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A forest of trees. even with modest numbers of tip species , the number of possible trees is frightening. Fitch W.M. 1971. Syst . Zool. 20: 406-416. Types of trees. trees that seem different – may be not. Orang Oetan. Orang Oetan. Chimpansee. Chimpansee. Macaque. Macaque.

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A forest of trees

even with modest numbers of tip species, the number of possible trees is frightening.

Fitch W.M. 1971. Syst. Zool. 20: 406-416.


Types of trees

trees that seem different – may be not.

OrangOetan

OrangOetan

Chimpansee

Chimpansee

Macaque

Macaque

Colobus

Colobus

Gibbon

Gibbon

Human

Human

Gorilla

Gorilla

=


Types of trees

there are always fewer unrooted trees than rooted trees.

Alpha

Delta

Gamma

Beta

Epsilon

Gamma

Alpha

Beta

>

Delta

Epsilon

FitchW.M. 1971. Syst. Zool. 20: 406-416.


Types of trees

there are more labeled than unlabeled trees.

Alpha

Delta

Gamma

Beta

Epsilon

>

FitchW.M. 1971. Syst. Zool. 20: 406-416.


Forests of labeled, rooted, bifurcating trees

2 tip species

a

b


Forests of labeled, rooted, bifurcating trees

3 tip species

c

c

b

a

a

b

a

b

c


Forests of labeled, rooted, bifurcating trees

4 tip species

d

c

b

c

b

a

c

a

b

d

d

a

d

b

a

d

a

d

c

a

b

b

c

c

a

a

b

a

b

a

a

b

c

d

b

a

d

c

c

d

c

c

d

d

c

d

b

b

b

d

b

c

a

c

a

d

c

d

a

b


Forests of labeled, rooted, bifurcating trees

n tip species

(2n -3)!

# possible trees =

2n-2(n - 2)!

= 1 x 3 x 5 x 7 x 9 x 11 x … x (2n-3)


Forests of labeled, rooted, bifurcating trees

n tip species

Avogadro

Eddington


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