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Most quantitative global-change assessments of rates of change have focused on future climate alone^{3, 5, 6, 8, 9}, without considering other factors. Conversely, most future land-use scenarios do not consider climate change^{10, 11, 12} and emphasize total habitat losses rather than rates of change. As the distributions of species and diversity are affected by multiple environmental factors, multivariate approaches to assess the rates of climate or land-use change are needed. Using a new joint measure of exposure to climate and land-use changes that combines elements of velocity-based^{3, 5, 6} and analogue-based methods^{6, 8, 9} (Methods), here we measure the combined speeds of climate and land-use change for the conterminous US based on multiple land-use and climate scenarios.

Our approach is based on the univariate velocity of change, measured as the ratio of temporal anomalies to spatial gradient³ (Methods); for example,

to translate estimates of temporal rates of changes into estimates of spatial velocities. This metric provides a standardized measure of exposure² of species to spatially rapid rates of change. Climatic velocities determine the rates at which a given species needs to move to stay within a given range of climate. Land-use velocities index the rapidity of land-cover conversion, which can lead to habitat loss, spatial isolation and the emergence of dispersal barriers.

We build on this to develop a new estimate of the exposure of ecosystems to rapid change across multiple dimensions of climate and land use (Methods), providing an overarching index that is independent of the natural history attributes of individual species. This measure combines the principle of individual velocity-based metrics^{3, 5, 6} with the multivariate assessments enabled by analogue-based methods^{6, 8, 9}. As with univariate velocity measurements, multivariate speed is the ratio of rates of changes in space and time, but the underlying variable is a multivariate dissimilarity index: standardized Euclidean distance (SED) calculated as

where a_{k, i} and b_{k, j} are means for the climatic or land-use variable k at the contrasted (j) and target (i) grid points, and is the historical interannual variability. SED is unitless, so that

Note that we define our multivariate rates as ‘speeds’ rather than ‘velocities’ because multivariate spatial estimates do not include direction⁵ but retain velocities when referring to univariate rates of change. Furthermore, in contrast to previous analogue-based estimates of spatiotemporal change^{6, 9}, the normalization by local spatial dissimilarity gradients means that our metric is an index of local climatic or land-use composition change across a spatially varying gradient, rather than regional displacement vectors typical of analogue-based approaches^{6, 9}.

We map estimates of univariate velocity and multivariate speeds for climate and land use from AD 2001–2011 to 2041–2051 for the conterminous US, using the Intergovernmental Panel on Climate Change scenarios of the 5th Assessment Report¹³, and future land-use changes under alternative socioeconomic scenarios, based on an econometric model extrapolations of the US Natural Resources Inventory for the period 2001–2051^{11, 12}. The primary results presented here are for intermediate climate and land-use scenarios (Representative Concentration Pathway (RCP) 6.0 for climate and land-use projections following 1990s trends), and thus are conservative with respect to future outcomes. Results for other scenarios are presented as figures and in the Supplementary Information.

Climate velocities varied widely among variables (Fig. 1a–i) and ecoregions (Table 1), ranging from 1.8 to 37.1 km decade⁻¹. Among climate variables, evapotranspiration and water deficit had faster velocities than annual mean temperature and precipitation (Fig. 1). Velocities were highest in regions with little topographic relief, such as the Great Plains and the northeast, and lowest in the western US, and varied greatly among ecoregions owing to variations in both temporal trends of climate change and contemporary spatial patterns. The spatial patterns of our projected future climate velocities closely resemble those for historic climate velocities in the US⁵, highlighting the importance of topographic controls on climate velocity. The projected velocities and speeds that we report are higher than previous estimates of historical velocities⁵ (0.80–1 km decade⁻¹ for 1916–2005, and 2–5 km decade⁻¹ for 1976–2005). However, these historical velocities were calculated from 1-km-resolution data sets, and these velocities increase by a factor of 10 when analysed at the 10-km resolution of our study⁵, bringing the previously estimated historic and our projected rates of change into closer alignment. Spatial patterns of multivariate climate speeds (Fig. 1a) are consistent with univariate patterns, with slower multivariate speeds in the topographically heterogeneous west and northeast.

a,b, Multivariate speeds represent the ratio between SEDs in time (temporal change) and space (spatial heterogeneity), integrated across climate (a) and land-use (b) variables. b–l, Univariate velocities represent the ratio between temporal and spatial gradients across climate (b–f) and land-use (h–l) variables. Multivariate speeds (a–g) are generally faster than for individual climatic (b–f) or land-use (h–l) variables.

We analysed present and future climatic decadal projections (to reduce the effect of interannual variability and extreme events), at 10-km resolution based on the ensemble forecast of 39 downscaled climatic simulations³⁰ for the periods 2001–2011 and 2041–2051 under a range of RCPs developed for the Intergovernmental Panel on Climate Change 5th Assessment Report¹³. Historical climate velocities have already been studied for this region⁵, and we focus here on the combination of future climate and land-use change.

Future climate change was initially mapped using the climate change velocity metric³. Univariate climate velocities were estimated as the ratio between univariate temporal trends (that is, anomalies between 2001–2010 and 2041–2050) and vector-based spatial gradients⁴ (that is, spatial dissimilarity in a 3 × 3 grid-cell neighbourhood, a neighbourhood size that maximizes the effective spatial resolution of the analysis)^{3, 5}. Our analyses were based on five variables, which all determine species’ distributions and diversity patterns: mean annual temperature, potential evapotranspiration, total annual precipitation, annual water deficit and winter minimum temperature. These variables are among the most commonly used in species distributions modelling to describe the environmental tolerances of Nearctic¹⁴ and Palaearctic²³ biota. We then calculated and mapped multivariate climate speeds based on all 5 variables as we describe below.

In adapting the climate velocity index to land-cover change, we first measured the rate of change of single land-cover types. Land-use velocities were determined as the ratio between the expected amount of change over time (that is, for the 10-km grid we calculated the area of each land use in the future minus the area of the same land use at the present time) and the spatial heterogeneity of land use (that is, for a 10-km grid we calculated the difference in coverage of each land use under present conditions in the 3 × 3 surrounding cells). This metric evaluates the degree of land-use-coverage stability (that is, prevalence of a given land-use coverage in the future weighted by the coverage in the surrounding areas), summarizing the exposure to future land-use changes relative to current heterogeneity in land composition. High land-use velocity occurs when the rate of land-cover change is high or when land use is locally uniform, implying few refuges for species displaced by land-use change.

We focused on five land-cover classes: forests, rangelands, pasture, croplands and urban. Present and future land-use coverage for each of the five land-cover classes were determined based on an econometric model^{11, 12} that predicts spatially explicit land-use changes across the conterminous US for the period 2001–2051. These projections of future land-use change are driven only by alternative economic incentives, which at the timescale of this study (~50 yr) are more important drivers of land-use change than climate. We focus on future conditions over historical changes to illustrate how alternative land-use policy and economic scenarios (increased crop commodity prices, restricted urban growth) could intersect with scenarios of future climates, together altering the local exposure to future changes.

Our multivariate spatiotemporal rates of change, which we define as ‘speeds’ owing to their no-directional nature, combine dissimilarity metrics such as those used in analogue-based analyses^{6, 8, 9} with the buffering effect of spatial heterogeneity used in climate-velocity analyses^{3, 5, 14}. This index measures the ratio between multivariate dissimilarities in space and time, and thus represents the expected reshuffling over time based on the changes in both climatic or land-use composition, weighted by the environmental similarity in the surrounding cells. By normalizing the changes by local spatial dissimilarity, we advance from regional displacement vectors^{6, 9} to an index of local speed of a climatic or land-use composition.

For both climate and land use, we quantified dissimilarities in time (between 2001–2010 and 2041–2051) and space (mean SED from all pairwise SEDs in the 3 × 3-cell neighbourhood) by using the SED as it equally weights all variables and emphasizes trends that are large relative to the 1950–2001 interannual variability:

where a_{k, j} and b_{k, i} are the means for climate or land-use variable k at grid points j (future or neighbouring cell conditions) and i (target cell), and is the historical standard deviation of the interannual variability for grid point i from 1950 to 2001.

Finally, we merge the climate and land-use multivariate metrics into a single combined speed map (Figs 2 and 3), representing the combined exposure to climate and land-use change. For this, we created a colour-coded composite of climatic and land-use speeds (multivariate, forest and rangeland).

1. Chapin, F. S. III et al. Consequences of changing biodiversity. Nature 405, 234–242 (2000).
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2. Dawson, T. P., Jackson, S. T., House, J. I., Prentice, I. C. & Mace, G. M. Beyond predictions: Biodiversity conservation in a changing climate. Science 332, 53–58 (2011).
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