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The concept of the gene seemed to be the missing piece in Darwin's jigsaw. It completed his picture of natural selection by showing that traits can't be blended away to insignificance...

  • away means somewhere else, or to or in a different place, position, or situation.
  • insignificance means the fact of being small or not noticeable, and therefore not considered important.

but I don't understand the phrase's meaning.

So could you please explain it to me?

The fuller text is here: The concept of the gene seemed to be the missing piece in Darwin's jigsaw. It completed his picture of natural selection by showing that traits can't be blended away to insignificance, although this wasn't recognised immediately. Genetics also solved another problem of Darwin's theory: the source of the variation within a population. Darwin's starting point was that any population naturally contains a variety of individuals, providing the raw material for natural selection. A key source of this variation was now shown to be mutation--spontaneous changes in the structure of a gene, leading it to code for something new. Such changes had been observed by Morgan and others as they traced the position of the genes on chromosomes.

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I think this definition is closer. From your source,

away adverb (GONE)
gradually until mostly or completely gone:

  • All the snow had melted away.
  • The music faded away as the procession moved slowly up the street.
  • We used to while away (= spend) the weekends at my aunt's house in the country.
  • We danced the night away (= until the night was over).

(Cambridge Dictionary)

So, blend away roughly means blend until gone/almost gone. We can roughly rephrase the original as

  • ... by showing that traits can't be blended until gone to insignificance...
  • ... by showing that traits can't be blended to insignificance...
  • ... by showing that traits can't be blended to the point that they become insignificant...
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traits can't be blended away to insignificance

I am not familiar with the theory, but I will say what I think about the phrase.

To blend is to mix, as you say.

If you put red oil color into a palette and then put navy blue oil color on top of it, the two will mix to form a purple color. If you keep blending the two by adding more and more blue to the mixture, the purple mixture will gradually start becoming more bluish. The color of the mixture will eventually have very insignificant hint of red. It will be more blue than red. You would have then blended away the "red" into insignificance.

What I understand from the text is that traits/characteristics in humans cannot be blended away into insignificance through generations of reproductions. A child will have a trait that is the average of his parents.

"The theory is that the progeny inherits any characteristic as the average of the parents' values of that characteristic. As an example of this a crossing of a red flower variety with a white variety of the same species would yield pink-flowered offspring." - Wikipedia

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