The botanical description is that the wild branches have overrun the roots. The allegorical reference is to some aspect of the gentile grafting that has altered or perhaps diluted. the power of the root.
With the root being the covenant, the overrunning of the root is some force that has made that covenant so that it is of lesser effect among mankind. This was not the way the grafting had begun. Indeed, the initial grafting showed great promise. The historical reference is the apostasy. The image of overrunning the roots is an interesting one, as it may be a very apt description of the way the apostasy occurred.
There is no single point at which one may make a division between apostasy and doctrinal purity. Even in the very earliest days, the myriad of questions surrounding the way one might embrace the gospel o Jesus assures us that there was no single orthodoxy, a fact indelibly impressed by the apparent differences of opinion between Paul and the Jerusalem church.
As the young church struggled to understand how to handle new possibilities, not the least off which was the opening of the gospel to the gentiles, the possible answers to those questions were volunteered from multiple sources. While the apostles did attempt to maintain the purity of doctrine, simple distance required that local leaders have great autonomous authority, and they certainly dealt with continual issues in the absence of one of the 12 apostles.
When any of us attempts to resolve a question, we do so with the best information and training available to us. In an intellectually Hellenized world, it was inevitable that the accepted modes of discourse and philosophy of the Hellenic world would infuse the decision making process of the early Christians as they attempted to answer new questions never touched upon by Jesus.
The mixing in of Hellenistic ideas. as well as information from other sources, became the pervasive mode of answering issues, rather than the appeal to revelation that Peter used when confronted with Cornelius. The weight of the intellectual world overran the purity of the roots when the logic of the world was subtly brought in to the realm of gospel teaching.