Yes. The process of invasion is just as natural as the process of extinction. And like extinction, under human influence it has been altered; it has been accelerated.
In fact I have compared rates of invasion from the prehistoric record and modern record, and the differences are many orders of magnitude. If you take as an extreme case Hawaii, which has been invaded at a rate of—let's say before humans arrived, before Polynesians arrived—one every 30,000 years, now you will get 20 new invaders per year. That's an 800,000-fold acceleration.
We've accelerated the rate to levels that have no historical precedent. Unlike extinction, which, pointing to the past when an asteroid hit the planet, let's say, you could find a mass extinction event similar to what's going on now—it's not much consolation, but you can find that—you cannot find any analogy in the fossil record of the mass invasion event that's occurring now.
You can take New Zealand as an example, which we brought up before. It has 35 European mammals on it. There is no way any of them could have arrived in New Zealand on their own. There are 12 birds that normally occur in Britain. There's not a single chance that any one of them could have arrived and established a population in New Zealand on its own.
These big jumps that we're seeing, like zebra mussels coming out of the Great Lakes, could not have happened without human vectors.
So it can happen naturally. It is happening naturally, on very small scales and at far slower rates than it is without our influence.