Towards Identifying Lateral Gene Transfer Events

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Towards Identifying Lateral Gene Transfer Events

• L. Addario-Berry, M. Hallett, J. Lagergren
• Presented By Jeff Mathew

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Roadmap

• Key terms
• t-transfer problem
• H-moves and I-moves algorithm
• Tree generation for simulation
• Experimental results
• Conclusions and future work

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Lateral transfer scenario

• LGT HGT
• Root of scenario tree must correspond to root of
  gene tree
• The scenario tree is connected and respects the
  direction of evolution implied by the arcs of T
  and S.

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a-activity

• An a-active scenario for a gene tree and species
  tree allows at most alpha copies of a gene to
  simultaneously exist in the genome of an
  ancestral taxon.
• Authors focus on 1-active scenarios though
  intractability results have been proved earlier
  for a 1.

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t-transfer problem

• Input Species tree S, gene tree T, integer t
• Output A t lateral transfer scenario for S and
  T, t t
• Intractability result
• The decision version of the a-Active, t-Transfer
  Problem (does there exist a a-active scenario
  with cost t?) is NP-complete.
• t is the number of lateral transfer events needed
  to explain the difference between S and T

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Algorithm

• 2 Phase approach
• Phase 1
• While H-fat or I-fat vertices remain
• Perform H-fat move or I-fat move
• At the end of phase 1, we are guaranteed that the
  scenario is 1-active. What about cycles?
• Phase 2
• Remove minimum number of LGT events from each
  candidate to make it acyclic.
• Running Time 24t n2

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Simulating species trees

• Create random species tree S on n-leaves. T(log
  n) expected depth
• S is supposed to reflect the actual evolutionary
  relationships between taxa
• S is ultrametric. Therefore, edge-weights
  correspond to time.
• Randomly assign weights to every edge such that
  every root-to-leaf path has weighted sum 1.

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Simulating gene trees

• Begin with generated ultrametric species tree
• Lateral transfer events occur according to a
  Poisson process with mean rate ?
• Moving from root to leaves, for each vertex x0
  with children x1 and x2, examine both edges
• If the Poisson process provides us with a lateral
  transfer event along (x0, x1), we add it and
  point it to a randomly chosen edge alive at that
  point in time.
• Else add a speciation event for x1
• Repeat the analysis for (x0, x2)

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Degenerate Cases

• Simulation can result in plausible biological
  events that are not detectable by the algorithm.
• Useless transfers LGTs that dont change the
  gene tree
• Transfer-loss events One child of a node is a
  LGT event. Another child is a loss event.

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Results

• O number of repetitions
• t true number of LGT events
• t minimum cost LGT scenario found by algorithm
• ? mean rate of LGTs from Poisson process

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Finding the saturation point

• The point when the average t stops increasing.
• Random trees from a large pool were chosen as
  gene trees and species trees
• Trials suggest that saturation point is slightly
  above n/2, i.e., when t gt n/2, the algorithms
  stops detecting new LGT events
• Thus, if t gt n/2, the correspondence between T
  and S via LGT events is not very meaningful.

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Results

• O number of repetitions
• t true number of LGT events
• t minimum cost LGT scenario found by algorithm
• ? mean rate of LGTs from Poisson process

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Results

• O number of repetitions
• t true number of LGT events
• t minimum cost LGT scenario found by algorithm
• ? mean rate of LGTs from Poisson process

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Results

• O number of repetitions
• t true number of LGT events
• t minimum cost LGT scenario found by algorithm
• ? mean rate of LGTs from Poisson process

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Conclusions

• Empirically verified feasibility of the
  t-transfer algorithm
• Degenerate events such as transfer-loss events
  that result in over-estimates of transfers occur
  with low probability
• Achieved near-optimal scenarios when ? is low
  enough not to cause saturation
• The cycle elimination phase of the algorithm is
  extremely rare in practice implying a O(22t n2)
  running time.

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Future work and open problems

• Use weighted gene trees and species trees
• Species trees are nearly ultra-metric while gene
  trees are not
• Do fast algorithms exist when the input is a set
  of gene trees with no species tree?
• Tractability on larger phylogenies
• Can we consider gene duplication, lateral gene
  transfers, and other events simultaneously?
• Can we use probabilistic models that assign
  likelihood events to various events and optimize
  over such models in a tractable manner?