  The growth of complex populations, such as microbial communities, forests,
and cities, occurs over vastly different spatial and temporal scales. Although
research in different fields has developed detailed, system-specific models to
understand each individual system, a unified analysis of different complex
populations is lacking; such an analysis could deepen our understanding of each
system and facilitate cross-pollination of tools and insights across fields.
Here, for the first time we use a shared framework to analyze time-series data
of the human gut microbiome, tropical forest, and urban employment. We
demonstrate that a single, three-parameter model of stochastic population
dynamics can reproduce the empirical distributions of population abundances and
fluctuations in all three data sets. The three parameters characterizing a
species measure its mean abundance, deterministic stability, and stochasticity.
Our analysis reveals that, despite the vast differences in scale, all three
systems occupy a similar region of parameter space when time is measured in
generations. In other words, although the fluctuations observed in these
systems may appear different, this difference is primarily due to the different
physical timescales associated with each system. Further, we show that the
distribution of temporal abundance fluctuations is described by just two
parameters and derive a two-parameter functional form for abundance
fluctuations to improve risk estimation and forecasting.
