Selection for local adaptation results in genetic differentiation in ecologically important traits. In a perennial, outcrossing model plant Arabidopsis lyrata, several differentiated phenotypic traits contribute to local adaptation, as demonstrated by fitness advantage of the local population at each site in reciprocal transplant experiments. Here we compared fitness components, hierarchical total fitness and differentiation in putatively ecologically important traits of plants from two diverged parental populations from different continents in the native climate conditions of the populations in Norway and in North Carolina (NC, U.S.A.). Survival and number of fruits per inflorescence indicated local advantage at both sites and aster life-history models provided additional evidence for local adaptation also at the level of hierarchical total fitness. Populations were also differentiated in flowering start date and floral display. We also included reciprocal experimental F1 and F2 hybrids to examine the genetic basis of adaptation. Surprisingly, the F2 hybrids showed heterosis at the study site in Norway, likely because of a combination of beneficial dominance effects from different traits. At the NC site, hybrid fitness was mostly intermediate relative to the parental populations. Local cytoplasmic origin was associated with higher fitness, indicating that cytoplasmic genomes also may contribute to the evolution of local adaptation.