Illustration of reconciliation events, inputs, outputs, and computational difficulties. Inputs are on the left of entries, output on the right.  Upper trees are drawn in blue, lower trees in red.
This table is intended to serve as illustration to the 2-Level reconciliation section of Menet et al. (2022) Phylogenetic reconciliation. PLoS Comput Biol 18(11): e1010621. doi:10.1371/journal.pcbi.1010621 and can be read along it. 

Adding the horizontal Transfer event adds new, more parsimonious solutions compared to the previous DL model (A).
With this new event, costs must be assigned to D,T and L events, and different costs give different solutions (B).
Not all scenarios including transfers are time feasible. Some might include time constraints incompatible with the upper tree (C).
Transfer can go from a species to one of its descendant via a sister lineages that went extinct (D).
In biogeography, a tree like structure can be constructed to account for the possible migrations between different geographical areas (E).
In some cases, an exponential number of scenarios might be most parsimonious, for example when two equivalent patterns have the same cost (F).
The lower tree can be
unrooted (G),
multifurcating (H), or
given as a sample of potential trees (I) and reconciliation can be used to resolve those uncertainties to get a binary rooted lower tree.
Reconciliation score can also be used to help construct an upper tree (J).
Dynamic programming is limited by the fact that it assumes independence between sister lineages, which makes it unable to consider
replacing transfers or gene conversion (K), as well as
Failure to diverge (L) and
Incomplete Lineage Sorting (M), two population level events.
Own work
Hugo Menet