I wonder when can complex simulations be formulated as possibly complex but still analytical equations. I'm particularly interested in agent based models, that are frequently used in evolutionary biology.
These models are composed of individuals on a regular grid of cells, and each individual have chances to migrate to neighbouring cells or stay where they are, chances to survive, chances to mate and produce offspring etc. all with probabilities coming from some known basic distributions.
These models look really nice and seem to be very intuitive and flexible (for non-technical people at least) so that you can resemble reality as close as you like. But I get the feeling like we are fooling ourselves for two reasons:
First, these simulations really take a long time, even in optimal conditions with well implemented algorithms with suitable programming languages on powerful computers.
Second, we try to deduce a general system behaviour based on replicates of the simulation and also using several alternative values for some simulation parameters. Selection of alternative parameter values and number of replicates for each parameter set is often based on intuition. Quantitative changes in parameter values may lead to qualitative changes in system behaviour and we may not be able to see whole picture with a few parameter values, and also a couple thousand replicates may not be enough for a reliable inference.
So, back to my question, are there any rules of thumb regarding when a simulation is effectively irreducible to closed-form equations? And as a side questions, are there methods to assess reliability of agent based models?