913 may also lead to dependence between species (phylogenetic structure) or populations of species (genetic structure) with more recent divergence will tend to be more similar than those which diverged longer ago (Harvey and Pagel 1991). While such underlying structures in the data are not fundamentally problematic for statistical analyses, they tend to create two undesirable outcomes. First, model error, as well as neglected processes and variables connected to these structures, often leads to dependence structures in the model residuals, which violates the critical assumption of independence present in many models and methods (Legendre and Fortin 1989, Miller et al. 2007). Second, because predictor variables are often correlated with underlying dependence structures (e.g. climate with space), models may use predic-tors to overfit the residual dependence structure and thereby remove it, partially or completely.

The velocity of climate change is an elegant analytical concept that can be used to evaluate the exposure of organisms to climate change. In essence, one divides the rate of climate change by the rate of spatial climate variability to obtain a speed at which species must migrate over the surface of the earth to maintain constant climate conditions. However, to apply the algorithm for conservation and management purposes, additional information is needed to improve realism at local scales. For example, destination information is needed to ensure that vectors describing speed and direction of required migration do not point toward a climatic cul-de-sac by pointing beyond mountain tops. Here, we present an analytical approach that conforms to standard velocity algorithms if climate equivalents are nearby. Otherwise, the algorithm extends the search for climate refugia, which can be expanded to search for multivariate climate matches. With source and destination information available, forward and backward velocities can be calculated allowing useful inferences about conservation of species (present-to-future velocities) and management of species populations (future-to-present velocities).

In ecology, the true causal structure for a given problem is often not known, and several plausible models and thus model predictions exist. It has been claimed that using weighted averages of these models can reduce prediction error, as well as better reflect model selection uncertainty. These claims, however, are often demonstrated by isolated examples. Analysts must better understand under which conditions model averaging can improve predictions and their uncertainty estimates. Moreover, a large range of different model averaging methods exists, raising the question of how they differ in their behaviour and performance. Here, we review the mathematical foundations of model averaging along with the diversity of approaches available. We explain that the error in model‐averaged predictions depends on each model's predictive bias and variance, as well as the covariance in predictions between models, and uncertainty about model weights. We show that model averaging is particularly useful if the predictive error of contributing model predictions is dominated by variance, and if the covariance between models is low. For noisy data, which predominate in ecology, these conditions will often be met. Many different methods to derive averaging weights exist, from Bayesian over information‐theoretical to cross‐validation optimized and resampling approaches. A general recommendation is difficult, because the performance of methods is often context dependent. Importantly, estimating weights creates some additional uncertainty. As a result, estimated model weights may not always outperform arbitrary fixed weights, such as equal weights for all models. When averaging a set of models with many inadequate models, however, estimating model weights will typically be superior to equal weights. We also investigate the quality of the confidence intervals calculated for model‐averaged predictions, showing that they differ greatly in behaviour and seldom manage to achieve nominal coverage. Our overall recommendations stress the importance of non‐parametric methods such as cross‐validation for a reliable uncertainty quantification of model‐averaged predictions.

As most regions of the earth transition to altered climatic conditions, new methods are needed to identify refugia and other areas whose conservation would facilitate persistence of biodiversity under climate change. We compared several common approaches to conservation planning focused on climate resilience over a broad range of ecological settings across North America and evaluated how commonalities in the priority areas identified by different methods varied with regional context and spatial scale. Our results indicate that priority areas based on different environmental diversity metrics differed substantially from each other and from priorities based on spatiotemporal metrics such as climatic velocity. Refugia identified by diversity or velocity metrics were not strongly associated with the current protected area system, suggesting the need for additional conservation measures including protection of refugia. Despite the inherent uncertainties in predicting future climate, we found that variation among climatic velocities derived from different general circulation models and emissions pathways was less than the variation among the suite of environmental diversity metrics. To address uncertainty created by this variation, planners can combine priorities identified by alternative metrics at a single resolution and downweight areas of high variation between metrics. Alternately, coarse-resolution velocity metrics can be combined with fine-resolution diversity metrics in order to leverage the respective strengths of the two groups of metrics as tools for identification of potential macro-and microrefugia that in combination maximize both transient and long-term resilience to climate change. Planners should compare and integrate approaches that span a range of model complexity and spatial scale to match the range of ecological and physical processes influencing persistence of biodiversity and identify a conservation network resilient to threats operating at multiple scales. K E Y W O R D Sclimate change adaptation, climatic velocity, conservation planning, environmental diversity, land facets, protected areas, refugia --

Metrics that synthesize the complex effects of climate change are essential tools for mapping future threats to biodiversity and predicting which species are likely to adapt in place to new climatic conditions, disperse and establish in areas with newly suitable climate, or face the prospect of extirpation. The most commonly used of such metrics is the velocity of climate change, which estimates the speed at which species must migrate over the earth’s surface to maintain constant climatic conditions. However, “analog-based” velocities, which represent the actual distance to where analogous climates will be found in the future, may provide contrasting results to the more common form of velocity based on local climate gradients. Additionally, whereas climatic velocity reflects the exposure of organisms to climate change, resultant biotic effects are dependent on the sensitivity of individual species as reflected in part by their climatic niche width. This has motivated development of biotic velocity, a metric which uses data on projected species range shifts to estimate the velocity at which species must move to track their climatic niche. We calculated climatic and biotic velocity for the Western Hemisphere for 1961–2100, and applied the results to example ecological and conservation planning questions, to demonstrate the potential of such analog-based metrics to provide information on broad-scale patterns of exposure and sensitivity. Geographic patterns of biotic velocity for 2954 species of birds, mammals, and amphibians differed from climatic velocity in north temperate and boreal regions. However, both biotic and climatic velocities were greatest at low latitudes, implying that threats to equatorial species arise from both the future magnitude of climatic velocities and the narrow climatic tolerances of species in these regions, which currently experience low seasonal and interannual climatic variability. Biotic and climatic velocity, by approximating lower and upper bounds on migration rates, can inform conservation of species and locally-adapted populations, respectively, and in combination with backward velocity, a function of distance to a source of colonizers adapted to a site’s future climate, can facilitate conservation of diversity at multiple scales in the face of climate change.

As climatic conditions shift in coming decades, persistence of many populations will depend on their ability to colonize habitat newly suitable for their climatic requirements. Opportunities for such range shifts may be limited unless areas that facilitate dispersal under climate change are identified and protected from land uses that impede movement. While many climate adaptation strategies focus on identifying refugia, this study is the first to characterize areas which merit protection for their role in promoting climate connectivity at a continental extent. We identified climate connectivity areas across North America by delineating paths between current climate types and their future analogs that avoided nonanalogous climates, and used centrality metrics to rank the contribution of each location to facilitating dispersal across the landscape. The distribution of connectivity areas was influenced by climatic and topographic factors at multiple spatial scales. Results were robust to uncertainty in the magnitude of future climate change arising from differing emissions scenarios and general circulation models, but sensitive to analysis extent and assumptions concerning dispersal behavior and maximum dispersal distance. Paths were funneled along north-south trending passes and valley systems and away from areas of novel and disappearing climates. Climate connectivity areas, where many potential dispersal paths overlapped, were distinct from refugia and thus poorly captured by many existing conservation strategies. Existing protected areas with high connectivity values were found in southern Mexico, the southwestern US, and western and arctic Canada and Alaska. Ecoregions within the Isthmus of Tehuantepec, Great Plains, eastern temperate forests, high Arctic, and western Canadian Cordillera hold important climate connectivity areas which merit increased conservation focus due to anthropogenic pressures or current low levels of protection. Our coarse-filter climate-type-based results complement and contextualize species-specific analyses and add a missing dimension to climate adaptation planning by identifying landscape features which promote connectivity among refugia.

North American tree species, subspecies and genetic varieties have primarily evolved in a landscape of extensive continental ice and restricted temperate climate environments. Here, we reconstruct the refugial history of western North American trees since the last glacial maximum using species distribution models, validated against 3571 palaeoecological records. We investigate how modern subspecies structure and genetic diversity corresponds to modelled glacial refugia, based on a meta-analysis of allelic richness and expected heterozygosity for 473 populations of 22 tree species. We find that species with strong genetic differentiation into subspecies had widespread and large glacial refugia, whereas species with restricted refugia show no differentiation among populations and little genetic diversity, despite being common over a wide range of environments today. In addition, a strong relationship between allelic richness and the size of modelled glacial refugia (r 2 ¼ 0.55) suggest that population bottlenecks during glacial periods had a pronounced effect on the presence of rare alleles.

Aim We assess the realism of bioclimate envelope model projections for anticipated future climates by validating ecosystem reconstructions for the late Quaternary with fossil and pollen data. Specifically, we ask: (1) do climate conditions with no modern analogue negatively affect the accuracy of ecosystem reconstructions?(2) are bioclimate envelope model projections biased towards under-predicting forested ecosystems? (3) given a palaeoecological perspective, are potential habitat projections for the 21st century within model capabilities?Location Western North America. MethodsWe used an ensemble classifier modelling approach (RandomForest) to spatially project the climate space of modern ecosystem classes throughout the Holocene (at 6000, 9000, 11,000, 14,000, 16,000, and 21,000 YBP) using palaeoclimate surfaces generated by two general circulation models (GFDL and CCM1). The degree of novel arrangement of climate variables was quantified with the multivariate Mahalanobis distance to the nearest modern climatic equivalent. Model projections were validated against biome classifications inferred from 1460 palaeoecological records. ResultsModel accuracy assessed against independent palaeoecology data is generally low for the present day, increases for 6000 YBP, and then rapidly declines towards the last glacial maximum, primarily due to the under-prediction of forested biomes. Misclassifications were closely correlated with the degree of climate dissimilarity from the present day. For future projections, no-analogue climates unexpectedly emerged in the coastal Pacific Northwest but were absent throughout the rest of the study area.Main conclusions Bioclimate envelope models could approximately reconstruct ecosystem distributions for the mid-to late-Holocene but proved unreliable in the Late Pleistocene. We attribute this failure to a combination of no-analogue climates and a potential lack of niche conservatism in tree species. However, climate dissimilarities in future projections are comparatively minor (similar to those of the mid-Holocene), and we conclude that no-analogue climates should not compromise the accuracy of model predictions for the next century.