿ Dk,g = ♠❛①(Dk,i, Dk,j)

❯P●▼❆✿ ◆❡✐❣❤❜♦r ❥♦✐♥✐♥❣✿ ❚r❛♥s❢♦r♠s ♦r✐❣✐♥❛❧ ❞✐st❛♥❝❡s t♦ ❛❝❝♦✉♥t ❢♦r ❤❡t❡r♦❣❡♥❡♦✉s r❛t❡s ♦❢ ❡✈♦❧✉t✐♦♥✳

✶✹

❲❤❛t ✐s t❤❡ ❞✐st❛♥❝❡ ❜❡t✇❡❡♥ ❛ ♥♦❞❡ ❛♥❞ t✐♣s❄

❍✐❡r❛r❝❤✐❝❛❧ ❝❧✉st❡r✐♥❣✿

k i j

Di,j

g

D =...

k,g

• s✐♥❣❧❡ ❧✐♥❦❛❣❡✿ Dk,g = ♠✐♥(Dk,i, Dk,j)
• ❝♦♠♣❧❡t❡ ❧✐♥❦❛❣❡✿ Dk,g = ♠❛①(Dk,i, Dk,j)
• ❯P●▼❆✿ Dk,g = Dk,i+Dk,j

2

◆❡✐❣❤❜♦r ❥♦✐♥✐♥❣✿ ❚r❛♥s❢♦r♠s ♦r✐❣✐♥❛❧ ❞✐st❛♥❝❡s t♦ ❛❝❝♦✉♥t ❢♦r ❤❡t❡r♦❣❡♥❡♦✉s r❛t❡s ♦❢ ❡✈♦❧✉t✐♦♥✳

✶✹

❲❤❛t ✐s t❤❡ ❞✐st❛♥❝❡ ❜❡t✇❡❡♥ ❛ ♥♦❞❡ ❛♥❞ t✐♣s❄

❍✐❡r❛r❝❤✐❝❛❧ ❝❧✉st❡r✐♥❣✿

k i j

Di,j

g

D =...

k,g

• s✐♥❣❧❡ ❧✐♥❦❛❣❡✿ Dk,g = ♠✐♥(Dk,i, Dk,j)
• ❝♦♠♣❧❡t❡ ❧✐♥❦❛❣❡✿ Dk,g = ♠❛①(Dk,i, Dk,j)
• ❯P●▼❆✿ Dk,g = Dk,i+Dk,j

2

◆❡✐❣❤❜♦r ❥♦✐♥✐♥❣✿ ❚r❛♥s❢♦r♠s ♦r✐❣✐♥❛❧ ❞✐st❛♥❝❡s t♦ ❛❝❝♦✉♥t ❢♦r ❤❡t❡r♦❣❡♥❡♦✉s r❛t❡s ♦❢ ❡✈♦❧✉t✐♦♥✳

✶✹

❉✐st❛♥❝❡✲❜❛s❡❞ ♣❤②❧♦❣❡♥❡t✐❝ r❡❝♦♥str✉❝t✐♦♥

❆❞✈❛♥t❛❣❡s

• s✐♠♣❧❡
• ✢❡①✐❜❧❡ ✭♠❛♥② ❞✐st❛♥❝❡s ❛♥❞ ❝❧✉st❡r✐♥❣ ❛❧❣♦r✐t❤♠s✮
• ❢❛st ❛♥❞ s❝❛❧❛❜❧❡ ✭❛♣♣❧✐❝❛❜❧❡ t♦ ❧❛r❣❡ ❞❛t❛s❡ts✮

▲✐♠✐t❛t✐♦♥s s❡♥s✐t✐✈❡ t♦ ❞✐st❛♥❝❡✴❝❧✉st❡r✐♥❣ ❝❤♦s❡♥ ❡✈♦❧✉t✐♦♥❛r② r❛t❡s ❛r❡ ♥♦t ❡st✐♠❛t❡❞ ♥♦ ♠❡❛s✉r❡ ♦❢ ✉♥❝❡rt❛✐♥t② ❢♦r t❤❡ tr❡❡ ♦❜t❛✐♥❡❞

✶✺

❉✐st❛♥❝❡✲❜❛s❡❞ ♣❤②❧♦❣❡♥❡t✐❝ r❡❝♦♥str✉❝t✐♦♥

❆❞✈❛♥t❛❣❡s

• s✐♠♣❧❡
• ✢❡①✐❜❧❡ ✭♠❛♥② ❞✐st❛♥❝❡s ❛♥❞ ❝❧✉st❡r✐♥❣ ❛❧❣♦r✐t❤♠s✮
• ❢❛st ❛♥❞ s❝❛❧❛❜❧❡ ✭❛♣♣❧✐❝❛❜❧❡ t♦ ❧❛r❣❡ ❞❛t❛s❡ts✮

▲✐♠✐t❛t✐♦♥s

• s❡♥s✐t✐✈❡ t♦ ❞✐st❛♥❝❡✴❝❧✉st❡r✐♥❣ ❝❤♦s❡♥
• ❡✈♦❧✉t✐♦♥❛r② r❛t❡s ❛r❡ ♥♦t ❡st✐♠❛t❡❞
• ♥♦ ♠❡❛s✉r❡ ♦❢ ✉♥❝❡rt❛✐♥t② ❢♦r t❤❡ tr❡❡ ♦❜t❛✐♥❡❞

✶✺

❖✉t❧✐♥❡

P❤②❧♦❣❡♥✐❡s✳✳✳ ❉✐st❛♥❝❡ tr❡❡s P❛rs✐♠♦♥② ▲✐❦❡❧✐❤♦♦❞✴❇❛②❡s✐❛♥ ❯♥❝❡rt❛✐♥t② P✐t❢❛❧❧s ✫ ❜❡st ♣r❛❝t✐❝❡s ❆♥❞ ♠♦r❡✳✳✳

✶✻

▼❛①✐♠✉♠ ♣❛rs✐♠♦♥② ♣❤②❧♦❣❡♥✐❡s

❆♣♣r♦❛❝❤❡s r❡❧②✐♥❣ ♦♥ ✜♥❞✐♥❣ t❤❡ tr❡❡ ✇✐t❤ t❤❡ s♠❛❧❧❡st ♥✉♠❜❡r ♦❢ ❝❤❛r❛❝t❡r ❝❤❛♥❣❡s ✭s✉❜st✐t✉t✐♦♥s✮ ❘❛t✐♦♥❛❧❡ ✶✳ st❛rt ❢r♦♠ ❛ ♣r❡✲❞❡✜♥❡❞ tr❡❡ ✷✳ ❝♦♠♣✉t❡ ✐♥✐t✐❛❧ ♣❛rs✐♠♦♥② s❝♦r❡ ✸✳ ♣❡r♠✉t❡ ❜r❛♥❝❤❡s ❛♥❞ ❝♦♠♣✉t❡ ♣❛rs✐♠♦♥② s❝♦r❡ ✹✳ ❛❝❝❡♣t ♥❡✇ tr❡❡ ✐❢ t❤❡ ♣❛rs✐♠♦♥② s❝♦r❡ ✐s ✐♠♣r♦✈❡❞ ✺✳ ❣♦ ❜❛❝❦ t♦ ✸✮ ✉♥t✐❧ ❝♦♥✈❡r❣❡♥❝❡

✶✼

▼❛①✐♠✉♠ ♣❛rs✐♠♦♥② ♣❤②❧♦❣❡♥✐❡s

score: 8 score: 5 score: 6

Initial tree

✶✽

▼❛①✐♠✉♠ ♣❛rs✐♠♦♥② ♣❤②❧♦❣❡♥✐❡s

score: 5 score: 6

Initial tree

score: 8

✶✽

▼❛①✐♠✉♠ ♣❛rs✐♠♦♥② ♣❤②❧♦❣❡♥✐❡s

score: 5 score: 6

Initial tree

score: 8

✶✽

▼❛①✐♠✉♠ ♣❛rs✐♠♦♥② ♣❤②❧♦❣❡♥✐❡s

score: 6

Initial tree

score: 5 score: 8

✶✽

▼❛①✐♠✉♠ ♣❛rs✐♠♦♥② ♣❤②❧♦❣❡♥✐❡s

score: 6

Initial tree

score: 5 score: 8

✶✽

▼❛①✐♠✉♠ ♣❛rs✐♠♦♥② ♣❤②❧♦❣❡♥✐❡s

❆❞✈❛♥t❛❣❡s

• ❛♣♣❧✐❝❛❜❧❡ t♦ ❛♥② ❞✐s❝♦♥t✐♥✉♦✉s ❝❤❛r❛❝t❡rs ✭♥♦t ❥✉st ❉◆❆✮
• ✐♥t✉✐t✐✈❡ ❡①♣❧❛♥❛t✐♦♥✿ ❵s✐♠♣❧❡st✬ ❡✈♦❧✉t✐♦♥❛r② s❝❡♥❛r✐♦

▲✐♠✐t❛t✐♦♥s ❡✈♦❧✉t✐♦♥❛r② r❛t❡s ❛r❡ ♥♦t ❡st✐♠❛t❡❞ ♥♦ ♠❡❛s✉r❡ ♦❢ ✉♥❝❡rt❛✐♥t② ❢♦r t❤❡ tr❡❡ ♦❜t❛✐♥❡❞ ❝♦♠♣✉t❡r✲✐♥t❡♥s✐✈❡ ❞✐✛❡r❡♥t t②♣❡s ♦❢ s✉❜st✐t✉t✐♦♥s ✐❣♥♦r❡❞ ❡✈♦❧✉t✐♦♥ ♥♦t ♥❡❝❡ss❛r✐❧② ♣❛rs✐♠♦♥✐♦✉s s❡♥s✐t✐✈❡ t♦ ❤❡t❡r♦❣❡♥❡♦✉s r❛t❡s ♦❢ ❡✈♦❧✉t✐♦♥ ✭❧♦♥❣ ❜r❛♥❝❤ ❛ttr❛❝t✐♦♥✮

✶✾

▼❛①✐♠✉♠ ♣❛rs✐♠♦♥② ♣❤②❧♦❣❡♥✐❡s

❆❞✈❛♥t❛❣❡s

• ❛♣♣❧✐❝❛❜❧❡ t♦ ❛♥② ❞✐s❝♦♥t✐♥✉♦✉s ❝❤❛r❛❝t❡rs ✭♥♦t ❥✉st ❉◆❆✮
• ✐♥t✉✐t✐✈❡ ❡①♣❧❛♥❛t✐♦♥✿ ❵s✐♠♣❧❡st✬ ❡✈♦❧✉t✐♦♥❛r② s❝❡♥❛r✐♦

▲✐♠✐t❛t✐♦♥s

• ❡✈♦❧✉t✐♦♥❛r② r❛t❡s ❛r❡ ♥♦t ❡st✐♠❛t❡❞
• ♥♦ ♠❡❛s✉r❡ ♦❢ ✉♥❝❡rt❛✐♥t② ❢♦r t❤❡ tr❡❡ ♦❜t❛✐♥❡❞
• ❝♦♠♣✉t❡r✲✐♥t❡♥s✐✈❡
• ❞✐✛❡r❡♥t t②♣❡s ♦❢ s✉❜st✐t✉t✐♦♥s ✐❣♥♦r❡❞
• ❡✈♦❧✉t✐♦♥ ♥♦t ♥❡❝❡ss❛r✐❧② ♣❛rs✐♠♦♥✐♦✉s
• s❡♥s✐t✐✈❡ t♦ ❤❡t❡r♦❣❡♥❡♦✉s r❛t❡s ♦❢ ❡✈♦❧✉t✐♦♥ ✭❧♦♥❣ ❜r❛♥❝❤

❛ttr❛❝t✐♦♥✮

✶✾

❖✉t❧✐♥❡

P❤②❧♦❣❡♥✐❡s✳✳✳ ❉✐st❛♥❝❡ tr❡❡s P❛rs✐♠♦♥② ▲✐❦❡❧✐❤♦♦❞✴❇❛②❡s✐❛♥ ❯♥❝❡rt❛✐♥t② P✐t❢❛❧❧s ✫ ❜❡st ♣r❛❝t✐❝❡s ❆♥❞ ♠♦r❡✳✳✳

✷✵

▲✐❦❡❧✐❤♦♦❞✲❜❛s❡❞ ♣❤②❧♦❣❡♥✐❡s ✭▼▲ ✴ ❇❛②❡s✐❛♥✮

❆♣♣r♦❛❝❤❡s r❡❧②✐♥❣ ♦♥ ❛ ♠♦❞❡❧ ♦❢ s❡q✉❡♥❝❡ ❡✈♦❧✉t✐♦♥✿

• ▼▲✿ ✜♥❞ tr❡❡ ❛♥❞ ❡✈♦❧✉t✐♦♥❛r② r❛t❡s ✇✐t❤ ❤✐❣❤❡st ❧✐❦❡❧✐❤♦♦❞
• ❇❛②❡s✐❛♥✿ ✜♥❞ tr❡❡ ❛♥❞ ❡✈♦❧✉t✐♦♥❛r② r❛t❡s t♦ ♣♦st❡r✐♦r

♣r♦❜❛❜✐❧✐t② ❘❛t✐♦♥❛❧❡ ✶✳ st❛rt ❢r♦♠ ❛ ♣r❡✲❞❡✜♥❡❞ tr❡❡ ✷✳ ❝♦♠♣✉t❡ ✐♥✐t✐❛❧ ❧✐❦❡❧✐❤♦♦❞✴♣♦st❡r✐♦r ✸✳ ♣❡r♠✉t❡ ❜r❛♥❝❤❡s✱ s❛♠♣❧❡ ♥❡✇ ♣❛r❛♠❡t❡rs ❛♥❞ ❝♦♠♣✉t❡ ❧✐❦❡❧✐❤♦♦❞✴♣♦st❡r✐♦r ✹✳ ❛❝❝❡♣t ♥❡✇ tr❡❡ ❛♥❞ ♣❛r❛♠❡t❡rs ❜❛s❡❞ ♦♥ ❧✐❦❡❧✐❤♦♦❞✴♣♦st❡r✐♦r ✐♠♣r♦✈❡♠❡♥t ✺✳ ❣♦ ❜❛❝❦ t♦ ✸✮ ✉♥t✐❧ ❝♦♥✈❡r❣❡♥❝❡

✷✶

▲✐❦❡❧✐❤♦♦❞✲❜❛s❡❞ ♣❤②❧♦❣❡♥✐❡s ✭▼▲ ✴ ❇❛②❡s✐❛♥✮

❆♣♣r♦❛❝❤❡s r❡❧②✐♥❣ ♦♥ ❛ ♠♦❞❡❧ ♦❢ s❡q✉❡♥❝❡ ❡✈♦❧✉t✐♦♥✿

• ▼▲✿ ✜♥❞ tr❡❡ ❛♥❞ ❡✈♦❧✉t✐♦♥❛r② r❛t❡s ✇✐t❤ ❤✐❣❤❡st ❧✐❦❡❧✐❤♦♦❞
• ❇❛②❡s✐❛♥✿ ✜♥❞ tr❡❡ ❛♥❞ ❡✈♦❧✉t✐♦♥❛r② r❛t❡s t♦ ♣♦st❡r✐♦r

♣r♦❜❛❜✐❧✐t② ❘❛t✐♦♥❛❧❡ ✶✳ st❛rt ❢r♦♠ ❛ ♣r❡✲❞❡✜♥❡❞ tr❡❡ ✷✳ ❝♦♠♣✉t❡ ✐♥✐t✐❛❧ ❧✐❦❡❧✐❤♦♦❞✴♣♦st❡r✐♦r ✸✳ ♣❡r♠✉t❡ ❜r❛♥❝❤❡s✱ s❛♠♣❧❡ ♥❡✇ ♣❛r❛♠❡t❡rs ❛♥❞ ❝♦♠♣✉t❡ ❧✐❦❡❧✐❤♦♦❞✴♣♦st❡r✐♦r ✹✳ ❛❝❝❡♣t ♥❡✇ tr❡❡ ❛♥❞ ♣❛r❛♠❡t❡rs ❜❛s❡❞ ♦♥ ❧✐❦❡❧✐❤♦♦❞✴♣♦st❡r✐♦r ✐♠♣r♦✈❡♠❡♥t ✺✳ ❣♦ ❜❛❝❦ t♦ ✸✮ ✉♥t✐❧ ❝♦♥✈❡r❣❡♥❝❡

✷✶

▲✐❦❡❧✐❤♦♦❞✲❜❛s❡❞ ♣❤②❧♦❣❡♥✐❡s ✭▼▲ ✴ ❇❛②❡s✐❛♥✮

Density

Likelihood / Posterior ✷✷

▲✐❦❡❧✐❤♦♦❞✲❜❛s❡❞ ♣❤②❧♦❣❡♥✐❡s ✭▼▲ ✴ ❇❛②❡s✐❛♥✮

❆❞✈❛♥t❛❣❡s

• ✈❡r② ✢❡①✐❜❧❡
• ❝♦♥s✐st❡♥t ✇✐t❤ ❛ ♠♦❞❡❧ ♦❢ ❡✈♦❧✉t✐♦♥
• st❛t✐st✐❝❛❧❧② ❝♦♥s✐st❡♥t ✭♠♦❞❡❧ ❝♦♠♣❛r✐s♦♥✮
• ♣❛r❛♠❡t❡r ❡st✐♠❛t✐♦♥
• ✭❇❛②❡s✐❛♥✮ s❡✈❡r❛❧ tr❡❡s → ♠❡❛s✉r❡ ♦❢ ✉♥❝❡rt❛✐♥t②

▲✐♠✐t❛t✐♦♥s ❝♦♠♣✉t❡r✲✐♥t❡♥s✐✈❡ ❝❤♦✐❝❡ ♦❢ t❤❡ ♠♦❞❡❧ ♦❢ ❡✈♦❧✉t✐♦♥ ✭▼▲✮ ♥♦ ♠❡❛s✉r❡ ♦❢ ✉♥❝❡rt❛✐♥t② ❢♦r t❤❡ tr❡❡ ♦❜t❛✐♥❡❞ ✭❇❛②❡s✐❛♥✮ ♥❡❡❞ t♦ ✜♥❞ ❛ ❝♦♥s❡♥s✉s tr❡❡

✷✸

▲✐❦❡❧✐❤♦♦❞✲❜❛s❡❞ ♣❤②❧♦❣❡♥✐❡s ✭▼▲ ✴ ❇❛②❡s✐❛♥✮

❆❞✈❛♥t❛❣❡s

• ✈❡r② ✢❡①✐❜❧❡
• ❝♦♥s✐st❡♥t ✇✐t❤ ❛ ♠♦❞❡❧ ♦❢ ❡✈♦❧✉t✐♦♥
• st❛t✐st✐❝❛❧❧② ❝♦♥s✐st❡♥t ✭♠♦❞❡❧ ❝♦♠♣❛r✐s♦♥✮
• ♣❛r❛♠❡t❡r ❡st✐♠❛t✐♦♥
• ✭❇❛②❡s✐❛♥✮ s❡✈❡r❛❧ tr❡❡s → ♠❡❛s✉r❡ ♦❢ ✉♥❝❡rt❛✐♥t②

▲✐♠✐t❛t✐♦♥s

• ❝♦♠♣✉t❡r✲✐♥t❡♥s✐✈❡
• ❝❤♦✐❝❡ ♦❢ t❤❡ ♠♦❞❡❧ ♦❢ ❡✈♦❧✉t✐♦♥
• ✭▼▲✮ ♥♦ ♠❡❛s✉r❡ ♦❢ ✉♥❝❡rt❛✐♥t② ❢♦r t❤❡ tr❡❡ ♦❜t❛✐♥❡❞
• ✭❇❛②❡s✐❛♥✮ ♥❡❡❞ t♦ ✜♥❞ ❛ ❝♦♥s❡♥s✉s tr❡❡

✷✸

❖✉t❧✐♥❡

P❤②❧♦❣❡♥✐❡s✳✳✳ ❉✐st❛♥❝❡ tr❡❡s P❛rs✐♠♦♥② ▲✐❦❡❧✐❤♦♦❞✴❇❛②❡s✐❛♥ ❯♥❝❡rt❛✐♥t② P✐t❢❛❧❧s ✫ ❜❡st ♣r❛❝t✐❝❡s ❆♥❞ ♠♦r❡✳✳✳

✷✹

❍♦✇ ❞♦ ✇❡ ❦♥♦✇ t❤❡ tr❡❡ ✐s r♦❜✉st❄

▼❛✐♥ ✐ss✉❡✿ ❛ss❡ss t❤❡ ✉♥❝❡rt❛✐♥t② ♦❢ t❤❡ tr❡❡ t♦♣♦❧♦❣② ✴ ✐♥❞✐✈✐❞✉❛❧ ♥♦❞❡s ❆♣♣r♦❛❝❤❡s ▼▲✿ ♠♦❞❡❧ s❡❧❡❝t✐♦♥ t♦ ❝♦♠♣❛r❡ tr❡❡s ✭✇❤♦❧❡ tr❡❡✮ ❇❛②❡s✐❛♥ ♠❡t❤♦❞s✿ ❜❡t✇❡❡♥✲s❛♠♣❧❡s ✈❛r✐❛❜✐❧✐t② ✭✐♥❞✐✈✐❞✉❛❧ ♥♦❞❡s✮ ❛♥② ♠❡t❤♦❞✿ ❜♦♦tstr❛♣ ✭✐♥❞✐✈✐❞✉❛❧ ♥♦❞❡s✮

✷✺

❍♦✇ ❞♦ ✇❡ ❦♥♦✇ t❤❡ tr❡❡ ✐s r♦❜✉st❄

▼❛✐♥ ✐ss✉❡✿ ❛ss❡ss t❤❡ ✉♥❝❡rt❛✐♥t② ♦❢ t❤❡ tr❡❡ t♦♣♦❧♦❣② ✴ ✐♥❞✐✈✐❞✉❛❧ ♥♦❞❡s ❆♣♣r♦❛❝❤❡s

• ▼▲✿ ♠♦❞❡❧ s❡❧❡❝t✐♦♥ t♦ ❝♦♠♣❛r❡

tr❡❡s ✭✇❤♦❧❡ tr❡❡✮ ❇❛②❡s✐❛♥ ♠❡t❤♦❞s✿ ❜❡t✇❡❡♥✲s❛♠♣❧❡s ✈❛r✐❛❜✐❧✐t② ✭✐♥❞✐✈✐❞✉❛❧ ♥♦❞❡s✮ ❛♥② ♠❡t❤♦❞✿ ❜♦♦tstr❛♣ ✭✐♥❞✐✈✐❞✉❛❧ ♥♦❞❡s✮

✷✺

❍♦✇ ❞♦ ✇❡ ❦♥♦✇ t❤❡ tr❡❡ ✐s r♦❜✉st❄

▼❛✐♥ ✐ss✉❡✿ ❛ss❡ss t❤❡ ✉♥❝❡rt❛✐♥t② ♦❢ t❤❡ tr❡❡ t♦♣♦❧♦❣② ✴ ✐♥❞✐✈✐❞✉❛❧ ♥♦❞❡s ❆♣♣r♦❛❝❤❡s

• ▼▲✿ ♠♦❞❡❧ s❡❧❡❝t✐♦♥ t♦ ❝♦♠♣❛r❡

tr❡❡s ✭✇❤♦❧❡ tr❡❡✮

• ❇❛②❡s✐❛♥ ♠❡t❤♦❞s✿

❜❡t✇❡❡♥✲s❛♠♣❧❡s ✈❛r✐❛❜✐❧✐t② ✭✐♥❞✐✈✐❞✉❛❧ ♥♦❞❡s✮ ❛♥② ♠❡t❤♦❞✿ ❜♦♦tstr❛♣ ✭✐♥❞✐✈✐❞✉❛❧ ♥♦❞❡s✮

✷✺

❍♦✇ ❞♦ ✇❡ ❦♥♦✇ t❤❡ tr❡❡ ✐s r♦❜✉st❄

▼❛✐♥ ✐ss✉❡✿ ❛ss❡ss t❤❡ ✉♥❝❡rt❛✐♥t② ♦❢ t❤❡ tr❡❡ t♦♣♦❧♦❣② ✴ ✐♥❞✐✈✐❞✉❛❧ ♥♦❞❡s ❆♣♣r♦❛❝❤❡s

• ▼▲✿ ♠♦❞❡❧ s❡❧❡❝t✐♦♥ t♦ ❝♦♠♣❛r❡

tr❡❡s ✭✇❤♦❧❡ tr❡❡✮

• ❇❛②❡s✐❛♥ ♠❡t❤♦❞s✿

❜❡t✇❡❡♥✲s❛♠♣❧❡s ✈❛r✐❛❜✐❧✐t② ✭✐♥❞✐✈✐❞✉❛❧ ♥♦❞❡s✮

• ❛♥② ♠❡t❤♦❞✿

❜♦♦tstr❛♣ ✭✐♥❞✐✈✐❞✉❛❧ ♥♦❞❡s✮

✷✺

❍♦✇ ❞♦ ✇❡ ❦♥♦✇ t❤❡ tr❡❡ ✐s r♦❜✉st❄

▼❛✐♥ ✐ss✉❡✿ ❛ss❡ss t❤❡ ✉♥❝❡rt❛✐♥t② ♦❢ t❤❡ tr❡❡ t♦♣♦❧♦❣② ✴ ✐♥❞✐✈✐❞✉❛❧ ♥♦❞❡s ❆♣♣r♦❛❝❤❡s

• ▼▲✿ ♠♦❞❡❧ s❡❧❡❝t✐♦♥ t♦ ❝♦♠♣❛r❡

tr❡❡s ✭✇❤♦❧❡ tr❡❡✮

• ❇❛②❡s✐❛♥ ♠❡t❤♦❞s✿

❜❡t✇❡❡♥✲s❛♠♣❧❡s ✈❛r✐❛❜✐❧✐t② ✭✐♥❞✐✈✐❞✉❛❧ ♥♦❞❡s✮

• ❛♥② ♠❡t❤♦❞✿

❜♦♦tstr❛♣ ✭✐♥❞✐✈✐❞✉❛❧ ♥♦❞❡s✮

✷✺

❇♦♦tstr❛♣♣✐♥❣ ♣❤②❧♦❣❡♥✐❡s

• ❛ss❡ss ✈❛r✐❛❜✐❧✐t② ❞✉❡ t♦ s❛♠♣❧✐♥❣ t❤❡ ❣❡♥♦♠❡ ❛♥❞

❝♦♥✢✐❝t✐♥❣ s✐❣♥❛❧s

• r❡❧✐❡s ♦♥ ❛♥❛❧②s✐♥❣ r❡s❛♠♣❧❡❞ ❞❛t❛s❡ts

❘❛t✐♦♥❛❧❡ ✶✳ ♦❜t❛✐♥ ❛ r❡❢❡r❡♥❝❡ tr❡❡ ✷✳ r❡s❛♠♣❧❡ t❤❡ s✐t❡s ✇✐t❤ r❡♣❧❛❝❡♠❡♥t ✸✳ ♦❜t❛✐♥ ❛ tr❡❡ ❢♦r t❤❡ r❡s❛♠♣❧❡❞ ❞❛t❛s❡t ✹✳ ❣♦ ❜❛❝❦ t♦ ✷✮ ✉♥t✐❧ t❤❡ ❞❡s✐r❡❞ ♥✉♠❜❡r ♦❢ ❜♦♦tstr❛♣♣❡❞ tr❡❡s ✐s ❛tt❛✐♥❡❞ ✺✳ ❝♦♠♣✉t❡ t❤❡ ❢r❡q✉❡♥❝② ♦❢ ❡❛❝❤ ❜✐❢✉r❝❛t✐♦♥ ♦❢ t❤❡ r❡❢❡r❡♥❝❡ tr❡❡ ♦❝❝✉r✐♥❣ ✐♥ ❜♦♦tstr❛♣♣❡❞ tr❡❡s

✷✻

❇♦♦tstr❛♣♣✐♥❣ ♣❤②❧♦❣❡♥✐❡s

• ❛ss❡ss ✈❛r✐❛❜✐❧✐t② ❞✉❡ t♦ s❛♠♣❧✐♥❣ t❤❡ ❣❡♥♦♠❡ ❛♥❞

❝♦♥✢✐❝t✐♥❣ s✐❣♥❛❧s

• r❡❧✐❡s ♦♥ ❛♥❛❧②s✐♥❣ r❡s❛♠♣❧❡❞ ❞❛t❛s❡ts

❘❛t✐♦♥❛❧❡ ✶✳ ♦❜t❛✐♥ ❛ r❡❢❡r❡♥❝❡ tr❡❡ ✷✳ r❡s❛♠♣❧❡ t❤❡ s✐t❡s ✇✐t❤ r❡♣❧❛❝❡♠❡♥t ✸✳ ♦❜t❛✐♥ ❛ tr❡❡ ❢♦r t❤❡ r❡s❛♠♣❧❡❞ ❞❛t❛s❡t ✹✳ ❣♦ ❜❛❝❦ t♦ ✷✮ ✉♥t✐❧ t❤❡ ❞❡s✐r❡❞ ♥✉♠❜❡r ♦❢ ❜♦♦tstr❛♣♣❡❞ tr❡❡s ✐s ❛tt❛✐♥❡❞ ✺✳ ❝♦♠♣✉t❡ t❤❡ ❢r❡q✉❡♥❝② ♦❢ ❡❛❝❤ ❜✐❢✉r❝❛t✐♦♥ ♦❢ t❤❡ r❡❢❡r❡♥❝❡ tr❡❡ ♦❝❝✉r✐♥❣ ✐♥ ❜♦♦tstr❛♣♣❡❞ tr❡❡s

✷✻

❇♦♦tstr❛♣♣✐♥❣ ♣❤②❧♦❣❡♥✐❡s

...ttttaaaccatggatctagg... ...ttttaaaccatggatctagg... ...atttcatacgtaggatcagg... ...aaatgtaccatggatcttgt... ...aaatgtaccatggatcttgt... ...aaatgcatcatggatcttgt...

...attaaacgtaggatctagg... ...attaaacgtaggatctagg... ...attcatacgtaggatcagg... ...attgtacgtaggatctttt... ...attgtacgtaggatctttt... ...attgcatgtaggatctttt...

Reconstructed phylogeny

...ttttaaaccatggatctagg... ...ttttaaaccatggatctagg... ...atttcatacgtaggatcagg... ...aaatgtaccatggatcttgt... ...aaatgtaccatggatcttgt... ...aaatgcatcatggatcttgt... Reconstructed phylogeny Reconstructed phylogeny Reconstructed phylogeny Reconstructed phylogeny Reconstructed phylogeny

sampling sites with replacement compare topologies

...ttttaaaccatggatctagg... ...ttttaaaccatggatctagg... ...atttcatacgtaggatcagg... ...aaatgtaccatggatcttgt... ...aaatgtaccatggatcttgt... ...aaatgcatcatggatcttgt... ...ttttaaaccatggatctagg... ...ttttaaaccatggatctagg... ...atttcatacgtaggatcagg... ...aaatgtaccatggatcttgt... ...aaatgtaccatggatcttgt... ...aaatgcatcatggatcttgt... ...ttttaaaccatggatctagg... ...ttttaaaccatggatctagg... ...atttcatacgtaggatcagg... ...aaatgtaccatggatcttgt... ...aaatgtaccatggatcttgt... ...aaatgcatcatggatcttgt...

✷✼

❇♦♦tstr❛♣♣✐♥❣ ♣❤②❧♦❣❡♥✐❡s

❆❞✈❛♥t❛❣❡s

• st❛♥❞❛r❞
• s✐♠♣❧❡ t♦ ✐♠♣❧❡♠❡♥t

▲✐♠✐t❛t✐♦♥s ♣♦ss✐❜❧② ❝♦♠♣✉t❡r✲✐♥t❡♥s✐✈❡ ❛ss✉♠❡s t❤❛t t❤❡ ❣❡♥♦♠❡ ❤❛s ❜❡❡♥ s❛♠♣❧❡❞ r❛♥❞♦♠❧② ✭♦❢t❡♥ ✇r♦♥❣✮

✷✽

❇♦♦tstr❛♣♣✐♥❣ ♣❤②❧♦❣❡♥✐❡s

❆❞✈❛♥t❛❣❡s

• st❛♥❞❛r❞
• s✐♠♣❧❡ t♦ ✐♠♣❧❡♠❡♥t

▲✐♠✐t❛t✐♦♥s

• ♣♦ss✐❜❧② ❝♦♠♣✉t❡r✲✐♥t❡♥s✐✈❡
• ❛ss✉♠❡s t❤❛t t❤❡ ❣❡♥♦♠❡ ❤❛s ❜❡❡♥ s❛♠♣❧❡❞ r❛♥❞♦♠❧② ✭♦❢t❡♥

✇r♦♥❣✮

✷✽

❖✉t❧✐♥❡

P❤②❧♦❣❡♥✐❡s✳✳✳ ❉✐st❛♥❝❡ tr❡❡s P❛rs✐♠♦♥② ▲✐❦❡❧✐❤♦♦❞✴❇❛②❡s✐❛♥ ❯♥❝❡rt❛✐♥t② P✐t❢❛❧❧s ✫ ❜❡st ♣r❛❝t✐❝❡s ❆♥❞ ♠♦r❡✳✳✳

✷✾

P❧♦tt✐♥❣ tr❡❡s ❛s r♦♦t❡❞

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

◆❡✈❡r ♣❧♦t ❛♥ ✉♥r♦♦t❡❞ tr❡❡ ❛s r♦♦t❡❞✳

✸✵

P❧♦tt✐♥❣ tr❡❡s ❛s r♦♦t❡❞

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

◆❡✈❡r ♣❧♦t ❛♥ ✉♥r♦♦t❡❞ tr❡❡ ❛s r♦♦t❡❞✳

✸✵

■♥t❡r♣r❡t✐♥❣ ❞✐st❛♥❝❡s

✸✶

■♥t❡r♣r❡t✐♥❣ ❞✐st❛♥❝❡s

✸✶

■♥t❡r♣r❡t✐♥❣ ❞✐st❛♥❝❡s

meaningful distance = sum of branch lengths meaningless ✸✶

❚❤❡ ♣❛r❛❞♦① ♦❢ ❞✐✈❡r❣❡♥t ❝❧✉st❡rs

▼❘❈❆ ❛♥❞ ❣❡♥❡t✐❝ ❞✐st❛♥❝❡s ♠❛② ❣✐✈❡ ❞✐✛❡r❡♥t ✐♥❢♦r♠❛t✐♦♥✳

✸✷

❚❤❡ ♣❛r❛❞♦① ♦❢ ❞✐✈❡r❣❡♥t ❝❧✉st❡rs

D(red, red)>D(red,blue)

▼❘❈❆ ❛♥❞ ❣❡♥❡t✐❝ ❞✐st❛♥❝❡s ♠❛② ❣✐✈❡ ❞✐✛❡r❡♥t ✐♥❢♦r♠❛t✐♦♥✳

✸✷

❚❤❡ ♣❛r❛❞♦① ♦❢ ❞✐✈❡r❣❡♥t ❝❧✉st❡rs

D(red, red)>D(red,blue)

▼❘❈❆ ❛♥❞ ❣❡♥❡t✐❝ ❞✐st❛♥❝❡s ♠❛② ❣✐✈❡ ❞✐✛❡r❡♥t ✐♥❢♦r♠❛t✐♦♥✳

✸✷

❚❛❦✐♥❣ ✉♥❝❡rt❛✐♥t② ✐♥t♦ ❛❝❝♦✉♥t

193 HIV−1 sequences from DRC (Strimmer & Pybus 2001)

0.2 0.15 0.1 0.05

❆t ❜❡st✱ t❤❡ tr❡❡ ✐s ❛♥ ❡st✐♠❛t❡ ♦❢ t❤❡ ❧✐❦❡❧② ❡✈♦❧✉t✐♦♥❛r② ❤✐st♦r② ♦❢ t❤❡ t❛①❛ st✉❞✐❡❞✳

✸✸

❚❛❦✐♥❣ ✉♥❝❡rt❛✐♥t② ✐♥t♦ ❛❝❝♦✉♥t

193 HIV−1 sequences from DRC (Strimmer & Pybus 2001)

0.2 0.15 0.1 0.05

Collapsed tree (threshold length 0.01)

0.2 0.15 0.1 0.05

❆t ❜❡st✱ t❤❡ tr❡❡ ✐s ❛♥ ❡st✐♠❛t❡ ♦❢ t❤❡ ❧✐❦❡❧② ❡✈♦❧✉t✐♦♥❛r② ❤✐st♦r② ♦❢ t❤❡ t❛①❛ st✉❞✐❡❞✳

✸✸

❚❛❦✐♥❣ ✉♥❝❡rt❛✐♥t② ✐♥t♦ ❛❝❝♦✉♥t

193 HIV−1 sequences from DRC (Strimmer & Pybus 2001)

0.2 0.15 0.1 0.05

Collapsed tree (threshold length 0.01)

0.2 0.15 0.1 0.05

❆t ❜❡st✱ t❤❡ tr❡❡ ✐s ❛♥ ❡st✐♠❛t❡ ♦❢ t❤❡ ❧✐❦❡❧② ❡✈♦❧✉t✐♦♥❛r② ❤✐st♦r② ♦❢ t❤❡ t❛①❛ st✉❞✐❡❞✳

✸✸

✭❖✈❡r✱ ▼✐s✮■♥t❡r♣r❡t✐♥❣ t❡♠♣♦r❛❧ tr❡♥❞s

t30 t46 t33 t64 t25 t99 t73 t8 t81 t31 t76 t91 t100 t42 t77 t74 t98 t65 t79 t36 t58 t32 t26 t59 t16 t54 t10 t18 t11 t94 t5t45t60 t53 t67 t88 t27 t52 t38 t40 t22 t90 t80 t37 t12t93 t78 t49 t82 t50 t57 t71 t21 t7 t1 t84 t70 t20 t97 t41 t43 t19 t47 t28 t17 t66 t55 t34 t61 t35 t3 t2 t89 t75 t86 t15 t13 t23 t56 t96 t24 t44 t39 t63 t69 t83 t72 t29 t14 t62 t6 t48 t4 t87 t92 t9 t95 t68 t51 t85 12 10 8 6 4 2

✏❚✐♠❡ tr❡❡s✑ ♦♥❧② ♠❛❦❡ s❡♥s❡ ✉♥❞❡r ❛ ♥❡❛r✲♣❡r❢❡❝t ♠♦❧❡❝✉❧❛r ❝❧♦❝❦✳

✸✹

✭❖✈❡r✱ ▼✐s✮■♥t❡r♣r❡t✐♥❣ t❡♠♣♦r❛❧ tr❡♥❞s

t30 t46 t33 t64 t25 t99 t73 t8 t81 t31 t76 t91 t100 t42 t77 t74 t98 t65 t79 t36 t58 t32 t26 t59 t16 t54 t10 t18 t11 t94 t5t45t60 t53 t67 t88 t27 t52 t38 t40 t22 t90 t80 t37 t12t93 t78 t49 t82 t50 t57 t71 t21 t7 t1 t84 t70 t20 t97 t41 t43 t19 t47 t28 t17 t66 t55 t34 t61 t35 t3 t2 t89 t75 t86 t15 t13 t23 t56 t96 t24 t44 t39 t63 t69 t83 t72 t29 t14 t62 t6 t48 t4 t87 t92 t9 t95 t68 t51 t85 12 10 8 6 4 2 20 40 60 80 2 4 6 8 10 12 Time to the root Mutations to the root

> anova(lm(d.root~-1+t.root)) anova(lm(d.root~-1+t.root)) Analysis of Variance Table Response: d.root Df Sum Sq Mean Sq F value Pr(>F) t.root 1 5434.7 5434.7 214.66 < 2.2e-16 *** Residuals 99 2506.4 25.3

✏❚✐♠❡ tr❡❡s✑ ♦♥❧② ♠❛❦❡ s❡♥s❡ ✉♥❞❡r ❛ ♥❡❛r✲♣❡r❢❡❝t ♠♦❧❡❝✉❧❛r ❝❧♦❝❦✳

✸✹

✭❖✈❡r✱ ▼✐s✮■♥t❡r♣r❡t✐♥❣ t❡♠♣♦r❛❧ tr❡♥❞s

t30 t46 t33 t64 t25 t99 t73 t8 t81 t31 t76 t91 t100 t42 t77 t74 t98 t65 t79 t36 t58 t32 t26 t59 t16 t54 t10 t18 t11 t94 t5t45t60 t53 t67 t88 t27 t52 t38 t40 t22 t90 t80 t37 t12t93 t78 t49 t82 t50 t57 t71 t21 t7 t1 t84 t70 t20 t97 t41 t43 t19 t47 t28 t17 t66 t55 t34 t61 t35 t3 t2 t89 t75 t86 t15 t13 t23 t56 t96 t24 t44 t39 t63 t69 t83 t72 t29 t14 t62 t6 t48 t4 t87 t92 t9 t95 t68 t51 t85 12 10 8 6 4 2 20 40 60 80 2 4 6 8 10 12 Time to the root Mutations to the root

> anova(lm(d.root~-1+t.root)) anova(lm(d.root~-1+t.root)) Analysis of Variance Table Response: d.root Df Sum Sq Mean Sq F value Pr(>F) t.root 1 5434.7 5434.7 214.66 < 2.2e-16 *** Residuals 99 2506.4 25.3

✏❚✐♠❡ tr❡❡s✑ ♦♥❧② ♠❛❦❡ s❡♥s❡ ✉♥❞❡r ❛ ♥❡❛r✲♣❡r❢❡❝t ♠♦❧❡❝✉❧❛r ❝❧♦❝❦✳

✸✹

❖✉t❧✐♥❡

P❤②❧♦❣❡♥✐❡s✳✳✳ ❉✐st❛♥❝❡ tr❡❡s P❛rs✐♠♦♥② ▲✐❦❡❧✐❤♦♦❞✴❇❛②❡s✐❛♥ ❯♥❝❡rt❛✐♥t② P✐t❢❛❧❧s ✫ ❜❡st ♣r❛❝t✐❝❡s ❆♥❞ ♠♦r❡✳✳✳

✸✺

❚❤✐s ✐s ♦♥❧② t❤❡ ❜❡❣✐♥♥✐♥❣

▼❛♥② t❤✐♥❣s ❝❛♥ ❜❡ ❞♦♥❡ ✇✐t❤ tr❡❡s

• ❡st✐♠❛t❡ ❞✐✈❡r❣❡♥❝❡ t✐♠❡

♠♦❞❡❧ tr❛✐t ❡✈♦❧✉t✐♦♥ ✭♣❤②❧♦❣❡♥❡t✐❝ ❝♦♠♣❛r❛t✐✈❡ ♠❡t❤♦❞✮ r❡❝♦♥str✉❝t ❛♥❝❡str❛❧ st❛t❡s ♠❡❛s✉r❡ ❞✐✈❡rs✐t② ✐♥❢❡r ♣❛st ❞❡♠♦❣r❛♣❤✐❝s✴❡✛❡❝t✐✈❡ ♣♦♣✉❧❛t✐♦♥ s✐③❡ ✭❝♦❛❧❡s❝❡♥❝❡✮ ✳✳✳ ❛♥❞ ❛❧s♦✱ ♦t❤❡r ❛♣♣r♦❛❝❤❡s t❤❛♥ ♣❤②❧♦❣❡♥❡t✐❝s t♦ ❛♥❛❧②s❡ ❣❡♥❡t✐❝ ❞❛t❛

✸✻

❚❤✐s ✐s ♦♥❧② t❤❡ ❜❡❣✐♥♥✐♥❣

▼❛♥② t❤✐♥❣s ❝❛♥ ❜❡ ❞♦♥❡ ✇✐t❤ tr❡❡s

• ❡st✐♠❛t❡ ❞✐✈❡r❣❡♥❝❡ t✐♠❡
• ♠♦❞❡❧ tr❛✐t ❡✈♦❧✉t✐♦♥ ✭♣❤②❧♦❣❡♥❡t✐❝

❝♦♠♣❛r❛t✐✈❡ ♠❡t❤♦❞✮ r❡❝♦♥str✉❝t ❛♥❝❡str❛❧ st❛t❡s ♠❡❛s✉r❡ ❞✐✈❡rs✐t② ✐♥❢❡r ♣❛st ❞❡♠♦❣r❛♣❤✐❝s✴❡✛❡❝t✐✈❡ ♣♦♣✉❧❛t✐♦♥ s✐③❡ ✭❝♦❛❧❡s❝❡♥❝❡✮ ✳✳✳ ❛♥❞ ❛❧s♦✱ ♦t❤❡r ❛♣♣r♦❛❝❤❡s t❤❛♥ ♣❤②❧♦❣❡♥❡t✐❝s t♦ ❛♥❛❧②s❡ ❣❡♥❡t✐❝ ❞❛t❛

✸✻

❚❤✐s ✐s ♦♥❧② t❤❡ ❜❡❣✐♥♥✐♥❣

▼❛♥② t❤✐♥❣s ❝❛♥ ❜❡ ❞♦♥❡ ✇✐t❤ tr❡❡s

• ❡st✐♠❛t❡ ❞✐✈❡r❣❡♥❝❡ t✐♠❡
• ♠♦❞❡❧ tr❛✐t ❡✈♦❧✉t✐♦♥ ✭♣❤②❧♦❣❡♥❡t✐❝

❝♦♠♣❛r❛t✐✈❡ ♠❡t❤♦❞✮

• r❡❝♦♥str✉❝t ❛♥❝❡str❛❧ st❛t❡s

♠❡❛s✉r❡ ❞✐✈❡rs✐t② ✐♥❢❡r ♣❛st ❞❡♠♦❣r❛♣❤✐❝s✴❡✛❡❝t✐✈❡ ♣♦♣✉❧❛t✐♦♥ s✐③❡ ✭❝♦❛❧❡s❝❡♥❝❡✮ ✳✳✳ ❛♥❞ ❛❧s♦✱ ♦t❤❡r ❛♣♣r♦❛❝❤❡s t❤❛♥ ♣❤②❧♦❣❡♥❡t✐❝s t♦ ❛♥❛❧②s❡ ❣❡♥❡t✐❝ ❞❛t❛

✸✻

❚❤✐s ✐s ♦♥❧② t❤❡ ❜❡❣✐♥♥✐♥❣

▼❛♥② t❤✐♥❣s ❝❛♥ ❜❡ ❞♦♥❡ ✇✐t❤ tr❡❡s

• ❡st✐♠❛t❡ ❞✐✈❡r❣❡♥❝❡ t✐♠❡
• ♠♦❞❡❧ tr❛✐t ❡✈♦❧✉t✐♦♥ ✭♣❤②❧♦❣❡♥❡t✐❝

❝♦♠♣❛r❛t✐✈❡ ♠❡t❤♦❞✮

• r❡❝♦♥str✉❝t ❛♥❝❡str❛❧ st❛t❡s
• ♠❡❛s✉r❡ ❞✐✈❡rs✐t②

✐♥❢❡r ♣❛st ❞❡♠♦❣r❛♣❤✐❝s✴❡✛❡❝t✐✈❡ ♣♦♣✉❧❛t✐♦♥ s✐③❡ ✭❝♦❛❧❡s❝❡♥❝❡✮ ✳✳✳ ❛♥❞ ❛❧s♦✱ ♦t❤❡r ❛♣♣r♦❛❝❤❡s t❤❛♥ ♣❤②❧♦❣❡♥❡t✐❝s t♦ ❛♥❛❧②s❡ ❣❡♥❡t✐❝ ❞❛t❛

✸✻

❚❤✐s ✐s ♦♥❧② t❤❡ ❜❡❣✐♥♥✐♥❣

▼❛♥② t❤✐♥❣s ❝❛♥ ❜❡ ❞♦♥❡ ✇✐t❤ tr❡❡s

• ❡st✐♠❛t❡ ❞✐✈❡r❣❡♥❝❡ t✐♠❡
• ♠♦❞❡❧ tr❛✐t ❡✈♦❧✉t✐♦♥ ✭♣❤②❧♦❣❡♥❡t✐❝

❝♦♠♣❛r❛t✐✈❡ ♠❡t❤♦❞✮

• r❡❝♦♥str✉❝t ❛♥❝❡str❛❧ st❛t❡s
• ♠❡❛s✉r❡ ❞✐✈❡rs✐t②
• ✐♥❢❡r ♣❛st ❞❡♠♦❣r❛♣❤✐❝s✴❡✛❡❝t✐✈❡

♣♦♣✉❧❛t✐♦♥ s✐③❡ ✭❝♦❛❧❡s❝❡♥❝❡✮ ✳✳✳ ❛♥❞ ❛❧s♦✱ ♦t❤❡r ❛♣♣r♦❛❝❤❡s t❤❛♥ ♣❤②❧♦❣❡♥❡t✐❝s t♦ ❛♥❛❧②s❡ ❣❡♥❡t✐❝ ❞❛t❛

✸✻

❚❤✐s ✐s ♦♥❧② t❤❡ ❜❡❣✐♥♥✐♥❣

▼❛♥② t❤✐♥❣s ❝❛♥ ❜❡ ❞♦♥❡ ✇✐t❤ tr❡❡s

• ❡st✐♠❛t❡ ❞✐✈❡r❣❡♥❝❡ t✐♠❡
• ♠♦❞❡❧ tr❛✐t ❡✈♦❧✉t✐♦♥ ✭♣❤②❧♦❣❡♥❡t✐❝

❝♦♠♣❛r❛t✐✈❡ ♠❡t❤♦❞✮

• r❡❝♦♥str✉❝t ❛♥❝❡str❛❧ st❛t❡s
• ♠❡❛s✉r❡ ❞✐✈❡rs✐t②
• ✐♥❢❡r ♣❛st ❞❡♠♦❣r❛♣❤✐❝s✴❡✛❡❝t✐✈❡

♣♦♣✉❧❛t✐♦♥ s✐③❡ ✭❝♦❛❧❡s❝❡♥❝❡✮

• ✳✳✳

❛♥❞ ❛❧s♦✱ ♦t❤❡r ❛♣♣r♦❛❝❤❡s t❤❛♥ ♣❤②❧♦❣❡♥❡t✐❝s t♦ ❛♥❛❧②s❡ ❣❡♥❡t✐❝ ❞❛t❛

✸✻

❚❤✐s ✐s ♦♥❧② t❤❡ ❜❡❣✐♥♥✐♥❣

▼❛♥② t❤✐♥❣s ❝❛♥ ❜❡ ❞♦♥❡ ✇✐t❤ tr❡❡s

• ❡st✐♠❛t❡ ❞✐✈❡r❣❡♥❝❡ t✐♠❡
• ♠♦❞❡❧ tr❛✐t ❡✈♦❧✉t✐♦♥ ✭♣❤②❧♦❣❡♥❡t✐❝

❝♦♠♣❛r❛t✐✈❡ ♠❡t❤♦❞✮

• r❡❝♦♥str✉❝t ❛♥❝❡str❛❧ st❛t❡s
• ♠❡❛s✉r❡ ❞✐✈❡rs✐t②
• ✐♥❢❡r ♣❛st ❞❡♠♦❣r❛♣❤✐❝s✴❡✛❡❝t✐✈❡

♣♦♣✉❧❛t✐♦♥ s✐③❡ ✭❝♦❛❧❡s❝❡♥❝❡✮

• ✳✳✳
• ❛♥❞ ❛❧s♦✱ ♦t❤❡r ❛♣♣r♦❛❝❤❡s t❤❛♥

♣❤②❧♦❣❡♥❡t✐❝s t♦ ❛♥❛❧②s❡ ❣❡♥❡t✐❝ ❞❛t❛

✸✻

✸✼