We introduce differential fitness transmission as a signature of adaptive, Darwinian evolution, which can be detected using genealogical records of a reproducing population. This method is motivated by the observation that Darwinian evolution fundamentally consists in the differential transmission of heritable, fitness-affecting traits that result in differential transmission of fitness itself: fitter parents should tend to produce fitter offspring. Based on this idea, we propose several statistics which allow us to detect the presence of differential fitness transmission under various conditions. As an experimental illustration, we apply our statistics to simple evolutionary algorithms using different selection and replacement regimes. We demonstrate that differential fitness transmission can be used to detect the presence of a force which consistently favours certain lineages at the expense of others, over more than one generation. We conclude that differential fitness transmission is a useful, practical signature of Darwinian evolution for situations in which a genealogical record of the population can be obtained.