Algorithms for phylogeny construction

A Hybrid Micro-Macroevolutionary Approach to Gene Tree

Reconstruction

ICE-TCS Inaugural Symposium

Bjarni V. Halldorsson

April 30, 2005

1

Character based phylogeny

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Genes, genomes

• Gene - a sequence having functional importance. AACG,

CACC, TACT

• Genome - a sequence containing genes as subsequences

TATAACGTTTCTACTCTATTACTCC

4

Evolution - changes in the genome

Original:

TATAACGTTTCTACTCTATTACTCC

Mutation:

TATAACGTTTCTAATCTCTTACTCC

Duplication:

TATAACGTTTCTACTCTATTACTCCTCTACTCT

Loss:

TA-TCTACTCTATTACTCC

5

Phylogenies

A species phylogeny shows the evolutionary history of a set of

species.

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A gene phylogeny shows the evolutionary history of a single gene.

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Why are gene phylogenies interesting?

• The same gene in different species is likely to play the same

role.

• We want to determine the function of a gene in human.

• Experiments in mouse, yeast or flies are less controversial

and take less time than in human.

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Phylogeny construction considering mutations A very large num-

ber of algorithms exist for this problem.

• Character based algorithms (as mentioned before).

• Distances between the sequences are computed (such as the

number of mutations that occured between the sequences).

• If the phylogeny has the ultrametric property an efficient

algorithm can be employed.

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Macroevolutionary phylogeny

Input: A rooted species tree, TS with s leaves; a list of multiplic-

ities m1 . . . ms, where ml is the number of gene family members

found in species l; weights cλ and cδ.

Output: A rooted gene tree {TG} with∑s

l=1 ml leaves such that

the D/L Score of TG is minimal.

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Phylogenies considering only cost of loss

• If the cost of losing a gene is much higher than the cost of

duplication we will construct a phylogeny that minimizes the

number of lost genes.

• All duplications will then take place after the speciations take

place.

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4 Duplications

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Phylogenies considering only cost of duplication

• If the cost of a duplication is much higher than the cost of a

loss we will construct a phylogeny that minimizes the number

of duplications.

• All duplications can then be assumed to occur before any

speciation occurs.

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1 Duplication, 3 Losses

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Phylogenies considering duplication and loss

Reconstruct[TS, {m1 . . . ms}]

Ascend[root(TS)];

Descend[root(TS), 1];

Construct[root(TS)];

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Ascend[v]

if v is not a leaf: Ascend[l(v)]; Ascend[r(v)];

if v is a leaf:

∀i s.t. 1 ≤ i ≤ m

costminv [i]← cδ ∗max(mv − i,0) + cλ ∗max(i−mv,0);

if v is not a leaf:

∀i, j s.t. 1 ≤ i, j ≤ m

costv[i, j]← cδ ∗max(j − i,0) + cλ ∗max(i− j,0) + costminl(v)

[j] + costminr(v)

[j];

∀i costminv [i]← min∀j{costv[i, j]};

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Descend

Descend[v, i]

if v is a leaf:

v.losses← max((i−mv),0); v.dups← max((mv − i),0);

v.out← 0;

else

repeat { v.out + + } until ( costv[i, v.out] == costminv [i] );

Descend[l(v), v.out]; Descend[r(v), v.out]

v.losses← max(i− v.out,0); v.dups← max (v.out− i,0)

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Construct

Construct[s]

g ← new gene node; g.species← s

if (s.currDup < s.dups)

s.currDup + +; l(g)← Construct[s]; r(g)← Construct[s];

else if (s.currLoss < s.losses)

s.currLoss + +;

else if (s.currSpec < s.out)

s.currSpec + +;

if s is not a leaf: l(g)← Construct[l(s)]; r(g)← Construct[r(s)];

return g;

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2 Duplications, 1 loss

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Time Complexity

Optimal history can be found in time O(nm2). Where n is the

number of nodes in the species tree and m is the maximum

number of genes drawn from any species.

In Ascendleaves of the species tree can be annotated with mul-

tiplicities in O(nm) time. The cost vector in each node is of

length m + 1 and each entry can be computed in time O(m),

total O(nm2).

Descend requires O(m) at each node, total O(nm). Construct

inserts duplication and loss nodes in the new tree, which can

number in total no more than m per node in TS. Total O(nm).

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Extensions

• Combining duplication and loss cost with cost of mutations.

– Some edges of a phylogeny tree are well supported by a

micro-evolutionary phylogenetic construction algorithms.

– Edges that are not as well supported can be rearranged

minimizing duplication and loss.

• Consider and display all possible optimal histories.

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Acknowledgements

• R. Ravi, Carnegie Mellon University

• Dannie Durand, Carnegie Mellon University

A Hybrid Micro-Macroevolutionary Approach to Gene Tree Re-

construction. D. Durand, B. V. Halldorsson, B. Vernot, 2005.

Proceedings of the Ninth Annual International Conference on

Computational Molecular Biology (RECOMB), To Appear.

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