Nutritional mutualisms are ancient, widespread, and profoundly influential in biological communities and ecosystems. Although much is known about these interactions, comprehensive answers to fundamental questions, such as how resource availability and structured interactions influence mutualism persistence, are still lacking. Mathematical modelling of nutritional mutualisms has great potential to facilitate the search for comprehensive answers to these and other fundamental questions by connecting the physiological and genomic underpinnings of mutualisms with ecological and evolutionary processes. In particular, when integrated with empirical data, models enable understanding of underlying mechanisms and generalisation of principles beyond the particulars of a given system. Here, we demonstrate how mathematical models can be integrated with data to address questions of mutualism persistence at four biological scales: cell, individual, population, and community. We highlight select studies where data has been or could be integrated with models to either inform model structure or test model predictions. We also point out opportunities to increase model rigour through tighter integration with data, and describe areas in which data is urgently needed. We focus on plant-microbe systems, for which a wealth of empirical data is available, but the principles and approaches can be generally applied to any nutritional mutualism.

中文翻译：

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营养共生建模：数据集成的挑战和机遇。

营养共生在生物群落和生态系统中是古老的，广泛的并且具有深远的影响。尽管对这些交互作用了解很多，但是仍然缺少对基本问题（例如资源可用性和结构化交互作用如何影响共生主义持久性）的全面解答。营养共生的数学模型通过将共生的生理和基因组基础与生态和进化过程联系起来，具有极大的潜力，可以促进对这些和其他基本问题的全面解答。特别是，当与经验数据集成时，模型可以使人们理解潜在的机制，并能对给定系统的细节以外的原理进行概括。这里，我们展示了如何将数学模型与数据集成在一起，以解决四个生物学尺度（单元，个体，种群和社区）的互惠持久性问题。我们重点介绍数据已经或可以与模型集成以告知模型结构或测试模型预测的精选研究。我们还指出了通过与数据的更紧密集成来提高模型严格性的机会，并描述了迫切需要数据的领域。我们关注的是植物-微生物系统，该系统具有大量的经验数据，但原理和方法通常可以应用于任何营养共存主义。我们重点介绍数据已经或可以与模型集成以告知模型结构或测试模型预测的精选研究。我们还指出了通过与数据的更紧密集成来提高模型严格性的机会，并描述了迫切需要数据的领域。我们关注的是植物-微生物系统，该系统具有大量的经验数据，但原理和方法通常可以应用于任何营养共存主义。我们重点介绍数据已经或可以与模型集成以告知模型结构或测试模型预测的精选研究。我们还指出了通过与数据的更紧密集成来提高模型严格性的机会，并描述了迫切需要数据的领域。我们关注的是植物-微生物系统，该系统具有大量的经验数据，但原理和方法通常可以应用于任何营养共存主义。