We measured the diameter at breast height of all trees and shrubs > 5 meters in height, including standing dead trees, on 68 0.04-hectare study plots in a montane, subtropical rain forest on Mauna Loa, Hawai`i. The canopy species consisted of 88 percent Metrosideros polymorpha (ohia) and 12 percent Acacia koa (koa). Negative associations were found between the densities of koa and ohia, the density of koa and the total basal area of ohia, and the total basal areas of koa and ohia. The two-species lottery competition model, a stochastic model in which the coexistence of two species in a space-limited community results from temporal variation in recruitment and death rates, predicts a quadratic-beta distribution for the proportion of space occupied by each species. A discrete version of the quadratic-beta distribution, the quadratic-beta binomial distribution, was fit to the live koa and ohia densities and assessed with goodness-of-fit tests. Likelihood ratio tests provided evidence that the mean adult death rates of the two species were equal but that the relative competitive abilities of the two species favored ohia. These tests were corroborated by a contingency table analysis of death rates based on standing dead trees and growth rate studies which report that koa grows much faster than ohia. The lottery model predicts a positive covariance between death rates and ohia recruitment when mean death rates are equal and koa has a higher growth rate than ohia. We argue that the competitive advantage of ohia is due to its superior dispersal ability into large gaps, which would yield the positive covariance described above, and it is this positive covariance term that skews the occupation of space in favor of ohia.