Thus, predicting species responses to novel climates is problematic, because we often lack sufficient observational data to fully determine in which climates a species can or cannot grow (Figure 3). Fortunately, the no-analog problem only affects niche modeling when (1) the envelope of observed climates truncates a fundamental niche and (2) the direction of environmental change causes currently unobserved portions of a species' fundamental niche to open up (Figure 5). Species-level uncertainties accumulate at the community level owing to ecological interactions, so the composition and structure of communities in novel climate regimes will be difficult to predict. Increases in atmospheric CO2 should increase the temperature optimum for photosynthesis and reduce sensitivity to moisture stress (Sage and Coleman 2001), weakening the foundation for applying present empirical plant–climate relationships to predict species' responses to future climates. At worst, we may only be able to predict that many novel communities will emerge and surprises will occur. Mechanistic ecological models, such as dynamic global vegetation models (Cramer et al. 2001), are in principle better suited for predicting responses to novel climates. However, in practice, most such models include only a limited number of plant functional types (and so are not designed for modeling species-level responses), or they are partially parameterized using modern ecological observations (and thus may have limited predictive power in no-analog settings).

In eastern North America, the high pollen abundances of temperate tree taxa (Fraxinus, Ostrya/Carpinus, Ulmus) in these highly seasonal climates may be explained by their position at the edge of the current North American climate envelope (Williams et al. 2006; Figure 3). This pattern suggests that the fundamental niches for these taxa extend beyond the set of climates observed at present (Figure 3), so that these taxa may be able to sustain more seasonal regimes than exist anywhere today (eg Figure 1), as long as winter temperatures do not fall below the −40°C mean daily freezing limit for temperate trees (Sakai and Weiser 1973).

To simulate equilibrium sagebrush cover under projected future climate, we applied average projected changes in precipitation and temperature to the observed climate time series. For each GCM and RCP scenario combination, we calculated average precipitation and temperature over the 1950–2000 time period and the 2050–2098 time period. We then calculated the absolute change in temperature between the two time periods (ΔT) and the proportional change in precipitation between the two time periods (ΔP) for each GCM and RCP scenario combination. Lastly, we applied ΔT and ΔP to the observed 28-year climate time series to generate a future climate time series for each GCM and RCP scenario combination. These generated climate time series were used to simulate equilibrium sagebrush cover.

Our process model (in Eq. (2)) includes a log transformation of the observations (log(yt − 1)). Thus, our model does not accommodate zeros. Fortunately, we had very few instances where pixels had 0% cover at time t − 1 (n = 47, which is 0.01% of the data set). Thus, we excluded those pixels from the model fitting process. However, when simulating the process, we needed to include possible transitions from zero to nonzero percent cover. We fit an intercept-only logistic model to estimate the probability of a pixel going from zero to nonzero cover: yi∼Bernoulli(μi)(8)logit(μi)=b0(9)where y is a vector of 0s and 1s corresponding to whether a pixel was colonized (>0% cover) or not (remains at 0% cover) and μi is the expected probability of colonization as a function of the mean probability of colonization (b0). We fit this simple model using the “glm” command in R (R Core Team 2014). For data sets in which zeros are more common and the colonization process more important, the same spatial statistical approach we used for our cover change model could be applied and covariates such as cover of neighboring cells could be included.

Our approach models interannual changes in plant cover as a function of seasonal climate variables. We used daily historic weather data for the center of our study site from the NASA Daymet data set (available online: http://daymet.ornl.gov/). The Daymet weather data are interpolated between coarse observation units and capture some spatial variation. We relied on weather data for the centroid of our study area.

Because SDMs typically rely on occurrence data, their projections of habitat suitability or probability of occurrence provide little information on the future states of populations in the core of their range—areas where a species exists now and is expected to persist in the future (Ehrlén and Morris 2015).

Whilst the consensus method we used provided the best predictions under AUC assessment – seemingly confirming its potential for reducing model-based uncertainty in SDM predictions [58], [59] – its accuracy to predict changes in occupancy was lower than most single models. As a result, we advocate great care when selecting the ensemble of models from which to derive consensus predictions; as previously discussed by Araújo et al. [21], models should be chosen based on aspects of their individual performance pertinent to the research question being addressed, and not on the assumption that more models are better.

Finally, by assuming the non-detection of a species to indicate absence from a given grid cell, we introduced an extra level of error into our models. This error depends on the probability of false absence given imperfect detection (i.e., the probability that a species was present but remained undetected in a given grid cell [73]): the higher this probability, the higher the risk of incorrectly quantifying species-climate relationships [73].