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We obtain the theoretically expected number of independent cultural traits at equilibrium in a population where one of four modes of social learning—random oblique, best-of-K, success bias, or one-to-many—is practiced by its members. Cultural traits can be classified as simple or complex, depending on the ease or difficulty of acquisition by social learning and innovation. The number of simple cultural traits may saturate as population size increases, in which case a statistical association between the two variables is not predicted. At smaller population sizes, there is a major effect of the mode of social learning on the number of simple cultural traits. By contrast, the relation between the number of complex cultural traits and population size is approximately linear and almost identical for all four modes of social learning. We suggest that empirical studies of statistical association between number of cultural traits …