Selecting different dated trees as part of the biogeographical model

[fvfreitas]

I am working on historical biogeographic analyses in RevBayes using DEC-style models with connectivity matrices.
I would like to ask for feedback on a model-selection strategy involving different dated phylogenetic trees.
My current workflow is:

1. Infer alternative time-calibrated trees under different software. My group does not have any fossils available, so I am using a secondary calibration at the root.
2. For each fixed dated tree, run two biogeographic models in RevBayes (different connectivity scenarios).
3. Use stepping-stone marginal likelihoods/Bayes factors to select the best biogeographic model within each tree.
4. Then compare the resulting marginal likelihoods across analyses that use different dated trees.
   Conceptually, (I think) this treats the dated tree as part of the overall biogeographic model specification.
   My questions are:
   • Does it make statistical sense to compare marginal likelihoods across analyses that differ in both:
   o the biogeographic model, and
   o the underlying dated tree?
   • Has anyone implemented or published a similar framework?
   • Would this be considered a valid comparison of integrated biogeographic hypotheses, or would it instead confound phylogenetic and biogeographic uncertainty?
   • Is there a preferred alternative approach for incorporating uncertainty among alternative dated trees in DEC-like analyses?

Thank you.

[davidcerny]

Just in case a late reply is better than none, here are some insightful comments that @afmagee made in the RevBayes developers' Slack after I posted a link to this discussion there (shared with his permission):

Marginal likelihoods are, for data Y and model M, Pr(Y | M). These can be used to select models or average them. How sensible this is when chained into a sequential analysis depends entirely on what gets put in and where it comes from/what's assumed about it.

In this case, it sounds like the M is "the combination of one of a handful of candidate trees and one of a handful of candidate DEC models" so you can pick "the best tree and DEC model combination."

But I don't really see what the best of those is good for here? Since point trees are being fed in, nothing can be said about distributions of divergence times or clade probabilities. Since they're summaries of inference of (1) different data (the molecular without the locations, presumably) under (2) models assuredly different in different ways, there's no particular obvious way to average over them.

I also think this is in danger of being a sort of XY problem (https://en.wikipedia.org/wiki/XY_problem). Starting with an analysis plan, rather than a clear analysis goal is dangerous.

If one had a posterior sample of trees from different analysis programs A_1, A_2, ..., and different DEC models G_1, G_2, ..., then one could probably find a way to handwave that you can pick the best G | A_i, that is, the best DEC model within whatever other model choices go into "I ran BEAST X under..." or "I used RevBayes with..." In that case, the different G | A_i look like a sensitivity analysis of some sort. And since distributions of trees go in, distributional summaries come out (node age distributions, clade probabilities) rather than being lost in the wash of point estimate trees.