There are few empirical or theoretical predictions of how per capita or per individual competition coefficients for pairs of plant species should relate to each other. In contrast, there are a considerable number of general hypotheses that predict competitive ability as a function of a range of ecological traits, together with a suite of increasingly sophisticated models for competitive interactions between plant species. We re-analyse a data set on competition between all pairwise combinations of seven species and show that competition coefficients relate strongly to differences between the maximum sizes, root allocation, emergence time and seed size of species. Regressions suggest that the best predictor of competition coefficients is the difference in the maximum size of species and that correlations of the other traits with the competition coefficients occur through effects on the maximum size. We also explore the patterns of association between coefficients across the competition matrix. We find significant evidence for coefficient reciprocity (inverse relationships between the interspecific coefficients for species pairs) and transitivity (numerically predictable hierarchies of competition between species) across competition matrices. These results therefore suggest simple null models for plant community structure when there is competition for resources.