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GATE 2019 BT Q.19: solution and answer

GATE 2019 · BTQ.19 · 1 mark · NAT

The number of possible rooted trees in a phylogeny of three species is ____.

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Answer and solution

ANSWER

The number of possible rooted trees in a phylogeny of three species is 3.

Official answer: 3Source: Official answer key, GATE 2019 BT (IIT Madras)

  1. For 3 species (X, Y, Z), a rooted bifurcating (binary) phylogenetic tree groups exactly two of them as a sister pair, with the root node joining this pair's most recent common ancestor to the third species (the outgroup).

  2. The number of ways to choose which two species form the sister pair is : (X,Y) with Z as outgroup, (X,Z) with Y as outgroup, or (Y,Z) with X as outgroup.

  3. Each choice of sister pair produces a structurally distinct rooted tree. Since a phylogenetic tree has no left/right ordering, swapping the two members within a sister pair, or swapping the pair with the outgroup label, does not create a new topology — it only relabels the same tree.

  4. This matches the general combinatorial formula for the number of distinct rooted bifurcating trees on labeled taxa: .

  5. Substituting : .

  6. Hence the number of possible rooted trees for a phylogeny of three species is .

KEY IDEA

For n labeled taxa, the number of distinct rooted bifurcating (binary) phylogenetic trees is . For , this gives : choose which 2 of the 3 species form a sister clade (root joins their common ancestor to the third species), and there are such choices.

WATCH OUT FOR

Confusing the ROOTED tree count with the UNROOTED tree count for 3 taxa: an unrooted tree topology for 3 species is unique (all three star-like arrangements are the same tree once the root is removed), so students sometimes answer 1. The question asks specifically for rooted trees, where placing the root creates 3 distinguishable topologies.

From the GATE 2019 BT paper. Every question of this paper · Download the full paper · All 11 Bioinformatics questions, with notes

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