Climate change can affect the habitat resources available to species by changing habitat quantity, suitability and spatial configuration, which largely determine population persistence in the landscape. In this context, dispersal is a central process for species to track their niche. Assessments of the amount of reachable habitat (ARH) using static snap-shots do not account, however, for the temporal overlap of habitat patches that may enhance stepping-stone effects. Here, we quantified the impacts of climate change on the ARH using a spatio-temporal connectivity model. We first explored the importance of spatio-temporal connectivity relative to purely spatial connectivity in a changing climate by generating virtual species distributions and analyzed the relative effects of changes in habitat quantity, suitability and configuration. Then, we studied the importance of spatio-temporal connectivity in three vertebrate species with divergent responses to climate change in North America (grey wolf, Canadian lynx and white-tailed deer). We found that the spatio-temporal connectivity could enhance the stepping-stone effect for species predicted to experience range contractions, and the relative importance of the spatio-temporal connectivity increased with the reduction in habitat quantity and suitability. Conversely, for species that are likely to expand their ranges, spatio-temporal connectivity had no additional contribution to improve the ARH. We also found that changes in habitat amount (quantity and suitability) were more influential than changes in habitat configuration in determining the relative importance of spatio-temporal connectivity. We conclude that spatio-temporal connectivity may provide less biased and more realistic estimates of habitat connectivity than purely spatial connectivity.

In the study, first, we used theoretical simulations by generating virtual species distributions, to explore the effect sizes of changes in habitat quantity, suitability and spatial configuration on the relative importance of spatio-temporal connectivity. These analysis were conducted through the combination of R scripts and a command version of software package "Conefor.exe" (Saura and Torne 2009). The R scripts to perform these analyses are "theoretic simulation.R", "runConefor. R", "main.R" and "statistical analysis.R" in the folder "R script"; and the generated results were put in the folder "virtual species". The software package "Conefor.exe" could be freely accessible through the supporting information of Martensen et al., 2017, or at Conefor.org. After downloading "Conefor.exe", it should be put in the sub-folder "input files" to ensure the successful runs of scripts "runConefor.R" and "main.R".

Second, we explored the importance of spatio-temporal connectivity to three real species residing in sourthern and central Ontario, Canada, with divergent responses to climate change. These species include: white-tailed deer, Canada Lynx and grey wolf. The R scripts to perform analyses for real species include: "species distribution model.R", "runConefor. R" and "main.R". The generated results are put in the folder "actual species".