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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.

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Presentation on theme: "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."— Presentation transcript:

1 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.

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

3 Fitch W.M. 1971. Syst. Zool. 20: 406-416. AlphaBetaDeltaGammaEpsilon Gamma Delta Alpha Beta Epsilon there are always fewer unrooted trees than rooted trees. Types of trees >

4 Fitch W.M. 1971. Syst. Zool. 20: 406-416. AlphaBetaDeltaGammaEpsilon there are more labeled than unlabeled trees. Types of trees >

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

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

7 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

8 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)

9 Forests of labeled, rooted, bifurcating trees n tip species #tips#trees 21 33 415 5105 6945 710395 8135135 92027025 1034459425 116.55E+08 121.37E+10 133.16E+11 147.91E+12 152.13E+14 208.2E+21 304.95E+38 401.01E+57 502.75E+76 Avogadro Eddington


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