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Background: Estimating relatedness is an important step for many genetic study designs. A variety of methods for estimating coefficients of pairwise relatedness from genotype data have been proposed. Both the kinship coefficient φ and the fraternity coefficient ψ for all pairs of individuals are of interest. However, when dealing with low-depth sequencing or imputation data, individual level genotypes cannot be confidently called. To ignore such uncertainty is known to result in biased estimates. Accordingly, methods have recently been developed to estimate kinship from uncertain genotypes. Results: We present new method-of-moment estimators of both the coefficients φ and ψ calculated directly from genotype likelihoods. We have simulated low-depth genetic data for a sample of individuals with extensive relatedness by using the complex pedigree of the known genetic isolates of Cilento in South Italy. Through this simulation, we explore the behaviour of our estimators, demonstrate their properties, and show advantages over alternative methods. A demonstration of our method is given for a sample of 150 French individuals with down-sampled sequencing data. Conclusions: We find that our method can provide accurate relatedness estimates whilst holding advantages over existing methods in terms of robustness, independence from external software, and required computation time. The method presented in this paper is referred to as LowKi (Low-depth Kinship) and has been made available in an R package (https://github.com/genostats/LowKi). [ABSTRACT FROM AUTHOR]