A major question in ecology is to know how ecosystem function is affected by the number of species. After two decades of research, the nature, shape, and causes of the relationships between biodiversity and ecosystem functioning remain unresolved. Huston () suggested that a statistical ‘sampling effect’ for a few dominant species produced the patterns observed in experiments, while Tilman et al. () argued that the observed responses were due to the number of species rather than the properties of a few. Here, we present a general, theoretical and parsimonious model using combinatorial probabilities to describe the assembly effect as a probabilistic process. Our basic assumption is that community function is determined by random drawing from a fixed species pool composed of three classes of species. The species classes differ in their effect on community function and are ordered in a simple dominance hierarchy (subordinate, dominant and super-dominant species). Community function is determined by prevalent dominance rules: the dominance by the majority of species mimics the effect of dominant species, i.e. the function is determined by the dominant or super-dominant species class the most numerous within the community; the dominance by the presence of species mimics the effect of keystone species, i.e. the function is determined by the species that is ranked highest in the dominance hierarchy. The model produces significant fits to four experimental data sets obtained for plant and microbial communities, including monotonic and hump-shaped curves. The results indicate that the model gave good fits under both the dominance rules in any data set, suggesting that the random sampling effect provides a parsimonious explanation for the various relationships observed in diversity-ecosystem functioning experiments. The model describes a random assembly process that produces variation in ecosystem functioning in response to number of species selected from a regional species pool composed of several classes of species differing in their ecosystem effects and relative dominance. This simple model reproduces all shapes of diversity-ecosystem functioning relationships reported in the experimental literature. The results suggest that the multi-faceted response of ecosystems to biodiversity may be nothing more than manifestations of random assembly effects and variation in species properties.