Do people change political affiliation when they move?

This article by Michael Barone in yesterday's Wall Street Journal is interesting. Barone suggests, as have others, that population increases in Republican-leaning areas will increase Republican political strength. E.g.: "...within California, House seats will shift from the Democratic coast to the Republican Inland Empire and Central Valley."

But if the increase in population in these areas come from immigrants (who lean Democratic, as Barone acknowledges) and from domestic migration from what he calls the "Coastal Megalopolises" and the Rust Belt, it seems that the only way Republicans gain strength is if the domestic migrants are Republicans or if they are Democrats who change their political affiliation when they move to Sacramento or Dallas.

So, is there any evidence that Republicans move from the big cities on the East and West Coast and the Rust Belt cities in greater numbers than Democrats? Are more Republicans than Democrats moving from Pittsburgh and Boston to Charlotte?

If this is not the case, is there any evidence that Democrats turn into Republicans when they move from San Francisco or Detroit to Las Vegas?

A sidenote: Barone notes what Chris Briem has been trying to get people to notice--that the rate of domestic migration from cities like Pittsburgh, Cleveland, Detroit is quite similar to that of metro areas like Washington, DC. And the Rust Belt, on average, is doing better than New York and San Francisco in terms of keeping the US-born in town. As everyone has noted, it's the lack of immigration that poses demographic problems for Pittsburgh et al.