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.

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Presentation transcript:

A forest of trees even with modest numbers of tip species, the number of possible trees is frightening. Fitch W.M Syst. Zool. 20:

Types of trees trees that seem different – may be not. Orang OetanGorillaChimpanseeHumanGibbonMacaqueColobusOrang OetanGorillaChimpanseeHumanGibbonMacaqueColobus =

Fitch W.M Syst. Zool. 20: AlphaBetaDeltaGammaEpsilon Gamma Delta Alpha Beta Epsilon there are always fewer unrooted trees than rooted trees. Types of trees >

Fitch W.M Syst. Zool. 20: AlphaBetaDeltaGammaEpsilon there are more labeled than unlabeled trees. Types of trees >

Forests of labeled, rooted, bifurcating trees ab 2 tip species

Forests of labeled, rooted, bifurcating trees ab 3 tip species c a bc bc a

Forests of labeled, rooted, bifurcating trees 4 tip species ab cd ac bd bc ad ab dc ad bc bd ac ac db ad cb dc ab bc da bd ca cd ba ab cd ac bd ad bc

Forests of labeled, rooted, bifurcating trees n tip species (2n -3)! 2 n-2 (n - 2)! # possible trees = = 1 x 3 x 5 x 7 x 9 x 11 x … x (2n-3)

Forests of labeled, rooted, bifurcating trees n tip species #tips#trees E E E E E E E E E+76 Avogadro Eddington