Table 1.

A summary of methods for SNP heritability estimation.

Main Text Sections	Methods	Modeling Assumptions	Estimation Algorithms	Trait Types	Software	Weblink	Comments	References
Modeling assumptions	BVSR	${\beta }_j~\pi N\left(0,{\sigma }_{\beta }^2\right)+\left(1-\pi \right){\delta }_0$	MCMC	Quantitative	GEMMA	https://github.com/genetics-statistics/GEMMA	Fast for large-scale data; Also useful for phenotype prediction and PRS construction; supports Mac and Linux platforms	[32], [33]
	BSLMM	${\beta }_j~\pi N\left(0,{\sigma }_a^2+{\sigma }_b^2\right)+\left(1-\pi \right)N\left(0,{\sigma }_b^2\right)$	MCMC					[22]
	LMM/REML	${\beta }_j~N\left(0,{\sigma }_{\beta }^2\right)$	REML	Quantitative	GEMMA/GCTA	https://github.com/genetics-statistics/GEMMAhttp://cnsgenomics.com/software/gcta/#Overview	Also useful for SNP association tests with LMM; supports Windows, Mac and Linux platforms	[12]
	LDAK	${\beta }_j~N\left(0,{\sigma }_j^2\right),{\sigma }_j^2\propto w_j{\left(f_j\left(1-f_j\right)\right)}^{0.75}$	REML	Quantitative	LDAK	http://dougspeed.com/ldak/	Over 30 functions, importantly, SNP heritability estimation and SNP-based prediction models construction, supported for Mac and Linux platforms	[41], [42]
	DPR	${\beta }_j~{\sum }_{\phi =1}^{+\infty }{\pi }_{\phi }N\left(0,{\sigma }_{\phi }^2\right),{\sigma }_{\phi }^2~G,G~DP\left(H,\lambda \right)$	MCMC/VB	Quantitative	DPR	https://github.com/biostatpzeng/DPR	Mainly for robust genetic prediction and PRS construction of complex traits; supports Mac and Linux platforms	[51]
Case-control study	HE/PCGC	${\beta }_j~N\left(0,{\sigma }_j^2\right)$	MoM	Binary	PCGC	https://data.broadinstitute.org/alkesgroup/PCGC/	Mitigate biases in REML heritability estimation for ascertained case-control studies; supports Linux platform	[58]
Count data	PQLseq	${\beta }_j~N\left(0,{\sigma }_{\beta }^2\right)$	MCMC	Binary/Count	PQLseq	https://cran.r-project.org/web/packages/PQLseq/index.html	For heritability estimation of count data in RNAseq and Bisulfite seq studies; supports Windows, Mac and Linux platforms	[71]
Summary statistics	LDSC	$E\left({\beta }_j\right)=0,{\sigma }_j^2=h_g^2/p$	MoM	Quantitative/Binary	LDSC	https://github.com/bulik/ldsc	A command tool for estimating heritability and genetic correlation using GWAS summary statistics	[72]
	MQS	${\beta }_j~N\left(0,{\sigma }_j^2\right)$	MoM	Quantitative/Binary	GEMMA	https://github.com/genetics-statistics/GEMMA	A general statistical framework for SNP heritability estimation using summary statistics; supports Mac and Linux platforms	[59]
	SumHer	$E\left({\beta }_j\right)=0,$$Var\left({\beta }_j\right)\propto w_j{\left(f_j\left(1-f_j\right)\right)}^{0.75}$	REML	Quantitative/Binary	SumHer	http://dougspeed.com/sumher/	Heritability estimation using summary statistics under the LDAK assumption; supports Linux platform	[74]

Table lists 10 methods described in the main text, with the first seven methods for analyzing individual level data and last three methods for analyzing summary statistics. Columns contain the main text section in which the method is described (1st column), method name (2nd column), modeling assumption on the SNP effect sizes (3rd column), estimation algorithms (4th column), phenotype type (5th column), implemented software (6th column), web link (7th column), additional comments (8th column) and references (9th column). In the 3rd column, ${\delta }_0$ denotes a point mass at zero; N(.,.) denotes a normal distribution with the mean and variance parameters; DP denotes a Dirichlet process. In the 4th column, MCMC represents Markov chain Monte Carlo method, VB represents variational Bayesian, REML represents restricted maximum likelihood method, and MoM represents method of moments. In the 8th column, PRS is short for polygenic risk scores.