1. Nestedness is a widespread pattern in mutualistic networks that has high ecological and evolutionary importance due to its role in enhancing species persistence and community stability. Nestedness measures tend to be correlated with fundamental properties of networks, such as size and connectance, and so nestedness values must be normalised to enable fair comparisons between different ecological communities. Current approaches, such as using null‐corrected nestedness values and z‐scores, suffer from extensive statistical issues. Thus a new approach called NODF_c was recently proposed, where nestedness is expressed relative to network size, connectance and the maximum nestedness that could be achieved in a particular network. While this approach is demonstrably effective in overcoming the issues of collinearity with basic network properties, it is computationally intensive to calculate, and current approaches are too slow to be practical for many types of analysis, or for analysing large networks.
2. We developed three highly optimised algorithms, based on greedy, hill climbing and simulated annealing approaches, for calculation of NODF_c, spread along a speed‐quality continuum. Users thus have the choice between a fast algorithm with a less accurate estimate, a slower algorithm with a more accurate estimate and an intermediate option.
3. We outline the package and its implementation, as well as provide comparative performance benchmarking and two example analyses. We show that maxnodf enables speed increases of hundreds of times faster than existing approaches, with large networks seeing the biggest improvements. For example, for a large network with 3,000 links, computation time was reduced from 50 min using the fastest existing algorithm to 11 s using maxnodf.
4. maxnodf makes correctly normalised nestedness measures feasible for complex analyses of even large networks. Analyses that would previously take weeks to complete can now be finished in hours or even seconds. Given evidence that correctly normalising nestedness values can significantly change the conclusions of ecological studies, we believe this package will usher in necessary widespread use of appropriate comparative nestedness statistics.

中文翻译：

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maxnodf：一个R包，用于公平，快速地比较网络之间的嵌套

1. 嵌套是互惠网络中的一种普遍模式，由于其在增强物种持久性和社区稳定性方面的作用，因此具有高度的生态和进化重要性。嵌套度量通常与网络的基本属性（例如大小和连通性）相关，因此必须对嵌套值进行归一化，以实现不同生态群落之间的公平比较。当前的方法（例如，使用经过零点校正的嵌套值和z分数）遭受广泛的统计问题。因此，一种称为NODF _c的新方法最近提出了一种方法，其中相对于网络规模，连接性和在特定网络中可以实现的最大嵌套度来表示嵌套度。尽管该方法在克服基本网络属性的共线性问题方面显然是有效的，但它的计算量很大，并且当前的方法太慢，无法用于许多类型的分析或大型网络分析。
2. 我们开发了三种高度优化的算法，基于贪婪，爬坡和模拟退火方法，用于NODF计算_Ç，沿着速度质量连续蔓延。因此，用户可以在估算精度较低的快速算法，估算精度较高的较慢算法和中间选项之间进行选择。
3. 我们概述了程序包及其实现，并提供了比较性能基准测试和两个示例分析。我们展示了maxnodf可以使速度提高到比现有方法快数百倍，而大型网络则看到了最大的改进。例如，对于具有3,000个链接的大型网络，使用现有最快的算法将计算时间从50分钟减少到使用maxnodf减少11秒。
4. maxnodf使正确标准化的嵌套度度量对于甚至大型网络的复杂分析都是可行的。以前需要数周才能完成的分析现在可以在几小时甚至几秒钟内完成。如果有证据表明正确地标准化嵌套值可以显着改变生态学研究的结论，我们相信该软件包将迎来必要的广泛使用适当的比较嵌套统计数据。