Supplementary material S1. Table S1. Key environmental variables considered in the BN and the spatial layer used. Key environmental Source of data Variable & spatial layer Values used Description of map in BN and assumptions used made when scaling to 25km2 grid Soil Moisture Bioclim Bioclim layers Too wet >1.7 Original data at 0.01 1. mean moisture index of generated for current Too dry < degree resolution. highest quarter climate and 2070 0.01; Just Resampled to 25 km 2. mean moisture index of medium and high right 0.04- grid via bilinear the driest quarter sensitivity scenarios 0.75 interpolation. As above Temperature Original data at 0.01 1. min temp for coldest too cold degree resolution. period <2.5ºC Resampled to 25 km 2. max temp for warmest Temperature grid via bilinear period too hot > interpolation. Temperature Bioclim 43ºC Rainfall Bioclim mean annual As above rainfall Low < Original data at 0.01 300mm; degree resolution. Moderate Resampled to 25 km 300-750; grid via bilinear High >750 interpolation. Suitable Original data at 0.01 ≥16ºC degree resolution. Temperature wettest quarter Bioclim mean temperature As above of wettest quarter Resampled to 25 km Unsuitable grid via bilinear <16ºC interpolation. Grazing Intensity ACRIS, stocking rates Livestock density Assumed Coverage only for DSE/km2 (DSE/sq km) for equal rangelands. rangeland IBRAs - probability of 1992 to 2004 (Bastin, low, AcRIS Management moderate committee 2008) and high http://www.environment grazing .gov.au/land/publication s/acris/report08.html Fire Frequency Australia Fire High fire Original data source Frequency, 1km frequency at 1 km resolution. AVHRR maps for 1997- calculated as Resampled to 25km 2008 covering the an area burnt grid using nearest whole of Australia. 3 times or neighbour http://138.80.128.152/n greater assignment. afi2/about/ausfrqdownlo during a 12 ad.htm year period NVIS - reclassified to Australia – Present Tree cover Original data source suitable (vegetation with Major Vegetation considered at 1km resolution. less than >70% tree cover) Subgroups – NVIS unsuitable Reclassified to and unsuitable (more than Stage 1, Version 3.1 – when greater classes ‘suitable’ and 70% tree cover and water) Albers, than 70% ‘unsuitable’ based on Tree cover http://www.environment major vegetation .gov.au/erin/nvis/mvg/in subgroup dex.html#mvs descriptions (ESCAVI, Australian Vegetation Attribute Manual version 6, 2003). Resampled to 25km grid via nearest neighbour assignment. Distance to source Current distribution of http://www.ersa.edu.au/ Close Point shapefile buffel grass from avh/ <100km buffered at 500 km Australian Virtual Mid 100- and 1000 km. Herbarium 500km; Converted to raster Far >500km 25km grid. Soil Surface Salinity Forecasted areas Australia Dryland low 0-2 dS/m Original data at containing land of high Salinity Assessment = suitable 1:2,500,000. hazard or risk of dryland Spatial Data medium 3-8 Resampled to 25km salinity from 2000 to 2050 (1:2,500,000) - NLWRA dS/m = grid via nearest 2001. partially neighbour Spatial coverage very suitable assignment. Current poor. Where gaps high >8 dS/m layer covers <10% of assumed equal = unsuitable Australia, there for probability of suitable dS/m=deci- did not use. vs unsuitable Siemens/m Soil pH for Australian Soil Ph < 5.0 Original data at 0.001 Areas of Intensive considered degree resolution. Agriculture of Top Soil, strongly Resampled to 25km NLWRA, acidic and grid via bilinear http://www.indexgeo.ne unsuitable interpolation. Soil pH t/asdd/anrdl/summary/s phaar9nnd_01611_.ht ml Soil Type Northcote key Atlas of Australian Soils Expert knowledge (Northcote et al. 1960- from John McIvor 1968), ASRIS. Original data source http://www.asris.csiro.a at 1:2,000,000 u/themes/Atlas.html resolution, Resampled to 25km grid via nearest neighbour assignment. S2. Description of elicited relationships within the BN The relationships between variables within the BN were determined by an expert panel and validated with empirical data where available. Influence of climate on suitability for buffel grass colonization According to experts, buffel grass establishment and persistence also responds directly to ‘soil moisture’. Ideal ‘soil moisture’ conditions for buffel grass ranged between 0.04 and 0.75 (see Fig 1 main paper, link 1). A value of 1 indicated complete soil saturation and values greater than 1.7 and less than 0.01 impeded buffel grass establishment and persistence (Lawson et al. 2004). Buffel grows in areas with average annual rainfall between 100-1000mm, but ideal conditions are between 300-750mm/year (http://www.tropicalforages.info/, accessed 17/02/2014; (Cox et al. 1988)). Nodes ‘Rainfall’ (Fig 1, link 2) and ‘grazing intensity’ combined to form a grazing index (discussed below). ‘Temperature’ affects buffel persistence directly through cold and heat stress (Fig 1, link 3). Below 2.5ºC and above 43ºC persistence of buffel is impeded (http://www.tropicalforages.info/, accessed 17/02/2014). Being a warm season growing grass (C4), the Kranz leaf anatomy of buffel grass is specialized for hot climates. Where buffel grows well, the growing period coincides with summer rains. In southern Australia, where buffel is currently absent, the rains fall in winter – when it is currently too cold for buffel establishment. In the future as winter temperatures increase, this impediment may no longer exist. We therefore used the BIOCLIM layer mean temperature of wettest quarter to capture this feature (Fig 1, Temperature wettest quarter, link 4). Influence of environmental variables on suitability for buffel grass colonization Evidence suggests that there is a positive feedback between fire and buffel grass colonization with its ability to withstand very hot fires and germinate quickly following fire, outcompeting other plants, in particular spinifex, which is killed in frequent hot fires (Fairfax, Fensham 2000) (Fig 1, link 5). High ‘fire frequency’ was calculated as an area burnt three times or greater during a 12 year period and was derived from a national fire frequency spatial layer (Table S1). According to experts, buffel grass responds positively to moderate to high grazing pressure by reducing competition from other less grazing tolerant native grasses (Fig 1, link 6). Nodes ‘grazing intensity’ and ‘rainfall’ combined to form a ‘grazing index’ node which was defined as; low - history of low stocking rates relative to landscape, understory intact; moderate - understory effects obvious - loss of some shrub structure, and; high - loss of understory structure, loss and decline of native perennial tussock grasses. The node ‘soil quality’ influenced buffel grass establishment and persistence (Fig 1, link 10) and was made up of ‘soil surface salinity’, ‘soil pH’ and ‘soil type’. The Australia Dryland Salinity Assessment Spatial Data (Table S1) was used to classify soil salinity into three categories; low 0-2 dS/m, medium 3-8 dS/m and high >8 dS/m (dS/m=deci-Siemens/m), where low was deemed suitable, medium partially suitable and high unsuitable (Fig 1, link 7). Similarly soil pH was classified using the Australian Areas of Intensive Agriculture of Top Soil (Fig 1, link 8, Table S1) as either unsuitable = strongly acidic pH water < 5.0 or suitable pH 7-8 (http://www.tropicalforages.info). Finally, suitable soil types were derived from expert knowledge (J. McIvor), and mapped using data from the Atlas of Australian Soils and ASRIS (http://www.asris.csiro.au/themes/Atlas.html) (Table S1, Fig 1, link 9). In general, buffel grass prefers lighter textured soils, although is well-adapted to deep, freely draining sandy loam, loam, clay loam, and well-structured red and dark clay soils (Cox et al. 1988). The node ‘distance to source’ of current buffel grass sites was used with a binary node ‘seeded’ delineating whether buffel grass had been deliberately seeded for pasture or not (Fig 1, link 12) to determine the invasion requirement ‘introduction’ (Fig 1, link 15). Distance from known buffel records was based on the Australian Virtual Herbarium (Table S1), and was used to classify current buffel records as close ~ <100 km, mid~ 100-500 km and far ~ >500 km. Based on their knowledge of dispersal ability experts deemed the category close to have a 15% chance of introduction and both mid and far a 1% chance (Fig 1, link 11). ‘Tree cover’ above 70% was deemed by the experts to impede buffel establishment (Fig 1, link 13). Together the ‘fire frequency’, ‘grazing index’ and ‘soil quality’ nodes influenced ‘plant competition’, which in turn influenced buffel grass ‘establishment’ (Fig 1, link 14). The node ‘introduction’ influenced landscape ‘susceptibility’ to buffel grass (Fig 1, link 15), and nodes ‘establishment’ and ‘persistence’ influenced ‘suitability’ (Fig 1, links 16 & 17). Finally nodes ‘suitability’ along with ‘introduction’ influenced ‘susceptibility’ (Fig 1, link 18).