John Gill Commentary 1 Chronicles 5:1

"And the sons of Reuben the first-born of Israel (for he was the first-born; but, forasmuch as he defiled his father`s couch, his birthright was given unto the sons of Joseph the son of Israel; and the genealogy is not to be reckoned after the birthright." — 1 Chronicles 5:1 (ASV)

Now the sons of Reuben, the firstborn of Israel
Are as follow in (1 Chronicles 5:3) where the account begins; for what comes between this and that is in a parenthesis:

for he was the firstborn ;
of Jacob by his wife Leah; that must be owned, and Jacob allows it, (Genesis 49:3) and yet the genealogy in this book begins not with him, as might on that account be expected; the reason follows:

but forasmuch as he defiled his father's bed :
by lying with Bilhah his concubine:

his birthright was given unto the sons of Joseph the son of Israel ;
his beloved son by his beloved wife Rachel and so had a double portion given him; his two sons being equally ranked with the other sons of Jacob, and became distinct tribes, and each had their lot in the land of Canaan, see (Genesis 48:5Genesis 48:22) compared with (Deuteronomy 21:17)

and the genealogy is not to be reckoned after the birthright ;
or, "but the genealogy" ^F15 ; neither after the birthright of Reuben, which he had by nature, being Jacob's firstborn; nor after the birthright of Joseph, which be had by his father's gift, as it might be thought it should; the reason of which follows.

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FOOTNOTES:

• F15: "Nee tamen", Tigurine version.