1. Epigenetic inheritance is hypothesized to mediate rapid adaptation to stresses via two fundamentally different routes: first, through spontaneous epimutations that arise in a largely stochastic manner in the presence or absence of stress; if these spontaneous epimutations are heritable and beneficial, they may be selected upon ('stochastic route'); and second, through environment-induced epialleles that arise uniformly among individuals; if heritable, these epialleles may lead to stress adaptation even in the absence of selection ('deterministic route'). Testing and teasing apart these two routes is challenging, largely because a suitable experimental approach is lacking. 2. Here, we propose an experimental approach that allows to simultaneously assess the contribution of the stochastic and deterministic route. The essence of the approach is to manipulate the efficacy of selection through the population size and thereby to test whether selection is required for adaptation (stochastic route). To this end, genetically uniform populations are grown under different environments across multiple generations ('pre-treatment') at two different population sizes: in large populations, in which selection is effective; and in small populations, in which drift overcomes the effect of selection. If the deterministic route contributes to adaptation, variation in fitness, phenotypes or epigenetic marks will arise between the small populations of the different pre-treatments. If the stochastic route contributes to adaptation, variation will arise between the small and large population within each pre-treatment. As a proof-of-principle, we tested whether small and large monoclonal populations of the aquatic duckweed Spirodela polyrhiza may adapt to copper excess outdoors. 3. After five to seven generations of pre-treatment and a subsequent multi-generational growth under control conditions, large populations outperformed small populations under copper excess. Furthermore, small populations pre-treated with copper excess tended to have higher fitness under copper excess than small populations pre-treated under control conditions. These data suggest that both the stochastic and deterministic route may alter plant fitness under recurring stress. 4. The proposed approach will allow to experimentally evaluate whether species may adapt to stresses through either stochastic and deterministic epigenetic changes, which is fundamental to understand whether and how epigenetic inheritance may lead to rapid stress adaptation.