Grasslands deliver the resources for food production and are among the most biologically diverse ecosystems. These characteristics are often in conflict as increasing yield through fertilization can lead to biodiversity loss. Thus, the challenge in grassland management is to sustain both yield and diversity. Biodiversity-ecosystem functioning experiments typically reveal a positive relationship between manipulated species diversity and productivity. In contrast, observations of the effect of increasing productivity via fertilization suggest a negative association with biodiversity. Using a mathematical model simulating species co-existence along a resource gradient, we show that trade-offs and species pool structure (size and trait distribution) determines the shape of the productivity-diversity relationship. At a constant resource level, over-yielding drives a positive relationship between biodiversity and productivity. In contrast, along a resource gradient, the shape of the productivity-diversity relationship is determined by the distribution of species along trade-off axes and often resulted in a bell-shaped relationship. In accordance to this theoretical result, we then explain the general trend of plant biodiversity loss with fertilisation in the European flora, by showing empirical evidence that trait distribution of plant species pools throughout Europe is biased toward species preferring poorer soils.