We use computer simulations in order to study the interplay between biodiversity and ecosystem functioning (BEF) both during the formation and during the ongoing evolution of large food webs. A species in our model is characterized by its own body mass, its preferred prey body mass, and the width of its potential prey body mass spectrum. On an ecological time scale, population dynamics determines which species are viable and which ones go extinct. On an evolutionary time scale, new species emerge as modications of existing ones. The network structure thus emerges and evolves in a self-organized manner. We analyse the relation between the functional diversity and ve community level measures of ecosystem functioning. These are the metabolic loss of the predator community, the total biomasses of the basal and the predator community and the consumption rates on the basal community and within the predator community. Clear BEF relations are observed during the initial build-up of the networks or when parameters are varied, causing bottom-up or top-down eects. However, ecosystem functioning measures uctuate only very little during long-term evolution under constant environmental conditions, despite changes in the functional diversity. This result supports the hypothesis that trophic cascades are weaker in more complex food webs.