Aim  Concerns over how global change will influence species distributions, in conjunction with increased emphasis on understanding niche dynamics in evolutionary and community contexts, highlight the growing need for robust methods to quantify niche differences between or within taxa. We propose a statistical framework to describe and compare environmental niches from occurrence and spatial environmental data. Location  Europe, North America and South America. Methods  The framework applies kernel smoothers to densities of species occurrence in gridded environmental space to calculate metrics of niche overlap and test hypotheses regarding niche conservatism. We use this framework and simulated species with pre‐defined distributions and amounts of niche overlap to evaluate several ordination and species distribution modelling techniques for quantifying niche overlap. We illustrate the approach with data on two well‐studied invasive species. Results  We show that niche overlap can be accurately detected with the framework when variables driving the distributions are known. The method is robust to known and previously undocumented biases related to the dependence of species occurrences on the frequency of environmental conditions that occur across geographical space. The use of a kernel smoother makes the process of moving from geographical space to multivariate environmental space independent of both sampling effort and arbitrary choice of resolution in environmental space. However, the use of ordination and species distribution model techniques for selecting, combining and weighting variables on which niche overlap is calculated provide contrasting results. Main conclusions  The framework meets the increasing need for robust methods to quantify niche differences. It is appropriate for studying niche differences between species, subspecies or intra‐specific lineages that differ in their geographical distributions. Alternatively, it can be used to measure the degree to which the environmental niche of a species or intra‐specific lineage has changed over time.

Local adaptation is a central feature of most species occupying spatially heterogeneous environments, and may factor critically in responses to environmental change. However, most efforts to model the response of species to climate change ignore intraspecific variation due to local adaptation. Here, we present a new perspective on spatial modelling of organism-environment relationships that combines genomic data and community-level modelling to develop scenarios regarding the geographic distribution of genomic variation in response to environmental change. Rather than modelling species within communities, we use these techniques to model large numbers of loci across genomes. Using balsam poplar (Populus balsamifera) as a case study, we demonstrate how our framework can accommodate nonlinear responses of loci to environmental gradients. We identify a threshold response to temperature in the circadian clock gene GIGANTEA-5 (GI5), suggesting that this gene has experienced strong local adaptation to temperature. We also demonstrate how these methods can map ecological adaptation from genomic data, including the identification of predicted differences in the genetic composition of populations under current and future climates. Community-level modelling of genomic variation represents an important advance in landscape genomics and spatial modelling of biodiversity that moves beyond species-level assessments of climate change vulnerability.

Biotic interactions drive key ecological and evolutionary processes and mediate ecosystem responses to climate change. The direction, frequency, and intensity of biotic interactions can in turn be altered by climate change. Understanding the complex interplay between climate and biotic interactions is thus essential for fully anticipating how ecosystems will respond to the fast rates of current warming, which are unprecedented since the end of the last glacial period. We highlight episodes of climate change that have disrupted ecosystems and trophic interactions over time scales ranging from years to millennia by changing species' relative abundances and geographic ranges, causing extinctions, and creating transient and novel communities dominated by generalist species and interactions. These patterns emerge repeatedly across disparate temporal and spatial scales, suggesting the possibility of similar underlying processes. Based on these findings, we identify knowledge gaps and fruitful areas for research that will further our understanding of the effects of climate change on ecosystems.

"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 climatedriven 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.fossil pollen | global change | paleoecology | generalized dissimilarity modeling V iewed 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 longterm 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)(20)(21). However, other factors, such as species history, site history, and species interactions, also influence compositional turnover, independently or...

Contents 38I.38II.Approaches for reconstructing refugia: strengths, limitations and recent advances39III.46IV.47V.48VI.4949References49 Summary Climate refugia, locations where taxa survive periods of regionally adverse climate, are thought to be critical for maintaining biodiversity through the glacial–interglacial climate changes of the Quaternary. A critical research need is to better integrate and reconcile the three major lines of evidence used to infer the existence of past refugia – fossil records, species distribution models and phylogeographic surveys – in order to characterize the complex spatiotemporal trajectories of species and populations in and out of refugia. Here we review the complementary strengths, limitations and new advances for these three approaches. We provide case studies to illustrate their combined application, and point the way towards new opportunities for synthesizing these disparate lines of evidence. Case studies with European beech, Qinghai spruce and Douglas‐fir illustrate how the combination of these three approaches successfully resolves complex species histories not attainable from any one approach. Promising new statistical techniques can capitalize on the strengths of each method and provide a robust quantitative reconstruction of species history. Studying past refugia can help identify contemporary refugia and clarify their conservation significance, in particular by elucidating the fine‐scale processes and the particular geographic locations that buffer species against rapidly changing climate.