If you want reproducible science, the software needs to be open source.

This is an article summarizing this Nature editorial, which is definitely worth reading as well.

From the link:

Modern scientific and engineering research relies heavily on computer programs, which analyze experimental data and run simulations. In fact, you would be hard-pressed to find a scientific paper (outside of pure theory) that didn’t involve code in some way. Unfortunately, most code written for research remains closed, even if the code itself is the subject of a published scientific paper. According to an editorial in Nature, this hinders reproducibility, a fundamental principle of the scientific method.

… Reproducibility becomes more difficult when results rely on software. The authors of the editorial argue that, unless research code is open sourced, reproducing results on different software/hardware configurations is impossible. The lack of access to the code also keeps independent researchers from checking minor portions of programs (such as sets of equations) against their own work.