Taylor's power law meets ecological networks: introducing TPLoN as a novel framework for heterogeneity scaling analysis

Taylor's power law (TPL), which relates population mean ( M ) and variance ( V ) in a power function ( V = aM b ), was originally discovered by L. R. Taylor (1961, Nature) in his studies of insect populations. It has been validated by numerous field observations and scrutinized by many theoretical analyses over the past six decades. It has found applications across many disciplines in the natural and social sciences, as well as the humanities, beyond ecology, and has been recognized as an important tool for describing order and patterns in nature. More recently, TPL has been extended to measure the spatial heterogeneity and temporal stability of ecological communities and landscapes, known as TPL extensions (TPLE). Here, we push the envelope by proposing TPL of ecological networks (TPLoN) to quantify interactions – a hallmark of ecological heterogeneity. To implement TPLoN, we define two key metrics: species connectedness (node degree divided by abundance) and weighted species connectedness (a vector of connectedness multiplied by neighbor correlation coefficients). We then compute variance–mean ( V‐M ) pairs for the vector elements of each species (network node) and fit the V‐M pairs of all species in the network to the TPL model. We demonstrate TPLoN using large datasets from the animal gastrointestinal microbiome (AGM) comprising 4903 samples from four major invertebrate groups and all six vertebrate classes. Compared with the traditional TPLE, TPLoN provided even better fits to the AGM datasets, although both were statistically significant. TPL, TPLE and TPLoN represent a hierarchy of ecological patterns, where: 1) TPL captures population‐scale spatial/temporal aggregation (stability) scaling; 2) TPLE extends this to community‐scale spatial/temporal heterogeneity (stability) scaling; and 3) TPLoN characterizes metacommunity‐scale heterogeneity scaling through network structure. Each level captures increasingly complex ecological organization. Finally, TPLoN inherits many theoretical and empirical insights from TPL studies over the past half‐century.