This paper explores how populations adapt to environmental change and the factors that determine their extinction risk. It presents a model to predict the critical rate of environmental change beyond which a population will decline and go extinct. The model incorporates phenotypic plasticity and environmental sensitivity of selection, which are key factors in population persistence. The study highlights the importance of understanding these mechanisms to improve predictions of population responses to environmental change and to guide conservation efforts. Two main approaches are used to study the impact of environmental change on species persistence: niche modelling and mechanistic population modelling. Niche models focus on environmental variables and predict range shifts and extinction rates, but they do not account for biological processes underlying adaptation. In contrast, mechanistic population models focus on biological processes and can predict population persistence based on ecological and evolutionary traits. The model presented in the paper considers three main factors that determine extinction risk: demographic properties of the population, evolutionary potential, and the biological impact of the environment. Demographic properties include generation time and intrinsic growth rate, while evolutionary potential is determined by genetic variance and stabilizing selection. The biological impact of the environment includes phenotypic plasticity and environmental sensitivity of selection. The study emphasizes the need for further research on phenotypic plasticity and environmental sensitivity of selection to improve predictions of population persistence in a changing environment. It also highlights the importance of measuring these factors in natural populations to understand their role in adaptation and extinction. The paper concludes that a mechanistic approach that incorporates evolutionary and demographic mechanisms is necessary for making accurate predictions about population responses to environmental change.This paper explores how populations adapt to environmental change and the factors that determine their extinction risk. It presents a model to predict the critical rate of environmental change beyond which a population will decline and go extinct. The model incorporates phenotypic plasticity and environmental sensitivity of selection, which are key factors in population persistence. The study highlights the importance of understanding these mechanisms to improve predictions of population responses to environmental change and to guide conservation efforts. Two main approaches are used to study the impact of environmental change on species persistence: niche modelling and mechanistic population modelling. Niche models focus on environmental variables and predict range shifts and extinction rates, but they do not account for biological processes underlying adaptation. In contrast, mechanistic population models focus on biological processes and can predict population persistence based on ecological and evolutionary traits. The model presented in the paper considers three main factors that determine extinction risk: demographic properties of the population, evolutionary potential, and the biological impact of the environment. Demographic properties include generation time and intrinsic growth rate, while evolutionary potential is determined by genetic variance and stabilizing selection. The biological impact of the environment includes phenotypic plasticity and environmental sensitivity of selection. The study emphasizes the need for further research on phenotypic plasticity and environmental sensitivity of selection to improve predictions of population persistence in a changing environment. It also highlights the importance of measuring these factors in natural populations to understand their role in adaptation and extinction. The paper concludes that a mechanistic approach that incorporates evolutionary and demographic mechanisms is necessary for making accurate predictions about population responses to environmental change.