Modeling and Inferring Metacommunity Dynamics with Maximum Caliber
A major challenge for community ecology is using spatio-temporal data to infer parameters of dynamical models without conducting laborious experiments. We present a novel framework from statistical physics -- Maximum Caliber -- to characterize the temporal dynamics of complex ecological systems in spatially extended landscapes and infer parameters from empirical data. As an extension of Maximum Entropy modeling, Maximum Caliber aims at modeling the probability of possible trajectories of a stochastic system, rather than focusing on system states. We demonstrate the ability of the Maximum Caliber framework to capture ecological processes ranging from near- to far from- equilibrium, using an array of species interaction motifs including random interactions, apparent competition, intraguild predation, and non-transitive competition, along with dispersal among multiple patches. For spatio-temporal data of species occupancy in a metacommunity, the parameters of a Maximum Caliber model can be estimated through a simple logistic regression to reveal migration rates between patches, interactions between species, and local environmental suitabilities. We test the accuracy of the method over a range of system sizes and time periods, and find that these parameters can be estimated without bias. We introduce ``entropy production'' as a measure of irreversibility in system dynamics, and use ``pseudo-$R^2$'' to characterize predictability of future states. We show that our model can predict the dynamics of metacommunities that are far from equilibrium. The capacity to estimate basic parameters of dynamical metacommunity models from spatio-temporal data represents an important breakthrough for the study of metacommunities with application to practical problems in conservation and restoration ecology.