Parabolic Dunes

I saw this article about invasive species being better at protecting a dune from erosion than native species, and it got me to thinking. When we were outside Wilbur Cross we talked about two different types of dunes, barchan dunes, and parabolic dunes. Barchan dunes move with the limbs first, while parabolic dunes move crest first because vegetation anchors down the limbs. I wonder if the parabolic dunes have invasive species anchoring their limbs so well that it could prevent movement of the limbs completely, and change the shape of the dune?