  On open source software (OSS) platforms such as GitHub, forking and accepting
pull-requests is an important approach for OSS projects to receive
contributions, especially from external contributors who cannot directly commit
into the source repositories. Having a large number of forks is often
considered as an indicator of a project being popular. While extensive studies
have been conducted to understand the reasons of forking, communications
between forks, features and impacts of forks, there are few quantitative
measures that can provide a simple yet informative way to gain insights about
an OSS project's forks besides their count. Inspired by studies on biodiversity
and OSS team diversity, in this paper, we propose an approach to measure the
diversity of an OSS project's forks (i.e., its fork population). We devise a
novel fork entropy metric based on Rao's quadratic entropy to measure such
diversity according to the forks' modifications to project files. With
properties including symmetry, continuity, and monotonicity, the proposed fork
entropy metric is effective in quantifying the diversity of a project's fork
population. To further examine the usefulness of the proposed metric, we
conduct empirical studies with data retrieved from fifty projects on GitHub. We
observe significant correlations between a project's fork entropy and different
outcome variables including the project's external productivity measured by the
number of external contributors' commits, acceptance rate of external
contributors' pull-requests, and the number of reported bugs. We also observe
significant interactions between fork entropy and other factors such as the
number of forks. The results suggest that fork entropy effectively enriches our
understanding of OSS projects' forks beyond the simple number of forks, and can
potentially support further research and applications.
