This paper introduces a novel quantitative metric called the Symbiosis Degree Index for measuring the degree of symbiosis between subjects, which we apply it to analyzing scientific collaboration patterns between researchers. We study the network characteristics of scientific collaboration based on the resultant published research papers indexed in the Web of Science, considering the role of symbiosis. Analyses through our symbiosis metric of the relationship between a pair of mentor and mentee show substantively distinct ramifications from the “old leads young” model. In a sustained collaboration relationship, young researchers do indeed draw support from mentors’ resources to improve their own level of scientific productivity and influence (as predicted in earlier models), but mentors also benefit by increasing their own productivity in publications. The collaborative symbiosis degree between mentor and mentee changes over time as the relationship matures. In the particular case studied here, even though the mentor’s output decreased later in the relationship, their influence (measured through citations) continued to develop at the same pace through these collaborations. This is intended to demonstrate the potential of the metric to produce new insights on the nature of collaboration.

中文翻译：

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共生视角下科学合作的结构与演化

本文介绍了一种新的定量指标，称为共生度指数，用于衡量主体之间的共生度，我们将其应用于分析研究人员之间的科学合作模式。考虑到共生的作用，我们基于在 Web of Science 中索引的已发表研究论文，研究科学协作的网络特征。通过我们对一对导师和受指导者之间关系的共生度量进行的分析显示，与“老领导年轻”模型有着本质上不同的后果。在持续的合作关系中，年轻研究人员确实从导师的资源中获得支持，以提高他们自己的科学生产力和影响力水平（如早期模型中预测的那样），但导师也可以通过提高他们自己在出版物中的生产力而受益。随着关系的成熟，导师和受训者之间的协作共生程度会随着时间而变化。在这里研究的特定案例中，即使导师的产出在关系后期下降，他们的影响力（通过引用衡量）通过这些合作继续以相同的速度发展。这旨在展示该指标在产生关于协作性质的新见解方面的潜力。