This work focuses on a special type of generic ecosystem model that allows to investigate self-organization in ecological networks. The experiments focus on the long-term behavior of dynamically adapting food webs that are constantly faced with invading new species. The emphasis lies on patterns that arise from within the system and their dependence on environmental factors. The model which has been built to simulate these patterns is a highly abstracted representation of nutrient flows in a food web. It is based on allometric relationships for the physiological rates and the diversity of time scales present in the system. Dynamic changes in the food web are introduced by way of immigration of new species and extinction of existing ones. We find that the food webs eventually arrive at a steady state with respect to species number and diversity, this climax state being dependent on nutrient availability. Fitting the resulting species-biomass distributions with different models from applied ecology, a remarkable agreement with MacArthur's Broken Stick model can be observed. This finding suggests that the limited resources are apportioned simultaneously rather than sequentially among the species, in spite of the successive nature of the invasion.