Abstract “Space-for-time” substitution is widely used in biodiversity modeling to infer past or future trajectories of ecological systems from contemporary spatial patterns. However, the foundational assumption—that drivers of spatial gradients of species composition also drive temporal changes in diversity—rarely is tested. Here, we empirically test the space-for-time assumption by constructing orthogonal datasets of compositional turnover of plant taxa and climatic dissimilarity through time and across space from Late Quaternary pollen records in eastern North America, then modeling climate-driven compositional turnover. Predictions relying on space-for-time substitution were ∼72% as accurate as “time-for-time” predictions. However, space-for-time substitution performed poorly during the Holocene when temporal variation in climate was small relative to spatial variation and required subsampling to match the extent of spatial and temporal climatic gradients. Despite this caution, our results generally support the judicious use of space-for-time substitution in modeling community responses to climate change.

Viewed broadly, space-for-time substitution encompasses analyses in which contemporary spatial phenomena are used to understand and model temporal processes that are otherwise unobservable, most notably past and future events. Many fields have developed and debated methods relying on space-for-time substitution, such as ecological chronosequences to study long-term nutrient cycling and plant succession (1⇓–3) and transfer functions for inferring past environmental changes from geological proxies (4, 5). The assumption of space-for-time substitutability has been queried and debated most closely in chronosequence studies, with conclusions ranging from strong support (6) to strong rejection (2) of space-for-time substitution. Increasingly, space-for-time substitution is being applied in biodiversity modeling to project climate-driven changes in species distributions, species richness, and compositional turnover (7⇓⇓⇓–11). Examination of transferability of models for individual species has exposed concerns regarding the projection of these spatial models across time (12⇓⇓–15), and it has been suggested that models based on collective biodiversity properties might be more robust (9, 16, 17). However, the fundamental assumption that spatial relationships between climate and biodiversity can be used to project temporal trajectories of biodiversity under changing climates remains largely untested (but see refs. 16 and 18).

The turnover of species among communities is particularly well suited for testing space-for-time substitution because it can be quantified independently across space or through time and because compositional turnover strongly correlates to climate variations in both space and time (19⇓–21). However, other factors, such as species history, site history, and species interactions, also influence compositional turnover, independently or interacting with climate (22⇓–24). Even when climate is the main determinant of community composition, certain aspects of climate (e.g., temporal variability, covariance among critical variables) may be fundamentally more different across space than through time (25, 26). Understanding the extent to which compositional turnover is related to climate, and whether these relationships are the same across space and time, is essential to evaluating the accuracy of projections of compositional turnover with future climate change.

Here, we test whether the environmental influences on compositional turnover across space are the same as those through time, by constructing orthogonal spatial and temporal datasets of compositional turnover, then using these datasets to assess the predictive skill of models relying on “space-for-time” vs. “time-for-time” substitution (Fig. S1; see Materials and Methods and SI Materials and Methods for details). These datasets were constructed from fossil pollen assemblages from the Neotoma Paleoecology Database (www.neotomadb.org) and paleoclimate simulations from the National Center for Atmospheric Research Community Climate System Model version 3 (CCSM3) (27) for the past 21,000 y (i.e., the Late Quaternary) in eastern North America. In the spatial dataset, the compositional dissimilarities between all site pairs across space were calculated for a single time period then pooled with spatial comparisons from all other 1,000-y time slices over the past 21,000 y (Fig. 1A). In the temporal dataset, the compositional dissimilarities between all sample pairs at a single site through time were calculated then pooled with temporal comparisons for all other sites in eastern North America (Fig. 1B).

Fig. 1. Spatial (A) and temporal (B) dataset construction, resulting predictions of temporal turnover (C–E), and fitted functions (F) for the Late Quaternary datasets (21–0 kyBP). In all cases, the red lines indicate spatial datasets, blue lines indicate temporal datasets, and dashed lines indicate the 1:1 line. (C) RMA regression between temporal turnover predicted by the temporal model and by the spatial model. (D) OLS regression between observed temporal turnover and temporal turnover predicted by the spatial model (space-for-time substitution). (E) OLS regression between observed temporal turnover and temporal turnover predicted by the temporal model (time-for-time substitution). (F) The fitted functions for each variable. b, Intercept of the regression line; cv, coefficient of variation; m, slope of the regression line; R2, goodness of fit.

We calibrated generalized dissimilarity models (28) using these spatial and temporal dissimilarities then predicted compositional dissimilarity through time (temporal turnover) using either a spatial model (space-for-time) or a temporal model (time-for-time) (Fig. S1). Three expectations emerge if climate affects compositional turnover similarly across space and time: (i) predictions using space-for-time substitution should be as reliable as time-for-time predictions, (ii) the same environmental factors should emerge in explaining compositional turnover across space and time, and (iii) the rates and magnitudes of compositional turnover along environmental gradients should be similar across space and time.

Materials and Methods Fossil Pollen Data. Fossil pollen data are based on those used in ref. 39. Briefly, fossil pollen sites from eastern North America from 21 kyBP to the present were drawn from the Neotoma Paleoecology Database (www.neotomadb.org) and represent genus-level pollen relative abundances for a suite of 106 genera across eastern North America. Age models were updated, recalibrated, and standardized across sites (41). The fossil pollen assemblage at each site thus consists of the relative abundances of pollen types in each sample, calculated relative to the sum of all upland pollen types. The fossil pollen taxonomy was standardized across sites, and only taxa identified to genus or better are included, except for closely related and palynologically indistinguishable genera such as Ostrya/Carpinus. If taxa were identified to a finer taxonomic resolution, they were binned into their constituent genus. The paleoclimate simulations are available at a 0.5 × 0.5° grid (∼50 × 50 km) (Paleoclimate Simulations); if more than one fossil pollen site occupied a climate grid cell, the relative abundance of each taxon across all sites within the cell was averaged. The final dataset encompasses 527 sites occupying 336 grid cells in eastern North America. Previous work with fossil pollen data has established that generalized dissimilarity modeling (GDM) is robust to variation in taxonomic level, sample size differences through time, climate models, and different methods of weighting the relative abundance of sites within climate grid cells (39). Paleoclimate Simulations. We paired the fossil pollen data with transient paleoclimate simulations from the National Center for Atmospheric Research CCSM3 (27). These data were debiased and downscaled to a 0.5 × 0.5° grid (∼50 × 50 km) and processed to infer seasonal temperatures and precipitation every 1,000 y since the LGM 21 kyBP (15). Downscaled paleoclimate simulations are available publicly through the University of Wisconsin Center for Climatic Research (http://purl.org/climate). We also included atmospheric CO 2 concentration as a predictor (42, 43), because this is an important influence on plant physiology and vegetation composition (44) that has varied through time and will continue to change in the future (45). CO 2 data were drawn from EPICA Dome C (42), an 800,000-y composite CO 2 record from East Antarctica on which the CO 2 data for 22–0 kyBP are based (46). The chronology was updated to EDC3_gas_a, the official chronology (47). Overall, final predictor variables used to construct models included six climatic predictors—mean precipitation and mean temperature for winter (December to February) and summer (June to August), plus indices of temperature seasonality and precipitation seasonality [equivalent to bioclimatic variables 4 and 15 in WorldClim (48)]—and CO 2 . We tested the influence of CO 2 by removing this variable and refitting all models without CO 2 . The pollen and climate datasets were used previously to model the relationship between climate and compositional dissimilarity across space using GDM and to investigate the temporal stability of these spatial relationships (39). This prior work showed that the differences in fossil pollen assemblage composition across space were robust to choice of paleoclimate simulation (39), so here we use only the CCSM3 simulations. GDM. We used GDM to explore space-for-time substitution in fossil pollen assemblages from the past 21,000 y in eastern North America. GDM fits compositional dissimilarity as a function of environmental and/or geographic separation (28) and allows inference of the relative contribution of each environmental variable to overall compositional dissimilarity. Fitted functions for each variable indicate the rate of compositional turnover along the environmental gradient, and the maximum height attained on the y-axis indicates the relative importance of the variable to overall compositional dissimilarity. We pooled data across all times for the spatial dataset and across all sites for the temporal dataset (Fig. 1 and Fig. S1). This approach pools community and climate data across multiple time periods and thus integrates across shifting niches, no-analog climates, and other factors to capture multiple realizations of community–climate relationships (49). Pooling also creates large datasets (383,287 pairwise dissimilarities in the spatial dataset and 18,584 in the temporal dataset), which increases analytical power. Finally, pooling controls for potential sources of bias and error; i.e., climate models may be inaccurate (50) and pollen data represent a biased sample of fossil plant taxa (51), but there is no reason to expect that these issues are differential in space vs. time. To build and evaluate models, we split each dataset into training and evaluation partitions by randomly assigning 70% of the sample pairs from each dataset to a training partition to build the models and the remaining 30% of the sample pairs to an evaluation partition for testing model predictions. We used GDM to fit models of compositional dissimilarity in the training datasets (Fig. S1 and Table S3). All models in the main paper are fitted with environmental variables only (as opposed to environment plus geographic or temporal distance) to focus on the substitutability of environment-based models. Each model then was used to predict both spatial and temporal compositional dissimilarity in each of the evaluation datasets. When making predictions to the evaluation datasets, we reset the intercept to zero within the parameter file output for each model. Mantel tests cannot be used to assess significance owing to the nonindependence of each point (the same sample may be involved in many different pairwise comparisons, thus the individual points are not independent), the structure of the datasets (each dissimilarity matrix for an individual time or individual site was aggregated with the matrices for other sites or times; Fig. 1), and the sampling procedure for dividing the datasets into training and evaluation partitions, which was based on pairs of sites rather than single sites. Instead, we evaluated how well the predictions correlate to each other (model-to-model comparisons) using RMA regression, because there was no a priori expectation for independent vs. dependent variables and both predictions should have similar uncertainty. We used OLS regression to compare the predictions with observed compositional dissimilarity (model-to-observation comparisons), because here there is a clear dependence of predictions on observations. We report only the slope, intercept, and R2 value for each model and not the significance level. We also quantify the “predictive skill” of space-for-time substitution as the performance of space-for-time substitution relative to time-for-time substitution, based on the R2 values of the respective correlation tests (i.e., Table S2; predictive skill = R2 space-for-time /R2 time-for-time ). To focus on the space-for-time transferability of climate-based models, we report only results of space-for-time substitution in the main paper. Time-for-space substitution results and sensitivity tests using different predictor variables are reported in SI Materials and Methods, Tables S1–S3, and Figs. S2–S6. We used a new version of the GDM software for R developed by Glenn Manion and Simon Ferrier to build models and make predictions to new data (GDM4Tables, version 1.0, available at http://purl.org/gdm). All other analyses also were done in R, version 2.15.1 (52). Climate Subsampling. We processed the Late Quaternary (21–0 kyBP), Late Pleistocene (21–11 kyBP), and Holocene (10–0 kyBP) training and evaluation datasets using coarsened exact matching with the R package MatchIt (53, 54). MatchIt considers the pairwise differences in each climate variable and extracts sets of sites in both the spatial and temporal datasets such that the underlying climate dissimilarities match as closely as possible. We did not include CO 2 in the set of variables to use for matching, because this variable varies across time only and not space. In effect, we preprocessed the datasets based only on their climate variables to give GDM the best chance possible at building models that are substitutable. This processing substantially reduced the size of the datasets [after processing, the spatial dataset included 3,086 dissimilarities for the Late Pleistocene (14.6% of the original dataset) and 15,441 (6.2% of the original dataset) for the Holocene, whereas the temporal dataset was reduced to 724 pairwise comparisons for the Late Pleistocene (72.4% of the original dataset) and 7,960 comparisons during the Holocene (99.3% of the original dataset)], and the resulting range of climate differences was comparable between the datasets (Fig. 3 and Fig. S6). We then refit models to each training dataset and predicted spatial and temporal dissimilarity of the subsampled evaluation datasets (Tables S1–S3 and Fig. S2).

Acknowledgments We thank the editor and three anonymous reviewers. This project was funded by the National Science Foundation (EAR-0844223 and DEB-0949308). M.C.F. acknowledges support from the US Department of Energy’s National Institute for Climate Change Research through Subaward 3892-HU-DOE-4157 and support from University of Maryland Center for Environmental Science. This is University of Wisconsin Center for Climatic Research Publication 1132.

Footnotes Author contributions: J.L.B., J.W.W., and S.F. designed research; J.L.B. performed research; S.F. contributed new reagents/analytic tools; J.L.B., J.W.W., M.C.F., S.T.J., and S.F. analyzed data; and J.L.B., J.W.W., M.C.F., S.T.J., and S.F. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.

Data deposition: The base data is publicly available through the Neotoma Paleoecology Database, www.neotomadb.org (for pollen data) and via the University of Wisconsin Center for Climatic Research, http://purl.org/climate (for downscaled paleoclimate simulations); and the generalized dissimilarity modeling datasets and supporting code used in this project have been deposited in the Dryad Repository, http://dx.doi.org/doi:10.5061/dryad.d5f1r.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1220228110/-/DCSupplemental.