Data for: 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

Centroid data used for the analysis in Roos et al. Eco Lett.

Transects, up to 99 m in length (dependent on the field's length), were surveyed in linear stable landscape features (field, track or ditch margins) to estimate vole abundance from November 2011 until September 2017. Each transect was divided into 3 m sections (33 in total) and the presence or absence of one or more signs of vole activity (i.e., latrines by burrows, fresh vegetation clippings, and recent burrow excavations) in each section was noted. The proportion of sections with signs of vole presence per transect was then used as the abundance index. The number of surveys carried out at any time varied adaptively with the perceived risk of an outbreak (according to changes in estimated abundance in previous monitoring surveys).

The response variable typically used in all models is proportional growth rate (r_{t,i}, where  is the abundance index for site  at time  (Royama 1992; Berryman 2002). A benefit of using r_{t,i}, rather than ln(N_{t,i}), is that any multiplicative effects of site quality are cancelled out, provided they are constant over time. To calculate r_{t,i}, vole abundance indices are required at the same location in successive time periods (i.e., N_{t,i} and N_{t+1,i}). Given that exact transect locations were rarely reused in successive months, and all transect measurements took place throughout the year rather than discrete seasons, the data had to be aggregated to consistent locations and times to allow growth rate to be calculated.  As such, transects were temporally aggregated into a respective yearly quarter (e.g., January to March 2014). Transects were spatially aggregated by sequentially selecting an unassigned transect as a reference point for the ith centroid and assigning all unassigned transects within a 5 km radius to the ith  centroid, and repeating until all transects had been allocated (see Figure 2 for a summary of the number of transects assigned to each centroid, centroid locations, and time series of growth rate of each centroid). Once complete, the mean Julian day, X and Y UTM (Universal Transverse Mercator) and the mean index was calculated for all transects assigned to each centroid  for each time period. Where a centroid had successive values of N_{t,i} and N_{t+1,i} available, the corresponding proportional growth rate was calculated.

A constant of 3.03 was added to N_{t,i} to avoid zero entries (3.03 was the lowest non-zero value of N observed). The final dataset consisted of 3,751 observations.