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This paper introduces an approach to estimate a convergence from discord between phylogenetic species trees and gene trees, using Gene Duplication and Expression events.

A Gene Duplication (GD) event refers to when a bifurcation of the phylogenetic gene tree occurs creating two duplicate gene loci. The first image marks them in solid white diamonds.

A Gene Expression (GE) event refers to the loss or Regulatory Mutation (RM) of genes. The types are:

  • Gene Loss (marked by the cross in the first image) refers to when a locus is lost/deleted along the lineage of an extant species.
  • Gene Inactivation (marked by the unfilled downward caret in the first image) refers to a Regulatory Mutation where a gene is rendered inactive.
  • Gene Reactivation (marked by the unfilled upward caret in the first image) refers to a Regulatory Mutation where a previously inactivated gene is reactivated and sampled in extant species.

Now, in the event of a discord between a gene tree and a species tree, we can attempt to establish concordance through assumptions about hypothetical duplication and expression events. The gene tree with a minimum count of (GD + GE) is the most likely assumption for concordance.

In the first image, the right locus resulting from the second bifurcation of the gene tree is sampled in extant species C and D and undergoes a loss event for species E. I would assume that it would also undergo a loss event for species A and B but the paper merges those two loss events into one.

On the other hand, based on the second image from this paper, I've simulated the Gene Duplication/Expression events on the gene tree and found that if such loss events are merged into one, the Duplication/Expression (D/E in the table) count I calculate is lower than what is mentioned in the table.

I'm confused as to whether there is an appropriate approach to this. The author of the first paper mentions that such assumptions regarding Gene Duplication and Expression events are not at all representative of real Gene Duplication and Expression events (established through observed evidence) and serve as a mechanism to approach likely solutions to discordance between species trees and gene trees.

My question is, how do I arrive at the minimum cost tree?

First Image

Second Image

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