Model structure

Scale

Space

• How should we deal with spatial autocorrelation at different scales? Nearby traps are correlated, nearby plots are correlated, etc.

Time

• How should we handle time? Daily updates? Euler steps with variable length?

Process model

• Do we want an actual population dynamics model with growth rates and carrying capacities and stuff, or just let the state diffuse according to a simpler model? Population dynamic model is more ecologically informative, but could be much harder to get working.

• How should we deal with potential nonlinearities and interactions in the process model? E.g., what functional form should rodents' response to temperature have?

• How should we build in annual cycling? By integrating over environmental conditions or with something simpler like simple periodic forcing?

• Discrete population sizes or not? Discrete population sizes won't work in Stan, because it can't sample discrete latent variables and there's no good way to marginalize them out.

• Do we track the lives of individual rodents (probably not) or just keep track of populations/densities?

Observation model

• Do we treat the traps as independent multinomial draws (i.e. roll a weighted die to determine which species shows up in each trap)? Or do we do something to account for the fact that local populations can be exhausted after a few traps are filled up with a given species? Maybe a multivariate hypergeometric distribution (i.e. pulling multi-colored marbles out of a finite-sized bag)? Would that require discrete population sizes and/or the ability to sample discrete variables and rule out Stan?

• Could we use individual IDs for a mark-recapture type estimate of population sizes, even if we don't do survival analyses on each critter?