A suite of bioclimatic variables including eleven temperature and eight precipitation measures were downloaded from WorldClim v2.083. These include average monthly climate data for the minimum, mean and maximum temperatures and for precipitation, for the years 1970–2000 at a spatial resolution of ~ 1 km2. The details of all bioclimatic variables can be found in Supplementary Table S1. Topographic data was also downloaded from WorldClim v2.0, derived from the Shuttle Radar Topography Mission (SRTM), and re-sampled to 1 km2 resolution84,85. As emus are known to have poor ability to conserve water, and therefore are thought to be more likely to occur near water bodies68, we obtained surface hydrology from GeoScience Australia and calculated a minimum distance to freshwater water per raster cell using ArcGIS 10.686. Since the Australian landscape is prone to fire, and fire has been anecdotally suggested to affect the ability for emus to persist in the landscape32, we included the frequency at which fire occurs across each pixel. Fire frequency (1997–2009) was derived from the 2009 ‘multi-criteria analysis shell for spatial decision support data pack’87,88. To predict for the influence of habitat on emu occurrence, we included land use data from the ‘Australian Land Use and Management Classification v8’88. We estimated the proportion cover of particular agricultural land classifications relevant to emu ecology, including native grazing, modified grazing, irrigated cropping and dry cropping. For native habitats, we combined major vegetation groups from the National Vegetation Information System v5.189 into rainforest, open-forest, woodland, shrubland and grassland (categorisation described in Supplementary Table S1). The emu is a generalist19, occupying a wide diversity of landscapes and a higher level of resolution of vegetation data was considered unlikely to be informative in understanding restrictions on emu distribution at a continental scale. As emus are thought to avoid areas of high urbanisation23, we included log-transformed mean human population calculated in R from gridded population estimates for years 2000, 2005, 2010 and 202090 and the ‘human footprint’ index91 as surrogates indices of urbanisation. The ‘human footprint’ index maps cumulative human pressure, accounting for built-up environments, population density, electric power infrastructure, crop lands, pasture lands, roads, railways, and navigable waterways.

Though some degree of collinearity can be handled by machine learning methods such as the algorithms used here92, we performed variance inflation factor (VIF) analysis to avoid misleading results93,94. This was conducted using the functions vif, vifcor and vifstep in the R package ‘usdm93,94. VIF indicates the degree to which the standard errors of variables are inflated due to the levels of multi-collinearity, which may skew variable importance. We calculated the VIF for all variables, using a stepwise process to exclude variables with the highest VIF, repeating this procedure until no variables with a VIF greater than 10 remained92,95. This process removed bio4, 5, 7, 10, 11, 12, 16 and 17 (see Supplementary Table S1 for layer details). All remaining variables were used to predict the current distribution of emus. Predictions of past and future emu distributions were made using only climatic variables, for reasons of parsimony and reliability (see “Results” above). All predictors were scaled and centred.

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