Timescale separated pollination-colonisation models

In flowering plant species con-specifies of distinct type may cross-pollinate. The type of offspring that result depends on both the pollen donor and the parent that produces the seed. Within a cellular automaton framework, this process fundamentally requires consideration of triplets of cells: a pollen donor, a seed producer, and a empty cell to be colonised. Such a triplet process cannot be captured by the standard second order analytical tool of pair approximation. We propose a general cellular automaton model for an arbitrary number of inter-pollinating con-specifics. Time scale separation between the dynamics of distinct pollination and colonisation processes permits aggregation of variables in mean field and pair approximation characterisations. The aggregated pair approximation successfully captures the triplet processes at work in the cellular automaton model.