Q.50
Agricultural Statistics- ICAR JRF/SRF 2024
MCQ (Single Correct) +4 −1
The number of possible unrooted trees for 5 operational taxonomic units is
  • Number of Possible Unrooted Trees:
  • For $n$ operational taxonomic units (taxa), the number of distinct unrooted bifurcating phylogenetic trees ($N_u$) is given by the double factorial formula:
$$N_u = (2n - 5)!! = 1 \times 3 \times 5 \times \dots \times (2n - 5)$$
  • For $n = 5$ taxa:
$$N_u = (2 \times 5 - 5)!! = 5!! = 1 \times 3 \times 5 = 15$$
  • (By comparison, the number of rooted trees for $n = 5$ is $(2n - 3)!! = 7!! = 105$).
  • Conclusion: The number of unrooted trees for 5 OTUs is 15 (Option 2).

Correct option: (2) 15

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