How the diversity of organisms competing for or sharing resources influences community function is an important question in ecology but has rarely been explored in natural microbial communities. These generally contain large numbers of species making it difficult to disentangle how the effects of different interactions scale with diversity. Here, we show that changing diversity affects measures of community function in relatively simple communities but that increasing richness beyond a threshold has little detectable effect. We generated self-assembled communities with a wide range of diversity by growth of cells from serially diluted seawater on brown algal leachate. We subsequently isolated the most abundant taxa from these communities via dilution-to-extinction in order to compare productivity functions of the entire community to those of individual taxa. To parse the effect of different types of organismal interactions, we defined relative total function (RTF) as an index for positive or negative effects of diversity on community function. Our analysis identified three overall regimes with increasing diversity. At low richness (<12 taxa), positive and negative effects of interactions were both weak, while at moderate richness (12-26 taxa), community resource uptake increased but the carbon use efficiency decreased. Finally, beyond 26 taxa, the effect of interactions on community function saturated and further diversity increases did not affect community function. Although more diverse communities had overall greater access to resources, on average individual taxa within these communities had lower resource availability and reduced carbon use efficiency. Our results thus suggest competition and complementation simultaneously increase with diversity but both saturate at a threshold.