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Aim There is enormous interest in applying connectivity modelling to resistance surfaces for identifying corridors for conservation action. However, the multiple analytical approaches used to estimate resistance surfaces and predict connectivity across resistance surfaces have not been rigorously compared, and it is unclear what methods provide the best inferences about population connectivity. Using a large empirical data set on puma (Puma concolor), we are the first to compare several of the most common approaches for estimating resistance and modelling connectivity and validate them with dispersal data. Location Southern California, USA. Methods We estimate resistance using presence‐only data, GPS telemetry data from puma home ranges and genetic data using a variety of analytical methods. We model connectivity with cost distance and circuit theory algorithms. We then measure the ability of each data type and connectivity algorithm to capture GPS telemetry points of dispersing pumas. Results We found that resource selection functions based on GPS telemetry points and paths outperformed species distribution models when applied using cost distance connectivity algorithms. Point and path selection functions were not statistically different in their performance, but point selection functions were more sensitive to the transformation used to convert relative probability of use to resistance. Point and path selection functions and landscape genetics outperformed other methods when applied with cost distance; no methods outperformed one another with circuit theory. Main conclusions We conclude that path or point selection functions, or landscape genetic models, should be used to estimate landscape resistance for wildlife. In cases where resource limitations prohibit the collection of GPS collar or genetic data, our results suggest that species distribution models, while weaker, may still be sufficient for resistance estimation. We recommend the use of cost distance‐based approaches, such as least‐cost corridors and resistant kernels, for estimating connectivity and identifying functional corridors for terrestrial wildlife.

hring utan ymbbearh, þaet heo þone fyrdhom ðurhfon ne mihte, locene leoðosyrcan laþan fingrum.On his shoulder lay braided breast-mail, barring death, withstanding entrance of edge or blade.Beowulf (Old English epic poem, c. 10th Century)

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Broad scale population estimates of declining species are desired for conservation efforts. However, for many secretive species including large carnivores, such estimates are often difficult. Based on published density estimates obtained through camera trapping, presence/absence data, and globally available predictive variables derived from satellite imagery, we modelled density and occurrence of a large carnivore, the jaguar, across the species’ entire range. We then combined these models in a hierarchical framework to estimate the total population. Our models indicate that potential jaguar density is best predicted by measures of primary productivity, with the highest densities in the most productive tropical habitats and a clear declining gradient with distance from the equator. Jaguar distribution, in contrast, is determined by the combined effects of human impacts and environmental factors: probability of jaguar occurrence increased with forest cover, mean temperature, and annual precipitation and declined with increases in human foot print index and human density. Probability of occurrence was also significantly higher for protected areas than outside of them. We estimated the world’s jaguar population at 173,000 (95% CI: 138,000–208,000) individuals, mostly concentrated in the Amazon Basin; elsewhere, populations tend to be small and fragmented. The high number of jaguars results from the large total area still occupied (almost 9 million km2) and low human densities (< 1 person/km2) coinciding with high primary productivity in the core area of jaguar range. Our results show the importance of protected areas for jaguar persistence. We conclude that combining modelling of density and distribution can reveal ecological patterns and processes at global scales, can provide robust estimates for use in species assessments, and can guide broad-scale conservation actions.

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