Estimation, testing, and inference of network heterogeneity

O_LIDiversity and heterogeneity are related but distinct and often conflated concepts. Diversity quantifies the number or relative abundance of discrete objects (e.g. species), whereas heterogeneity includes interactions among them (i.e. in networks) and between them and their environments. Although estimation, testing, and inference of diversity is well established and understood in ecology, comparable methods for heterogeneity are themselves diverse and rarely applied consistently or coherently. C_LIO_LIWe propose a consistent and coherent methodology for estimation, testing, and inference of heterogeneity of ecological networks. Estimation of heterogeneity is scalable from individuals to populations using the variance-to-mean (V/M) ratio and extensions of Taylors power law (TPL) to analyzing networks. Bootstrapping is used to partition heterogeneous and random clusters, whereas permutation tests are used to compare individual- and network-level heterogeneity. Inference includes the identification of "important" (e.g. dominant, foundation, keystone) species and "rich clubs" in heterogeneous networks, detection of biomarkers, and analysis of heterogeneity-stability relationships. C_LIO_LIWe demonstrate this methodology using the global Earth Microbiome Project dataset. The method could reliably distinguish heterogeneous nodes and networks; identified significant differences in heterogeneity among microbial assemblages in different habitats and in specific sites within habitats; and supported established principles of host filtering, species sorting, and niche partitioning. C_LIO_LIOur methods for estimation, testing, and inference of heterogeneity are modular, scalable, and applicable to a wide range of ecological systems. They also provide a quantitative method for understanding how evolutionary and ecological forces jointly shape both topology and heterogeneity in ecological networks. C_LI