The biodiversity-ecosystem function debate has been dominated by studies carried out in terrestrial grassland ecosystems. This thesis represents an attempt at progressing the 'debate' by extending the study of species richness effects on ecosystem function, into an aquatic marine environment. To date few marine ecologists have studied the consequences of changing biodiversity for the functioning of ecosystems. The reasons for this disparity are examined in detail. Experimental designs and null models are developed that allow for the separation of 'sampling effects' from the effects of 'species complementarity'. Experiments are detailed at both a range of spatial scales and using biogeographically separated species pools. These approaches overcome artifactual difficulties that have emerged as a consequence of the biodiversity-function debate. Data from empirical field and laboratory experiments are analysed and methods for evaluating the effects of species richness relative to the effects of functional diversity are explored. Both are shown to contribute to ecosystem functioning, although functional diversity consistently explains more of the variability in the data presented here. The effects of species complementarity and resource use overlap on ecosystem function are explored mathematically using standard Lotka-Volterra dynamics. Simulations of community assembly demonstrate that the degree of resource use overlap has highly significant consequences for the form of the relationship between diversity and ecosystem function. Varying the degree of resource use overlap and therefore the amount of resource use complementarity that occurs also has consequences for the stability of ecosystem processes (total community biomass - a measure of ecosystem function commonly employed by plant community ecologists). Overall this thesis represents an amalgamation of extensive empirical field and laboratory work with mathematical theory.