The article discusses the challenges and mechanisms of population persistence in a changing environment, particularly due to human activities. It highlights the need to understand the limits of population persistence and the factors that determine extinction risk. The authors present a simple evolutionary model to identify the critical rate of environmental change beyond which a population must decline and go extinct. Two key parameters, phenotypic plasticity and environmental sensitivity of selection, are identified as important but under-studied factors. The article emphasizes the importance of incorporating these parameters into models of population persistence and suggests research directions to improve predictions based on projected environmental changes. The introduction reviews two main approaches: niche modeling and mechanistic population modeling, highlighting their strengths and limitations. The article concludes by proposing a research program to address the identified gaps and make more accurate predictions about population persistence in a changing environment.The article discusses the challenges and mechanisms of population persistence in a changing environment, particularly due to human activities. It highlights the need to understand the limits of population persistence and the factors that determine extinction risk. The authors present a simple evolutionary model to identify the critical rate of environmental change beyond which a population must decline and go extinct. Two key parameters, phenotypic plasticity and environmental sensitivity of selection, are identified as important but under-studied factors. The article emphasizes the importance of incorporating these parameters into models of population persistence and suggests research directions to improve predictions based on projected environmental changes. The introduction reviews two main approaches: niche modeling and mechanistic population modeling, highlighting their strengths and limitations. The article concludes by proposing a research program to address the identified gaps and make more accurate predictions about population persistence in a changing environment.