Three markedly different models of multispecies competition-one mechanistic, one phenomenological, and one statistical-all predict that greater diversity increases the temporal stability of the entire community, decreases the temporal stability of individual populations, and increases community productivity. We define temporal stability as the ratio of mean abundance to its standard deviation. Interestingly, the temporal stability of entire communities is predicted to increase fairly linearly, without clear saturation, as diversity increases. Species composition is predicted to be as important as diversity in affecting community stability and productivity. The greater temporal stability of more diverse communities is caused by higher productivity at higher diversity (the "overyielding" effect), competitive interactions (the "covariance" effect), and statistical averaging (the "portfolio" effect). The relative contribution of each cause of temporal stability changes as diversity increases, but the net effect is that greater diversity stabilizes the community even though it destabilizes individual populations. This theory agrees with recent experiments and provides a degree of resolution to the diversity-stability debate: both sides of the longstanding debate were correct, but one addressed population stability and the other addressed community stability.