In fields ranging from immunology and ecology to economics and thermodynamics, multi-scale complex systems are ubiquitous. They are also notoriously difficult to model. Conventional approaches take either a bottom-up or top-down approach. But in disturbed systems, such as a post-fire forest ecosystem or a society in a pandemic, these unidirectional models can’t capture the interactions between the small-scale behaviors and the system-level properties. SFI External Professor John Harte (UC Berkeley) and his collaborators have worked to resolve this challenge by building a hybrid method that links bottom-up behaviors and top-down causation in a single theory.
Harte et al’s paper in PNAS, published on December 6, outlines their approach and provides four pared-down examples where it could be applied.
“Over the past 14 years, we have written a series of papers showing that in ecology, this top-down approach is very powerful and reveals patterns in ecosystems,” says Harte. “It accurately predicts ecological patterns such as the species-area relationship (how diversity increases with plot area) and the distribution of abundances and body sizes of species. But six years ago, we discovered that when an ecosystem is heavily disturbed — and as a result, the system-level properties are in flux — then the top-down approach fails miserably.” And so, Harte and his colleagues set out to develop a theory that could describe both the system-level dynamics and the probability distributions that characterize the system components for complex systems in flux.
Disturbances and the two-way feedback they can cause show up in many types of systems. In the case of a pandemic, conventional bottom-up Susceptible-Infected-Recovered (SIR) equations help measure the probability that an individual could get sick through proximity to an infected person. What this approach doesn’t capture, though, is the interplay between the micro and macro scales. As cases of the disease rise at the macro level, individuals might take notice and change their behaviors, causing case levels to fall.
Similarly, in an economy, the decisions individuals make on whether or not to take a job or make a purchase are influenced by system-level properties like GNP growth and inflation rates. Meanwhile, consumer spending is a driving factor in the economy and can impact economic growth or decline.
In 2021, Harte and colleagues first presented their new approach in the journal Ecology Letters with their paper “DynaMETE: a hybrid MaxEnt-plus-mechanism theory of dynamic macroecology.” Testing their theory against data from a heavily disturbed forest in Panama, the team showed that their hybrid model could explain changes in species distribution. Now, the authors generalize their model for possible application in other scenarios.
“This model allows us to calculate things that haven’t been calculable before,” says Harte. “In these bi-level systems, when there’s both top-down and bottom-up influence, how do you calculate, when the system is disturbed, how the system and the individuals will respond over time? There was not an adequate theory before. This theory allows us to predict the trajectory of the system-level variables and the probability distribution of individual parts in that system.”
Harte proposes a test of the theory in a combustion tank — a simple thermodynamic system — and says other tests are needed. “The biggest insight here was realizing the importance of the question. We think this theory is good, but it may not be right. It’s still got to be tested across many types of systems.”
In nonequilibrium thermodynamics such as the proposed combustion tank experiment, predicting the probability distribution of molecular kinetic energies has been a frontier issue. “It has resisted calculation,” says Harte.
The hybrid theory offers a new way to study dynamics, whether in controlled lab settings or in some of the most tantalizing and critical problems facing humanity, from climate change and pandemics to economic volatility.
Read the paper "Dynamical theory of complex systems with two-way micro–macro causation" in PNAS (December 6, 2024). DOI: 10.1073/pnas.2408676121