The overall methodological framework for deriving the BERI indicator is described in Ferrier et al. (2019).  This framework is underpinned by global models of spatial turnover in species composition, or 'ecological similarity', established as part of CSIRO's Biogeographic modelling Infrastructure for Large-scale Biodiversity Indicators (BILBI; Hoskins et al. 2019). These correlative models predict the ecological similarity expected between any two grid-cells on the planet as a function of fine-scaled spatial variation in climate, terrain and soils within major biomes and biogeographic realms (Table 1). The models were fitted to best-available occurrence records for large numbers of species, and best-available environmental surfaces, using generalised dissimilarity modelling (Ferrier et al. 2007). Nonlinear functions generated by this model-fitting process describe the relative importance of different environmental gradients in driving spatial turnover in species composition, and how rates of turnover vary between different positions along each of these gradients.

For the purposes of deriving the BERI indicator, these functions are used to project potential shifts in species composition over time, under a plausible range of climate scenarios. These projected shifts in species composition then serve as a set of filters through which to assess the capacity of an observed configuration of habitat condition (Table 2) to retain biological diversity under climate change. This capacity is assessed in relation to each individual grid-cell in turn (serving as a 'focal cell') by analysing the connectedness of this cell to areas of habitat in the surrounding landscape which are both: 1) in relatively good condition; and 2) projected to support an assemblage of species under plausible future climates (Table 3) which is similar in composition to that associated with the focal cell under present climatic conditions. The value of BERI assigned to each cell is then calculated as a robust summary statistic of resulting levels of connectedness for the evaluated climate scenarios. This is expressed as a ratio relative to the connectedness achievable if the cell were surrounded by a continuous expanse of intact habitat, and were not subjected to any change in climate.

Table 1. Ecological similarity models (Ferrier et al. 2007; Hoskins et al. 2019). 

Description	Data Types	Components	Sources
The fitted generalized dissimilarity models (GDMs) represent spatial turnover in species composition as a function of environmental variables, the geographical distance between records, and the identity of WWF ecoregions within which they occur. "Ecological similarity" equals the predicted proportional overlap in species composition between any given pair of locations (grid cells) - i.e. the mean proportion of species occurring at one of the locations that would be expected to also occur at the other location (in the absence of habitat degradation at both locations).	Abiotic Environmental Surfaces	Min Monthly Min Temperature	WorldClim, WorldGrids
		Max Monthly Max Temperature
		Max Diurnal Temperature Range
		Annual Precipitation
		Actual Evaporation
		Potential Evaporation
		Min Monthly Water Deficit
		Max Monthly Water Deficit
		Soil pH	SoilGrids
		Soil Clay Proportion
		Soil Silt Proportion
		Soil Bulk Density
		Soil Depth
		Ruggedness Index	EarthEnv
		Topographic Wetlands Index
	Global Occurrence Records for Terrestrial Species	Amphibians, Birds, Mammals	Map of Life
		Vascular plants, Reptiles, Ants, Bees, Beetles, Bugs, Butterflies, Centipedes, Dragonflies, Flies, Grasshoppers, Millipedes, Snails, Moths, Spiders, Termites, Wasps	Global Biodiversity Information Facility (GBIF)
	Bio-realms	N/A	WWF

 Table 2. Change in habitat condition.

Description	Data Types	Sources
Change in condition was estimated through an extension of CSIRO's statistical downscaling of coarse-resolution land-use data using 1km-resolution environmental and remotely-sensed land-cover covariates (Hoskins et al 2016). This recent work has adapted Hoskins et al's approach to employ Version 2, in place of Version 1, of the Land Use Harmonization product, thereby generating downscaled estimates of 12, rather than the original five, land-use classes, and MODIS Vegetation Continuous Fields as remote-sensing covariatesin place of discrete land-cover classes (Di Marco et al. 2019). Applying this downscaling approach across multiple years provides an effective means of translating observed changes in remote-sensing covariates into estimated changes in the proportions of land-use classes occurring in each and every 1km terrestrial grid-cell on the planet. These proportions are then, in turn, translated into an estimate of habitat condition, for any given cell in any given year, using coefficients derived from global meta-analyses of land-use impacts on local retention of species diversity undertaken by the PREDICTS project (Newbold et al. 2016; https://www.predicts.org.uk/), augmented and harmonized with coefficients derived independently by Chaudhary and Brooks (2018). These harmonized coefficients scale condition in terms of the proportion of native species (i.e. alpha diversity), originally associated with a given cell, which are expected to still be present at that location.	Land Cover	Land Use Harmonization, Version 2
	Vegetation	MODIS Vegetation Continuous Fields

Table 3. Climate scenarios.

Description	Data Types	Sources
Six climate scenarios were used, all projected to 2050. Each of these scenarios combines a particular climate model (GCM) with a particular level of greenhouse gas concentration (RCP). Four of the scenarios employ the IPSL-CM5A-LR GCM, combined with RCP 2.6, RCP 4.5, RCP 6.0 and RCP 8.5 respectively.  To account for potential differences between climate models, RCP 8.5 (the highest greenhouse-gas concentration) was further combined with two alternative GCMs: ACCESS1-0 and GFDL-CM3.	Downscaled CMIP5 climate projections	WorldClim