Both local adaptation and adaptive phenotypic plasticity can influence the match between phenotypic traits and local environmental conditions. Theory predicts that environments stable for multiple generations promote local adaptation, while highly heterogeneous environments favor adaptive phenotypic plasticity. However, when environments have periods of stability mixed with heterogeneity, the relative importance of local adaptation and adaptive phenotypic plasticity is unclear. Here, we used Drosophila suzukii as a model system to evaluate the relative influence of genetic and plastic effects on the match of populations to environments with periods of stability from three to four generations. This invasive pest insect can develop within different fruits, and persists throughout the year in a given location on a succession of distinct host fruits, each one being available for only a few generations. Using reciprocal common environment experiments of natural D. suzukii populations collected from cherry, strawberry and blackberry, we found that both oviposition preference and offspring performance were higher on medium made with the fruit from which the population originated, than on media made with alternative fruits. This pattern, which remained after two generations in the laboratory, was analyzed using a statistical method we developed to quantify the contributions of local adaptation and adaptive plasticity in determining fitness. Altogether, we found that genetic effects (local adaptation) dominate over plastic effects (adaptive phenotypic plasticity). Our study demonstrates that spatially and temporally variable selection does not prevent the rapid evolution of local adaptation in natural populations. The speed and strength of adaptation may be facilitated by several mechanisms including a large effective population size and strong selective pressures imposed by host plants.