The size-distribution of Earth’s lakes

Abstract

Globally, there are millions of small lakes, but a small number of large lakes. Most key ecosystem patterns and processes scale with lake size, thus this asymmetry between area and abundance is a fundamental constraint on broad-scale patterns in lake ecology. Nonetheless, descriptions of lake size-distributions are scarce and empirical distributions are rarely evaluated relative to theoretical predictions. Here we develop expectations for Earth’s lake area-distribution based on percolation theory and evaluate these expectations with data from a global lake census. Lake surface areas ≥0.46 km[superscript 2] are power-law distributed with a tail exponent (τ = 2.14) and fractal dimension (d = 1.4), similar to theoretical expectations (τ = 2.05; d = 4/3). Lakes <0.46 km[superscript 2] are not power-law distributed. An independently developed regional lake census exhibits a similar transition and consistency with theoretical predictions. Small lakes deviate from the power-law distribution because smaller lakes are more susceptible to dynamical change and topographic behavior at sub-kilometer scales is not self-similar. Our results provide a robust characterization and theoretical explanation for the lake size-abundance relationship, and form a fundamental basis for understanding and predicting patterns in lake ecology at broad scales.