I have no idea what they mean, but invasibillity has a specific definition, generally not applied to genetics or genomics. While there is a way I could see this term being used in genetics, the way they've used it, the clearly don't understand.
Invasibillity is the tendency for an organism to expand into an environment and out-compete its native flora/fauna. I've got enough training in biology to understand that there are some cases where individual genes, sets of genes, chromosomes, plastids, viroids, etc.. could be considered invasive? Genes move, so it could be framed that way, but its also clearly not what the author means.
My assumption was that they were using the term as it's used in the medical field. A procedure such as a sonogram is noninvasive because it does not penetrate the organism or cause large changes or damage. Surgery is an invasive procedure.
My understanding of the comment is that breeding plants together and selecting for traits is noninvasive while going in and directly modifying the genome through enzymatic means is more invasive. I don't know if this is the correct way to use these terms in this circumstance, but this is my perspective.
Invasibillity is the tendency for an organism to expand into an environment and out-compete its native flora/fauna. I've got enough training in biology to understand that there are some cases where individual genes, sets of genes, chromosomes, plastids, viroids, etc.. could be considered invasive? Genes move, so it could be framed that way, but its also clearly not what the author means.