Summary Below-ground competition is intense, and may dramatically reduce plant performance. However, there is still no consensus on the best strategies plants should use to maximize competitive ability in soil. Some suggest plants should grow roots according to nutrient availability, while others suggest plants should grow roots taking into account both nutrients and neighbours. Unambiguously testing between these two alternative hypotheses has been challenging. This manuscript had three objectives. First we presented a model of root growth under competition that is based on an ideal free distribution (IFD). Second, we develop the concept of the best response curve as a tool for clearer experimental tests of plant responses to neighbours. Third, we test these ideas by growing fast cycling Brassica rapa either alone or with neighbours to examine this species’ root growth strategy both alone and under competition. We hypothesize that those plants with no direct response to neighbours should grow roots according to an IFD. This means that if plants produce x roots in a soil volume of quality R, they should produce x/n roots in a soil volume of quality R/n. The experimental data were consistent with this prediction. Growing plants with neighbours was statistically identical to growing them with half as many nutrients. Thus, the only effect of neighbours was to reduce nutrient availability. This model provides an alternative to previous game theoretic models, and suggests an experimental protocol based on the concept of the best response curve. We hope that testing the game theoretic model with a clear alternative model will guide experiment and debate. Synthesis: The data in the literature are mixed, with species sometimes responding to nutrients only, and sometimes responding interactively to both nutrients and neighbours. At present we lack a general understanding of the causes or consequences of this diversity of strategies. We suggest that a greater understanding of trade-offs among traits that are important for other biotic interactions (above-ground competition, enemy defence, mutualisms) will lead to a greater understanding of why some species over-proliferate roots when in competition but other species do not.

27Adaptations can be thought of as evolutionary technologies that allow organisms to 28 exploit their environment. Like human technologies, adaptations can be 'progressive', increasing 29 in their ability to accomplish a task. Progressive adaptations which also fundamentally alter the 30 rules of trade-offs are known as key adaptations. Key adaptations allow a taxon to expand its 31 niche space thereby radiating to larger species numbers and spread beyond its original range. If 32 so, then of two otherwise ecologically equivalent taxa, the one with the greater geographical 33 range may have a key adaptation. We tested this hypothesis by comparing the global 34 biogeographic patterns of hummingbirds (Trochilidae) and sunbirds (Nectariniidae), ecologically 35 equivalent families with distinct evolutionary technologies. Though many species of both 36 families feed on nectar, hummingbirds also possess adaptations permitting hovering flight. We 37 analyzed each family's species diversity with latitude and elevation, charting how they decline 38 with movement towards poles and peaks. Hummingbirds persist into higher elevation and more 39 extreme latitudes than sunbirds, reaching their 50% species richness value at 22.14º and 2087 m 40 versus 18.92º and 2533 m for sunbirds. Looking at morphology, the evolution of hovering is 41 likely the constraint breaking adaptation that allowed hummingbirds to radiate into more species 42 and inhabit more extreme climes than sunbirds. Comparing the biogeography of ecologically-43 equivalent taxa has the potential to reveal insights into the species adaptations and niche 44 expansion.