Two widely tested empirical patterns in ecology are combined here to predict how the variation of population density relates to the average body size of organisms. Taylor's law (TL) asserts that the variance of the population density of a set of populations is a power-law function of the mean population density. Density-mass allometry (DMA) asserts that the mean population density of a set of populations is a power-law function of the mean individual body mass. Combined, DMA and TL predict that the variance of the population density is a power-law function of mean individual body mass. We call this relationship "variance-mass allometry" (VMA). We confirmed the theoretically predicted power-law form and the theoretically predicted parameters of VMA, using detailed data on individual oak trees (Quercus spp.) of Black Rock Forest, Cornwall, New York. These results connect the variability of population density to the mean body mass of individuals.self-thinning | fluctuation scaling | Damuth's law | nonlinear least squares | spatial Taylor's law U nderstanding how and why living populations, natural and engineered, vary in space and time is a core problem of ecology. When a population fluctuates to a low density, its risk of extinction may rise and its genetic diversity may pass through a bottleneck with enduring evolutionary consequences. In fisheries, forests, and agriculture, population fluctuations may directly affect human supplies of food, fiber, and timber and have economic consequences. Outbreaks of arthropod and molluscan vectors of diseases of humans and animals may raise risks of disease. These scientific and practical reasons make it important to understand how and why population densities fluctuate.An important generalization about population variability is Taylor's law (1-3). Taylor's law (TL) is the subject of an estimated 1,000 papers (4) and has been confirmed for hundreds of species or groups of species in field observations and laboratory experiments (5, 6). The censused populations may include a single species, a single genus, or more loosely related organisms. TL asserts that variance of population density = aðmean population densityÞ b ; a > 0:[1]On logarithmic scales, TL becomes a linear relationship: logðvariance of population densityÞ = logðaÞ + b × logðmean population densityÞ: Typically, b > 0: The mean and variance of population density increase together. In many empirical examples, 1 ≤ b ≤ 2. Density-mass allometry (DMA) (7-13) asserts that mean population density = uðmean body mass per individualÞ v ; u > 0:Typically, bigger organisms are rarer and v < 0. DMA is sometimes called the self-thinning law (14). DMA applies to single species, collections of species (15-18), and foodwebs (19-23).Substituting DMA, Eq. 2, into TL, Eq. 1, gives variance of population density = au b ðmean body mass per individualÞ bv :We called this predicted relation variance-mass allometry (VMA). If b > 0 and v < 0, as is typical, then bv < 0: Increasing mean body mass will be associated with decreasing variance ...