game of thrones - What is the meaning of "The seed is strong"?

In ASOIAF, Jon Arryn repeated several times while dying, "The seed is strong":

Eddard: "Was there nothing else? No final word?

Pycelle: "When I saw that all hope had fled, I gave the Hand milk of the poppy [...] He whispered something to the king and his lady wife, a blessing for his son. The seed is strong, he said. At the end the speech was too slurred to comprehend. Death did not come until the next morning, but Lord Jon was at peace after that. He never spoke again."

_{A Game of Thrones, Eddard V}

But so far (I have read all the books), it doesn't seem to me that he was talking about sickly Robert. But who else? What is the evidence that he was/wasn't talking about his son?

Answer

The clear implication made in the books is that when Jon Arryn, Hand of the King, said "The seed is strong" he was referring to the indications - based on documented bloodlines and inherited genetic characteristics - that Robert Baratheon did not father Joffrey, Tommen, or Myrcella on Cersei Lannister.

(Of course, in Westeros, no one would think of them as "genetic characteristics". But the inherited traits which we know to be genetics have long been recognized as having a bloodline relationship - more so, frankly, in systems where nobility intermarries and documents their births and marriages better than is the average. And seed is slang for sperm, which leads to births, or so I'm led to believe...)

As for evidence:

Lysa Arryn remembering:

Jon knew. The seed is strong, he told me. His last words. He kept saying Robert's name, and he grabbed my arm so hard he left marks. Tell them, the seed is strong

_{A Game of Thrones, Catelyn VI}

She goes on to interpret it as "[Jon's] seed. He wanted everyone to know what a good strong boy my baby was going to be." But she's an idiot (that's clearly established in the books). Robert is the name of both her son and the King. He was trying to get a message out, she was hearing what she wanted to.

Ned confronted Cersei when he figured it out:

"All three are Jaime's," he said. It was not a question.

"Thank the gods."

The seed is strong, Jon Arryn had cried on his deathbed, and so it was. All those bastards, all with hair as black as night. Grand Maester Malleon recorded the last mating between stag and lion, some ninety years ago,... Their only issue, an unnamed boy described in Malleon's tome as a large and lusty lad boar with a full head of black hair. ... No matter how far back Ned searched in the brittle yellowed pages, always he found the gold yielding before the coal.

_{A Game of Thrones, Eddard XII}