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1. Demographic and evolutionary modelling approaches are critical to understanding and projecting species responses to global environmental changes. Population matrix models have been a favoured tool in demography, but until recently, they failed to account for short-term evolutionary changes. Evolutionary-explicit demographic models remain computationally intensive, difficult to use and have yet to be widely adopted for empirical studies. Researchers focusing on short-term evolution often favour individual-based simulations, which are more flexible but less transferable and computationally efficient. Limited communication between fields has led to differing perspectives on key issues, such as how life-history traits affect adaptation to environmental change. We develop a new EvoDemo hyperstate matrix population model (EvoDemo-Hyper MPM) that incorporates the genetic inheritance of quantitative traits, enabling fast computation of evolutionary and demographic dynamics. We evaluate EvoDemo-Hyper MPM against individual-based simulations and provide analytical approximations for adaptation rates across six distinct scales in response to selection. We show that different methods yield equivalent results for the same biological scenario, although semantic differences between fields may obscure these similarities. Our results demonstrate thatEvoDemo-Hyper MPM provides accurate, computationally efficient solutions, closely matching outcomes from individual-based simulations and analytical approximations under similar biological conditions. Adaptation rates per generation remain constant across species when selection acts on fertility but vary with other vital rates. Adaptation per time decreases with generation time unless selection targets adult survival, where intermediate life histories adapt fastest. Rates per generation, defined as the relative change in individual fitness, remain constant across species and vital rates.4. We discuss that no general prediction emerges about which species or life-history traits yield higher adaptation rates, as outcomes depend on life cycles, vital rates | 1645 VAN de WALLE et al.