Is the increase in screwcaps and plastic corks due to a cork shortage?

Hello there! I'm Dr. Vinifera, but you can call me Vinny. Ask me your toughest wine questions, from the fine points of etiquette to the science of winemaking. And don't worry, I'm no wine snob—you can also ask me those "dumb questions" you're too embarrased to ask your wine geek friends! I hope you find my answers educational, empowering and even amusing. And don't forget to check out my most asked questions and my full archives for all my Q&A classics.
Dear Dr. Vinny,
Is it true that there is a worldwide shortage of cork, and that is the reason that some wineries are switching to screwcaps and plastic corks?
—Javier E., Mexico City
Dear Javier,
Despite the growing popularity of wine, it doesn't appear that there is a shortage of corks, at least not long-term. Cork trees are pretty cool—you don't have to cut down the tree to get the bark (which is the source of wine corks), and stripping the trees of their bark doesn't hurt them, though you do have to wait a few years between strippings. I've read that that cork producers say they comfortably have enough resources to cork wines for the next 100 years without changing a thing.
So why are some wineries abandoning the traditional cork stopper? Alternative closures, including things like screw caps, plastic corks and glass toppers, are one way to deal with an unwanted compound called 2,4,6-trichloroanisole, or TCA, which makes wines taste musty and dank. TCA is created by an interaction of phenols (organic compounds found in all plants) with things sometimes found in wineries, like mold and chlorine. TCA is often traced to faulty corks; hence, the flavors it imparts are often simply referred to as "cork taint," and a wine that suffers from TCA contamination is often called "corked" or "corky." In fairness to corks, though, TCA can also originate in cardboard cases or wooden pallets; it can even contaminate an entire winery. But corks are probably the most common source of TCA, and that's the principal reason wineries are abandoning them.
—Dr. Vinny