The hybrid model links micro and macro scales in complex systems

In fields ranging from immunology and ecology to economics and thermodynamics, complex multi-scale systems are ubiquitous. They are also notoriously difficult to model. Conventional approaches either adopt a bottom-up approach Or top-down approach. But in disrupted systems, such as a forest ecosystem after a fire or a society during a pandemic, these unidirectional models cannot capture the interactions between small-scale behaviors and system-level properties. SFI external professor John Harte (UC Berkeley) and his collaborators worked to solve this challenge by building a hybrid method that connects bottom-up behavior and top-down causation into a single theory.

The article by Harte et al in the Proceedings of the National Academy of Sciencespublished on December 6, presents their approach and provides four refined examples where it could be applied.

“Over the last 14 years, we’ve 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 patch area) and the distribution of species abundance and size. But six years ago, we discovered that when an ecosystem is heavily perturbed – and as a result, system-level properties evolve – then the top-down approach fails miserably.” Harte and his colleagues therefore set out to develop a theory capable of describing the ecosystem. times system-level dynamics and the probability distributions that characterize the components of complex flow systems.

Disturbances and the bidirectional reactions they can cause appear in many types of systems. In the case of a pandemic, conventional bottom-up Susceptible-Infected-Recovered (SIR) equations help measure the likelihood that an individual could become ill in close proximity to an infected person. What this approach does not take into account, however, is the interaction between the micro and macro scales. As cases of disease increase at the macro level, individuals might take notice and change their behaviors, leading to a decline in cases.

Similarly, in an economy, the decisions individuals make about whether or not to accept a job or make a purchase are influenced by system-level properties such as 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 article “DynaMETE: a hybrid MaxEnt-plus-mechanism theory of dynamic macroecology”. By testing their theory with data from a heavily disturbed forest in Panama, the team showed that their hybrid model could explain changes in species distributions. Now, the authors generalize their model for possible application in other scenarios.

“This model allows us to calculate things that were not calculable before,” says Harte. “In these two-tier systems, when there is both top-down and bottom-up influence, how do you calculate, when the system is disrupted, how does the system And will individuals respond over time? There was no adequate theory before. This theory allows us to predict the trajectory of system-level variables and the probability distribution of different parts of that system. »

Harte proposes testing the theory in a combustion tank – a simple thermodynamic system – and says further testing is needed. “The biggest idea here was realizing the importance of the question. We think this theory is good, but it may not be right. It still needs to be tested on 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 question. “It stood up to the math,” says Harte.

Hybrid theory offers a new way to study dynamics, whether in controlled laboratories or in some of the most exciting and critical problems facing humanity, from climate change and pandemics to economic volatility.