How GenABEL, and particurlary polygenic function, decomposes the variance of a trait? That is, imagine that I have a trait A with total (phenotypic variance) equals to var(A).

1.- how heritability (h2) is defined? is the ratio between genetic variance of A/ var(A)? Is this genetic variance equal to polygenic variance? Can I, therefore, say that

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`h^2=polygenic_variance/var(A)=polygenic_variance/(polygenic_variance + residual_variance)`

and therefore, that

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`polygenic_variance=(polygenic_variance + residual_variance)*h^2`

2.- What percentage of genetic variance is assigned to markers? It seems that mmscore function uses the residualY from polygenic function. My idea was that genetic variance could be split into one part explained by markers and another part not captured by these markers but included in the polygenic effect. The residualY variable used by mmscore seems to include both, the variance explained and not explained by markers. Is there a way to estimate both components, to split both variance components?

3.- How the variance components reported by the polygenic function (polygenic + residual variance; variance of residualY, variance of pgresidualY; and variance of grresidualY) relate to total variance of the trait?

I found the variance decomposition reported by GenABEL difficult to understand, at least for myself. Could anyone help me to understand it better?

Thank you for your help!

Regards

Manuel