Cophylogeny reconstruction allowing for multiple associations through approximate Bayesian computation

Phylogenetic tree reconciliation is extensively employed for the
examination of coevolution between host and symbiont species. An important
concern is the requirement for dependable cost values when selecting
event-based parsimonious reconciliation. Although certain approaches
deduce event probabilities unique to each pair of host and symbiont trees,
which can subsequently be converted into cost values, a significant
limitation lies in their inability to model the invasion of diverse host
species by the same symbiont species (termed as a spread event), which is
believed to occur in symbiotic relationships. Invasions lead to the
observation of multiple associations between symbionts and their hosts
(indicating that a symbiont is no longer exclusive to a single host),
which are incompatible with the existing methods of coevolution. 
Here, we present a method called AmoCoala (an enhanced version of the tool
Coala) that provides a more realistic estimation of cophylogeny event
probabilities for a given pair of host and symbiont trees, even in the
presence of spread events. We expand the classical 4-event coevolutionary
model to include 2 additional spread events (vertical and horizontal
spreads) that lead to multiple associations. In the initial step, we
estimate the probabilities of spread events using heuristic frequencies.
Subsequently, in the second step, we employ an approximate Bayesian
computation (ABC) approach to infer the probabilities of the remaining 4
classical events (cospeciation, duplication, host switch, and loss) based
on these values. By incorporating spread events, our reconciliation model
enables a more accurate consideration of multiple associations. This
improvement enhances the precision of estimated cost sets, paving the way
to a more reliable reconciliation of host and symbiont trees. To validate
our method, we conducted experiments on synthetic datasets and
demonstrated its efficacy using real-world examples. Our results showcase
that AmoCoala produces biologically plausible reconciliation scenarios,
further emphasizing its effectiveness.The software is accessible
at https://github.com/sinaimeri/AmoCoala.