Experiments suggest that increasing species diversity increases productivity. At present, there is controversy on which mechanisms mediate this relationship. Many existing models study productivity at equilibrium, such as in communities of coexisting competitors. Here we highlight an ambiguity of this choice, that it makes it difficult to determine if all mechanisms are acting on the same response variable. To illustrate this problem, we propose a formal link between dynamic models of population growth and analyses of diversity-productivity relationships. Using this link, we show that mechanisms which are thought to shape diversity productivity relationships act on different responses. In particular, niche complementarity, which describes the reduction of antagonistic interactions in diverse communities, shapes productivity, but selection does not change productivity directly; instead, it leads to temporal changes in productivity. This ambiguity is analogous to confusing a vehicle’s speed and its acceleration (i.e., change in speed over time). We measure each of the terms using data from one of Gauses’ competition experiments. For this experiment, the effects of niche differentiation are negligible at low density and weak at high density. Selection is likewise modest compared to overall changes in the environment. These results highlight how the effects of diversity on productivity can be obscured by our choice or response variable.