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Following severe environmental change that reduces mean population fitness below replacement, populations must adapt to avoid eventual extinction, a process called evolutionary rescue. Models of evolutionary rescue demonstrate that initial size, genetic variation and degree of maladaptation influence population fates. However, many models feature populations that grow without negative density dependence or with constant genetic diversity despite precipitous population decline, assumptions likely to be violated in conservation settings. We examined the simultaneous influences of density-dependent growth and erosion of genetic diversity on populations adapting to novel environmental change using stochastic, individual-based simulations. Density dependence decreased the probability of rescue and increased the probability of extinction, especially in large and initially well-adapted populations that previously have been predicted to be at low risk. Increased extinction occurred shortly following environmental change, as populations under density dependence experienced more rapid decline and reached smaller sizes. Populations that experienced evolutionary rescue lost genetic diversity through drift and adaptation, particularly under density dependence. Populations that declined to extinction entered an extinction vortex, where small size increased drift, loss of genetic diversity and the fixation of maladaptive alleles, hindered adaptation and kept populations at small densities where they were vulnerable to extinction via demographic stochasticity. 

ABSTRACT Predicting the effects of climate change on plant and animal populations is an urgent challenge for understanding the fate of biodiversity under global change. At the surface, quantifying how climate drives the vital rates that underlie population dynamics appears simple, yet many decisions are required to connect climate to demographic data. Competing approaches have emerged in the literature with little consensus around best practices. Here we provide a practical guide for how to best link vital rates to climate for the purposes of inference and projection of population dynamics. We first describe the sources of demographic and climate data underlying population models. We then focus on best practices to model the relationships between vital rates and climate, highlighting what we can learn from mechanistic and phenomenological models. Finally, we discuss the challenges of prediction and forecasting in the face of uncertainty about climate‐demographic relationships as well as future climate. We conclude by suggesting ways forward to build this field of research into one that makes robust forecasts of population persistence, with opportunities for synthesis across species.