Most founding events entail a reduction of population size, which in turn leads to genetic drift effects that can deplete alleles. Besides reducing neutral genetic variability, founder effects can in principle shift additive genetic variance for phenotypes that underlie fitness. This could then lead to different rates of adaptation among populations that have undergone a population size bottleneck as well as an environmental change, even when these populations have a common evolutionary history. Thus theory suggests that there should be an association between observable genetic variability for both neutral markers and phenotypes related to fitness. Here we test this scenario by monitoring the early evolutionary dynamics of six laboratory foundations derived from founders taken from the same source natural population of Drosophila subobscura. Each foundation was in turn three-fold replicated. During their first few generations, these six foundations showed an abrupt increase in their genetic differentiation, within and between foundations. The eighteen populations that were monitored also differed in their patterns of phenotypic adaptation according to their immediately ancestral founding sample. Differences in early genetic variability and in effective population size were found to predict differences in rate of adaptation during the first 21 generations of laboratory evolution. We show that evolution in a novel environment is strongly contingent not only on the initial composition of a newly-founded population but also on the stochastic changes which occur during the first generations of colonization. Such effects make laboratory populations poor guides to the evolutionary genetic properties of their ancestral wild populations.