Novel Covariance-Based Neutrality Test of Time-Series Data Reveals Asymmetries in Ecological and Economic Systems
Authors: Washburne Alex , Burby Josh , Lacker Daniel 
Published: March 2016

Systems as diverse as the interacting species in a community, alleles at a genetic locus, and companies in a market are characterized by competition (over resources, space, capital, etc) and adaptation. Neutral theory, built around the hypothesis that individual performance is independent of group membership, has found utility across the disciplines of ecology, population genetics, and economics, both because of the success of the neutral hypothesis in predicting system properties and because deviations from these predictions provide information about the underlying dynamics. However, most tests of neutrality are weak, based on static system properties such as species-abundance distributions or the number of singletons in a sample. Time-series data provide a window onto a system’s dynamics, and should furnish tests of the neutral hypothesis that are more powerful to detect deviations from neutrality and more informative about to the type of competitive asymmetry that drives the deviation.

Here, we present a neutrality test for time-series data. We apply this test to several microbial time-series and financial time-series and find that most of these systems are not neutral. Our test isolates the covariance structure of neutral competition, thus facilitating further exploration of the nature of asymmetry in the covariance structure of competitive systems. Much like neutrality tests from population genetics that use relative abundance distributions have enabled researchers to scan entire genomes for genes under selection, we anticipate our time-series test will be useful for quick significance tests of neutrality across a range of ecological, economic, and sociological systems for which time-series data are available. Future work can use our test to categorize and compare the dynamic fingerprints of particular competitive asymmetries (frequency dependence, volatility smiles, etc) to improve forecasting and management of complex adaptive systems.

Author Summary

From fisheries and forestries to game parks and gut microbes, managing a community of organisms is much like managing a portfolio. Managers care about diversity, and calculations of risk - for extinction or financial ruin - require accurate models of the covariance between the parts of the portfolio.

To model the covariances in portfolios or communities, it helps to start simple with a null model assuming the equivalence of species or companies relative to one another (termed “neutrality”) and letting the data suggest otherwise. Researchers in biology and finance have independently entertained and tested neutral models, but the existing tests have used snapshots of communities or the variance of fluctuations of individual populations, whereas tests of the covariances between species can better inform the development of alternative models.

We develop a covariance-based neutrality test for time-series data and use it to show that the human microbiome, North American birds, and companies in the S&P 500 all have a similar deviation from neutrality. Understanding and incorporating this non-neutral covariance structure can yield more accurate alternative models of community dynamics which can improve our management of “portfolios” of multi-species systems.