General definitions of demographic and environmental variances as well as demographic covariance are given from first principles. The sum of the environmental variance and the demographic covariance is the covariance between two individuals' contributions to the population growth within a year and corresponds to the coefficient of x² in the expression for the variance of the change in population size. Hence, this coefficient may actually be negative. The demographic variance is the variance among individuals. It is shown that the definitions are consistent with use of these terms in models with additive effects and in diffusion approximations to population processes. The connection to classical birth and death processes, in which the environmental variance and demographic covariance is always zero, is discussed. The concepts are illustrated by some stochastic simulations.