The linear mixed model (LMM) is now routinely used to estimate heritability. Unfortunately, as we demonstrate, LMM estimates of heritability can be inflated when using a standard model. To help reduce this inflation, we used a more general LMM with two random effects-one based on genomic variants and one based on easily measured spatial location as a proxy for environmental effects. We investigated this approach with simulated data and with data from a Uganda cohort of 4,778 individuals for 34 phenotypes including anthropometric indices, blood factors, glycemic control, blood pressure, lipid tests, and liver function tests. For the genomic random effect, we used identity-by-descent estimates from accurately phased genomewide data. For the environmental random effect, we constructed a covariance matrix based on a Gaussian radial basis function. Across the simulated and Ugandan data, narrow-sense heritability estimates were lower using the more general model. Thus, our approach addresses, in part, the issue of "missing heritability" in the sense that much of the heritability previously thought to be missing was fictional. Software is available at https://github.com/MicrosoftGenomics/ FaST-LMM. A n important causal question comes from the age-old debate about nature versus nurture. For any phenotype such as height or intelligence quotient, how much of the phenotype is inherited and how much is determined by environment? This question was made precise by Fisher (1) and Wright (2) almost a century ago: Given observations of a phenotype from a population of individuals, what is the fraction of variance of the phenotype that is caused by inherited factors relative to the total variance of the phenotype due to both inherited and environmental factors? This fraction, termed "heritability," has been the subject of intense study across various phenotypes and populations since it was defined. Note that, in contrast to how some interpret the informal question around the nature-versus-nurture debate, heritability is not an absolute quantity but rather a quantity relative to a given population. For example, a phenotype in a population where environmental factors have large variation will have a smaller heritability than in an otherwise similar population where environmental factors have a small variation.Over the years, many approaches have been developed to estimate heritability from data (3, 4). Here, we concentrate on an approach made possible by the recent ability to sequence genomes at a modest cost (5, 6). The approach uses a linear mixed model (LMM), a form of multivariate regression of the genomic and environmental factors on the phenotype, which we examine in detail in the next section.In the standard LMM approach, the effects of environmental factors on the phenotype are modeled as noise. Specifically, the phenotype of each individual is assumed to be the sum of two random effects, one based on genomic factors and one based on environmental factors, where the latter is assumed to be mutually independent across indivi...
