There are two prominent and competing hypotheses that disagree about the effect of competition on diversification processes. The first, the bounded hypothesis, suggests that species diversity is limited (bounded) by competition between species for finite ecological niche space. The second, the unbounded hypothesis, proposes that innovations associated with evolution render competition unimportant over macroevolutionary timescales. Here we use phylogenetically structured niche modelling to show that processes consistent with both of these diversification models drive species accumulation in conifers. In agreement with the bounded hypothesis, niche competition constrained diversification, and in line with the unbounded hypothesis, niche evolution and partitioning promoted diversification. We then analyse niche traits to show that these diversification enhancing and inhibiting processes can occur simultaneously on different niche dimensions. Together these results suggest a new hypothesis for lineage diversification based on the multi-dimensional nature of ecological niches that can accommodate both bounded and unbounded evolutionary processes.