The coexistence of many competing species in an ecological community is a long-standing theoretical and empirical puzzle. Classic approaches in ecology assume that species fitness and interactions in a given environment are mainly driven by a few essential species traits, and coexistence can be explained by trade-offs between these traits. The apparent diversity of species is then summarized by their positions (“ecological niches”) in a low-dimensional trait space. Yet, in a complex community, any particular set of traits and trade-offs is unlikely to encompass the full organization of the community. A diametrically opposite approach assumes that species interactions are disordered, i.e., essentially random, as might arise when many species traits combine in complex ways. This approach is appealing theoretically, and can lead to novel emergent phenomena, fundamentally different from the picture painted by low-dimensional theories. Nonetheless, fully disordered interactions are incompatible with many-species coexistence, and neither disorder nor its dynamical consequences have received direct empirical support so far. Here we ask what happens when random species interactions are minimally constrained by coexistence. We show theoretically that this leads to testable predictions. Species interactions remain highly disordered, yet with a “diffuse” statistical structure: interaction strengths are biased so that successful competitors subtly favor each other, and correlated so that competitors partition their impacts on other species. We provide strong empirical evidence for this pattern, in data from grassland biodiversity experiments that match our predictions quantitatively. This is a first-of-a-kind test of disorder on empirically measured interactions, and unique evidence that species interactions and coexistence emerge from an underlying high-dimensional space of ecological traits. Our findings provide a new null model for inferring interaction networks with minimal prior information and a set of empirical fingerprints that support a statistical physics-inspired approach of complex ecosystems.

中文翻译：

---

复杂生态系统中高维共存的指纹

生态社区中许多竞争物种的共存是一个长期存在的理论和经验难题。生态学中的经典方法假定在给定环境中物种适应性和相互作用主要是由一些基本物种性状驱动的，而共存可以通过这些性状之间的权衡来解释。然后通过其在低维特征空间中的位置（“生态位”）来概括物种的表观多样性。但是，在一个复杂的社区中，任何特定的特征和折衷组合都不可能涵盖社区的整个组织。截然相反的方法假设物种相互作用是无序的，即基本上是随机的，这可能是由于许多物种性状以复杂的方式结合而产生的。从理论上讲，这种方法很有吸引力，并可能导致出现新颖的现象，这与低维理论所描绘的画面完全不同。然而，完全无序的相互作用与多种物种的共存是不相容的，到目前为止，无序及其动力学后果均未得到直接的经验支持。在这里，我们问当随机物种的相互作用受到共存的影响最小时会发生什么。我们从理论上证明，这导致可检验的预测。物种之间的相互作用仍然高度混乱，但是具有“分散”的统计结构：相互作用的强度存在偏差，因此成功的竞争者会巧妙地彼此取宠，并且相互关联，从而使竞争者将其影响分配给其他物种。我们为这种模式提供了有力的经验证据，来自草地生物多样性实验的数据与我们的预测在数量上相符。这是对通过经验测得的相互作用进行的无序检验，也是唯一的证据，表明物种相互作用和共存来自潜在的高维生态特征空间。我们的发现为推断交互网络提供了一个新的空模型，该模型以最少的先验信息和一组经验指纹来支持复杂物理生态系统的统计学启发。