A package/library for energy landscape analysis available for:
Mathematica (ela.wl): https://doi.org/10.5281/zenodo.5492161
Tutorial is here
Energy landscape analysis is a systematic method for analyzing an energy landscape represented as a weighted network (Fig. 1). In the energy landscape, the nodes of the network represent unique community compositions, and the links represent the transition paths between them. The community composition is described as a binary vector that represents the presence (1) and absence (0) of a species, and the links connect all nodes that differ only in the presence or absence of one species. The nodes are weighted by their energies, and the difference in energy level drives the direction of transitions in community composition. Transitions from high-energy states to low-energy states occur more frequently than vice versa. The energy is assigned by a pairwise maximum entropy model or its extension with an external force (environmental effect) term. The parameters of the model are estimated by matching the expected probability of community compositions given by the model to empirical probabilities calculated from the observed data. (For details of the method, see Suzuki et al. 2021.)
Figure 1. Illustrative explanation of our approach. (A) we assume that the dataset to be analyzed includes occurrence of species in local communities sampled from multiple targets (e.g., sites, hosts) and/or timepoints, with possibly accompanying values representing local environmental condition (environmental factors). (B) the state space of community compositions is formally defined as a graph. (C) observational data is used to fit parameters in a pairwise maximum entropy model. (D) the fitted pairwise maximum entropy model specifies an energy landscape which is a network with nodes representing community states and links representing transitions between community compositions. Energy landscape analysis acknowledges the stable states and tipping points. The disconnectivity graph summarizes the hierarchical relationships between the stable states and tipping points, and its change over environmental conditions can be described as a stable state diagram.
- Suzuki, K., Nakaoka, S., Fukuda, S., & Masuya, H. (2021). Energy landscape analysis elucidates the multistability of ecological communities across environmental gradients. Ecological Monographs, 91(3), e01469. https://esajournals.onlinelibrary.wiley.com/doi/abs/10.1002/ecm.1469