Resolving the confusions on the complete spatial randomness of species - Youhua Chen; Yongbin Wu; Tsung-Jen Shen (International Journal of Applied Earth Observations and Geoinformation)
Complete spatial randomness (CSR) describes a fully homogeneous random distribution of species across space, where every location within a study area has an equal probability of hosting individuals. However, previous literature often conflates the roles of the Poisson and uniform distributions in representing CSR. While the homogeneous nature of CSR intuitively suggests a connection to the uniform distribution, it is less clear how the Poisson distribution can achieve this. In this study, we provide a statistical explanation, demonstrating that the Poisson distribution, and the exponential waiting time derived from it, the uniform distribution, and CSR are all mathematically equivalent under the same probabilistic framework. We present interpretations from both a simulation algorithm perspective and a statistical sampling perspective, supported by appropriate statistical reasoning. Our ecology-oriented discussion aims to clarify the conceptual confusion surrounding CSR and establish a coherent link to foundational knowledge in spatial ecology. Ultimately, we hope to deepen ecologists’ and biologists’ understandings of species distribution patterns and support future developments of distributional ecology.