The persistence of local populations exposed to climate change depends on their adaptive potential and on the ability of local individuals to compete with migrating conspecifics tracking environmental shifts. Modern coexistence theory (MCT) offers a framework for studying such competitive interactions among genotypes. However, MCT often focuses on emerging population-level outcomes, aggregating over the underlying individual-level interactions. We present a cross-scale application of MCT, combining it with an Integral Projection Model (IPM), explicitly connecting individual performance to population-level dynamics. We parameterise our model using experimental data on competing Daphnia genotypes from two latitudes. Consistent with observations, our model shows that higher temperatures increase the likelihood of competitive exclusion of Northern genotypes by Southern genotypes. Moreover, it reveals latitudinal variation in neonate sex ratios as a driver of temperature-dependent evolutionary shifts. By identifying vital rates underlying population-level competitive outcomes, our approach preserves the straightforward theoretical interpretability of MCT, while providing enhanced process-level resolution through IPMs.