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Evolve and resequence (E&R) experiments, in which artificial selection is imposed on organisms in a controlled environment, are becoming an increasingly accessible tool for studying the genetic basis of adaptation. Previous work has assessed how different experimental design parameters affect the power to detect the quantitative trait loci (QTL) that underlie adaptive responses in such experiments, but so far there has been little exploration of how this power varies with the genetic architecture of the evolving traits. In this study, we use forward simulation to build a more realistic model of an E&R experiment in which a quantitative polygenic trait experiences a short, but strong, episode of truncation selection. We study the expected power for QTL detection in such an experiment and how this power is influenced by different aspects of trait architecture, including the number of QTL affecting the trait, their starting frequencies, effect sizes, clustering along a chromosome, dominance, and epistasis patterns. We show that all of these parameters can affect allele frequency dynamics at the QTL and linked loci in complex and often unintuitive ways, and thus influence our power to detect them. One consequence of this is that existing detection methods based on models of independent selective sweeps at individual QTL often have lower detection power than a simple measurement of allele frequency differences before and after selection. Our findings highlight the importance of taking trait architecture into account when designing and interpreting studies of molecular adaptation with temporal data. We provide a customizable modeling framework that will enable researchers to easily simulate E&R experiments with different trait architectures and parameters tuned to their specific study system, allowing for assessment of expected detection power and optimization of experimental design. [ABSTRACT FROM AUTHOR]