From pattern to process? Dual travelling waves, with contrasting propagation speeds, best describe a self-organised spatio-temporal pattern in population growth of a cyclic rodent.

The dynamics of cyclic populations distributed in space result from the relative strength of synchronising influences and the limited dispersal of destabilising factors (activators and inhibitors), known to cause multi-annual population cycles. However, while each of these have been well studied in isolation, there is limited empirical evidence of how the processes of synchronisation and activation-inhibition act together, largely owing to the scarcity of datasets with sufficient spatial and temporal scale and resolution. We assessed a variety of models that could be underlying the spatio-temporal pattern, designed to capture both theoretical and empirical understandings of travelling waves using large-scale (>35,000 km ), multi-year (2011-2017) field monitoring data on abundances of common vole (Microtus arvalis), a cyclic agricultural rodent pest. We found most support for a pattern formed from the summation of two radial travelling waves with contrasting speeds that together describe population growth rates across the region.