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.

翻译：在GitHub等开源软件平台上，复刻（fork）与接收拉取请求（pull-request）是开源项目获取外部贡献的重要途径——尤其是来自无法直接向源仓库提交代码的外部贡献者。拥有大量复刻常被视为项目受欢迎程度的指标。尽管已有广泛研究探讨复刻动机、复刻间通信、复刻特征及其影响，但目前除复刻数量外，鲜有定量指标能以简单且富有洞见的方式揭示开源项目复刻的整体状况。受生物多样性及开源团队多样性研究的启发，本文提出一种测量开源项目复刻多样性（即复刻种群多样性）的方法。我们基于Rao二次熵构建了一种新型复刻熵度量，通过分析复刻对项目文件的修改来量化其多样性。该度量具有对称性、连续性和单调性等特性，能有效量化项目复刻种群的多样性。为验证所提度量的实用性，我们利用从GitHub上五十个项目中获取的数据进行实证研究。结果表明，项目复刻熵与多项结果变量存在显著相关，包括以外部贡献者提交次数衡量的外部生产力、外部贡献者拉取请求的接受率以及报告的缺陷数量。同时，我们还发现复刻熵与复刻数量等其他因素之间存在显著的交互效应。研究证实，复刻熵能超越简单的复刻数量统计，显著丰富我们对开源项目复刻行为特征的理解，并有望为后续研究与应用提供支撑。