Is there a method for continuous (in time) sampling?

[LeoFeatherstone]

Hi @mcelentano and @wsdewitt ,

I greatly appreciate your work in Celentano et al. (2025) PNAS, and to have discovered BDMS as a result.

I am wondering if there is an existing or planned method for sampling tips continuously in time?

I can see the Tree.sample_survivors method which I gather corresponds to sampling extant tips w.p. $\rho$ in Celentano et al. Is there a corresponding method for sampling with rate $\psi$ ? If not, do you think this could be achieved with creative use of the discrete mutation process where one state is absorbing and pruned later to emulate to sampling?

Thanks again for your wonderful work here. I think it's going to open a lot of doors for applying the birth death.

All the best,
Leo

[wsdewitt]

Hi Leo,

Many thanks for noticing our work! We did consider this as something we should do, so thanks for raising this issue to keep it on our radar. In principle, it would be nice to implement both a rate-based sampling process as well as concerted sampling events at specified times.

I think your suggestion would work, but note:

1. The particles in the absorbing state will still count toward the total population size during simulation, so the carrying capacity (if you are using one) may not behave as expected.
2. Before pruning, you could pre-order traverse and for any node in the absorbing state you would prune the subtree below it (it is a stick if the absorbing state has zero birth and death rate) and assign the attribute node.event = TreeNode._SAMPLING_EVENT.

A possible alternative formulation would be to interpret the death rate process as a sum of death and sampling $r(t)=\mu(t)+\psi(t)$, so after simulating you then resurrect each death event w.p. ${\psi(t)}/{r(t)}$ (where the death events are the leaves with node.event = TreeNode._DEATH_EVENT and "resurrect" means setting node.event = TreeNode._SAMPLING_EVENT).

Let me know if you make headway with this! If you get something working, we'd be happy to consider a PR.

[LeoFeatherstone]

Many thanks @wsdewitt!

I think your suggestion of what I will term "post-thinning" makes the most sense.

If you are using a Gillespie algorithm, the particles in the sampled state I suggested would convolute the mass action rate.

I will let you know if I make any progress here.

Cheers,
Leo