Is there evidence that open source research software produces more uptake of methods?

In recent years there has been a drive to make science more open. This includes making the software used to perform research open source. The main argument in favour of this idea is that research should be reproducible, which has been addressed in other questions on this site.

I am more interested in the 'impact' that this produces. In particular, is there evidence that by publishing software alongside research papers means that more people use the methods described in the paper?

I am especially concerned with papers in applied mathematics but also more generally.