Structurally complex habitats tend to contain more species and higher total abundances than simple habitats. This ecological paradigm is grounded in first principles: species richness scales with area, and surface area and niche density increase with three-dimensional complexity. Here we present a geometric basis for surface habitats that unifies ecosystems and spatial scales. The theory is framed by fundamental geometric constraints between three structure descriptors—surface height, rugosity and fractal dimension—and explains 98% of surface variation in a structurally complex test system: coral reefs. Then, we show how coral biodiversity metrics (species richness, total abundance and probability of interspecific encounter) vary over the theoretical structure descriptor plane, demonstrating the value of the theory for predicting the consequences of natural and human modifications of surface structure.

与简单的栖息地相比，结构复杂的栖息地往往包含更多的物种和更高的总丰度。这种生态学范式以第一原理为基础：物种丰富度随面积而定，表面积和生态位密度随三维复杂性而增加。在这里，我们提出了统一生态系统和空间尺度的地表生境的几何基础。该理论由三个结构描述符（表面高度，皱纹和分形维）之间的基本几何约束构架，并解释了结构复杂的测试系统（珊瑚礁）中98％的表面变化。然后，我们展示了珊瑚生物多样性指标（物种丰富度，总丰度和种间遭遇的概率）在理论结构描述符平面上如何变化，