1 / 9

Exploring Tree Diversity: The Frightening Number of Possible Trees in Forest Ecosystems

This document examines the intricate diversity of tree species in forest ecosystems, highlighting the alarming number of potential trees that can exist even with a modest number of tip species. Citing findings from Fitch W.M. (1971), it discusses the distinctions between rooted and unrooted trees, the prevalence of labeled versus unlabeled trees, and the complex structures of bifurcating trees. The text emphasizes the mathematical framework underlying tree diversity, exploring fundamental principles that govern the possibilities of tree arrangement in forests.

fayre
Télécharger la présentation

Exploring Tree Diversity: The Frightening Number of Possible Trees in Forest Ecosystems

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

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. OrangOetan OrangOetan Chimpansee Chimpansee Macaque Macaque Colobus Colobus Gibbon Gibbon Human Human Gorilla Gorilla =

  3. 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.

  4. Types of trees there are more labeled than unlabeled trees. Alpha Delta Gamma Beta Epsilon > FitchW.M. 1971. Syst. Zool. 20: 406-416.

  5. Forests of labeled, rooted, bifurcating trees 2 tip species a b

  6. Forests of labeled, rooted, bifurcating trees 3 tip species c c b a a b a b c

  7. 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

  8. 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)

  9. Forests of labeled, rooted, bifurcating trees n tip species Avogadro Eddington

More Related