add in multiple merger coalescence events

[GertjanBisschop]

We can add an argument that specifies the number of lineages that can coalesce. Regular coalescence events would have a parameter equalling 2.

[GertjanBisschop]

Having thought about this a bit more, there are quite a few separate issues.

1. the ability to merge multiple lineages in a single step, this should not be exposed to the user.
2. modelling multiple merger coalescences: for each step 2 up to infinity lineage can coalesce. Each of these events will have their own rate (see beta -coalescent for example). Is this what you where thinking of @A-J-F-Mackintosh?
3. A single discrete multi-merger event (this is akin to the sweep scenario).

[A-J-F-Mackintosh]

Yes, I am interested in implementing a multiple-merger coalescent model.

To be more specific, I am thinking of a 'continuous' version of the sweeps in time model, where the time between sweeps at a coding site is exponentially distributed. Then, for a focal neutral locus on the same chromosome I would (somehow) integrate over all coding sites and their recombination distances from that locus. This should yield a multi-merger coalescent where the rate of k lineages merging would depend on the distribution of recombination distances from coding sites, the rate of beneficial mutations, and the selection coefficient of those mutations.

A similar coalescent model has been described by Durrett and Schweinsberg (2005) with beneficial mutations distributed uniformly across an infinitely long chromosome.

Having said all that, all agemo would need is a general multiple-merger event class, where the user provides a probability distribution for k of n lineages coalescing. This could be a beta distribution, a uniform distribution, or whatever.

Happy to chat more about this

[GertjanBisschop]

Cool, sounds interesting. You want to model recurrent sweeps happening at some rate and resulting in a multi-merger. The time in between these phases should be governed by a regular coalescent I assume. We should probably try and make sure that the fully custom case can be simplified to for example the beta-coalescent.

Like in the coalescent model described by Durrett and Schweinsberg, most (non-haploid) multi-merger coalescents will allow for multiple simultaneous multi-merger events. This is very similar to the Yule-process-based way of modelling the effect of a sweep.

Let's see if we can coordinate with @DerekSetter and find where there is overlap between the discrete sweep we want to get into agemo as well.