Narrow sense heritability [Formula: see text] is a key concept in quantitative genetics, as it expresses the proportion of the observed phenotypic variation that is transmissible from parents to offspring. [Formula: see text] determines the resemblance among relatives, and the rate of response to artificial and natural selection. Classical methods for estimating [Formula: see text] use random samples of individuals with known relatedness, as well as response to artificial selection, when it is called realized heritability. Here, we present a method for estimating realized [Formula: see text] based on a simple assessment of a random-mating population with no artificial manipulation of the population structure, and derive SE of the estimates. This method can be applied to arbitrary phenotypic segments of the population (for example, the top-ranking p parents and offspring), rather than random samples. It can thus be applied to nonpedigreed random mating populations, where relatedness is determined from molecular markers in the p selected parents and offspring, thus substantially saving on genotyping costs. Further, we assessed the method by stochastic simulations, and, as expected from the mathematical derivation, it provides unbiased estimates of [Formula: see text] We compared our approach to the regression and maximum-likelihood approaches utilizing Galton's dataset on human heights, and all three methods provided identical results.

Camcore Department of Forestry and Environmental Resources North Carolina State University Raleigh North Carolina 27695

Department of Biological Sciences and Program in Genetics North Carolina State University Raleigh North Carolina 27695

Faculty of Forestry and Wood Sciences Czech University of Life Sciences Prague 165 21 Praha 6 Czech Republic

Faculty of Science Humanities and Education Technical University of Liberec 461 17 Liberec 1 Czech Republic

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