Q.29 The number of possible rooted trees in a phylogeny of three species is ________.
The number of possible rooted trees in a phylogeny of three species is 3.
Understanding Rooted Trees
Rooted phylogenetic trees represent evolutionary relationships among species with a designated root, indicating the common ancestor and direction of evolution from past to present. For three labeled species (A, B, C), the trees differ only in branching order: ((A,B),C), ((A,C),B), or ((B,C),A). This assumes fully resolved (bifurcating) binary trees, standard in such exam questions.
Formula and Calculation
The number of rooted binary trees for n taxa follows (2n−3)!!, where !! denotes the double factorial (product of odd numbers down to 1). For n=3: (2×3−3)!! = 3!! = 3×1 = 3. Unrooted trees for three species number 1, but each gains 3 possible root positions (on branches), confirming 3 rooted variants.
Common Options Explained
- 1: Incorrect; represents unrooted trees only (no evolutionary direction).
- 3: Correct; matches formula and exhaustive enumeration.
- 15: For four species (5!! = 15).
- 105: For five species (7!! = 105).
Introduction: Unlocking the Number of Possible Rooted Trees in Phylogeny of Three Species
In phylogenetics, understanding the number of possible rooted trees in phylogeny of three species is crucial for evolutionary biology exams like IIT JAM Biotechnology. This key concept reveals exactly 3 possible rooted trees, derived from the double factorial formula (2n−3)!!. Mastering rooted trees phylogeny three species helps tackle competitive questions efficiently.
Why Rooted Trees Matter in Phylogeny of Three Species
Rooted trees specify evolutionary direction with a common ancestor root, unlike unrooted versions. For three species phylogeny, only 3 topologies exist: one species branches first, with the other two as sisters. This grows exponentially: 3 for 3 taxa, 15 for 4, 105 for 5.
Step-by-Step Calculation
- Apply formula: For n=3, compute (6−3)!! = 3!! = 3.
- Enumerate manually: Label species A,B,C—trees are ((A,B),C), ((A,C),B), ((B,C),A).
- Verify: Unrooted tree (1) × root positions (3 branches) = 3.
Exam Tips for Rooted Phylogenetic Trees
- Differentiate rooted (directional) vs. unrooted (1 for 3 taxa).
- Memorize sequence: 1 (n=2), 3 (n=3), 15 (n=4), 105 (n=5).
- Practice: Questions often test formula application for small n.
This guide optimizes number of possible rooted trees in phylogeny of three species for search and study—ideal for biotech aspirants.
