1. Uncertainty is an irreducible part of predictive science, causing us to over- or underestimate the magnitude of change that a system of interest will face. In a reductionist approach, we may use predictions at the level of individual system components (e.g. species biomass), and combine them to generate predictions for system-level properties (e.g. ecosystem function).
2. Here we show that this process of scaling up uncertain predictions to higher levels of organisation has a surprising consequence: it tends to systematically underestimate the magnitude of system-level change, an effect whose significance grows with the system's dimensionality. This stems from a geometric observation: in high dimensions there are more ways to be more different, than ways to be more similar.
3. We focus on ecosystem-level predictions generated from the combination of predictions at the species level. In this setting, the ecosystem's relevant dimensionality is a measure of its diversity (and not simply the number of species). We explain why dimensional effects do not play out when predicting change of a single linear aggregate property (e.g. total biomass), yet are revealed when predicting change of nonlinear properties (e.g. absolute biomass change, stability or diversity), and when several properties are considered at once to describe the ecosystem, as in multi-functional ecology.
4. As an application we discuss the consequences of our theory for multiple-stressor research. This empirical field focuses on interactions between stressors, defined as the error made by a prediction based on their observed individual effects. Our geometric approach can be visualised and explored with a web application (https://doi.org/10.5281/zenodo.4611133), and we provide pseudocode outlining how our theory can be applied. Our findings highlight and describe the counter-intuitive effects of scaling up uncertain predictions, effects that can occur in any field of science where a reductionist approach is used to generate predictions.

中文翻译：

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将不确定的预测扩大到更高级别的组织往往会低估变化

1. 不确定性是预测科学中不可减少的部分，导致我们高估或低估感兴趣的系统将面临的变化幅度。在还原论方法中，我们可以在单个系统组件（例如物种生物量）的水平上使用预测，并将它们结合起来以生成对系统级属性（例如生态系统功能）的预测。
2. 在这里，我们表明，将不确定性预测扩大到更高组织层次的过程具有令人惊讶的结果：它倾向于系统地低估系统级变化的幅度，这种影响的重要性随着系统的维度而增长。这源于几何观察：在高维度上，有更多的方式可以变得更不同，而不是更相似的方式。
3. 我们专注于从物种层面的预测组合产生的生态系统层面的预测。在这种情况下，生态系统的相关维度是对其多样性（而不仅仅是物种数量）的衡量。我们解释了为什么在预测单个线性聚合特性（例如总生物量）的变化时维度效应不会发挥作用，但在预测非线性特性（例如绝对生物量变化、稳定性或多样性）的变化时以及当考虑多个特性时会显示出来立即描述生态系统，就像在多功能生态学中一样。
4. 作为一个应用，我们讨论了我们的理论对多压力源研究的影响。这个经验领域侧重于压力源之间的相互作用，定义为基于观察到的个体效应的预测所产生的错误。我们的几何方法可以通过 Web 应用程序 (https://doi.org/10.5281/zenodo.4611133) 进行可视化和探索，并且我们提供了概述如何应用我们的理论的伪代码。我们的发现强调并描述了扩大不确定预测的反直觉影响，这种影响可能发生在任何使用还原论方法生成预测的科学领域。