PT  - JOURNAL ARTICLE
AU  - Kenta Suzuki
AU  - Shinji Nakaoka
AU  - Shinji Fukuda
AU  - Hiroshi Masuya
TI  - Energy landscape analysis elucidates the multistability of ecological communities across environmental gradients
AID  - 10.1101/709956
DP  - 2021 Jan 01
TA  - bioRxiv
PG  - 709956
4099  - http://biorxiv.org/content/early/2021/05/17/709956.short
4100  - http://biorxiv.org/content/early/2021/05/17/709956.full
AB  - Compositional multistability is widely observed in multispecies ecological communities. Since differences in community composition often lead to differences in community function, understanding compositional multistability is essential to comprehend the role of biodiversity in maintaining ecosystems. In community assembly studies, it has long been recognized that the order and timing of species migration and extinction influence structure and function of communities. The study of multistability in ecology has focused on the change in dynamical stability across environmental gradients, and was developed mainly for low-dimensional systems. As a result, methodologies for studying the compositional stability of empirical multispecies communities are not well developed. Here, we show that models previously used in ecology can be analyzed from a new perspective - the energy landscape - to unveil compositional stability in observational data. To show that our method can be applicable to real-world ecological communities, we simulated assembly dynamics driven by population level processes, and show that results were mostly robust to different simulation assumptions. Our method reliably captured the change in the overall compositional stability of multispecies communities over environmental change, and indicated a small fraction of community compositions that may be channels for transitions between stable states. When applied to murine gut microbiota, our method showed the presence of two alternative states whose relationship changes with age, and suggested mechanisms by which aging affects the compositional stability of the murine gut microbiota. Our method provides a practical tool to study the compositional stability of communities in a changing world, and will facilitate empirical studies that integrate the concept of multistability from different fields.Competing Interest StatementThe authors have declared no competing interest.Glossary of termsActual featuresfeatures characterizing the stability landscape and is calculated by LV data set; these features are comparable to the features of an energy landscape.Basin of attractionin an energy landscape, defined as a set of community compositions that reach one distinct stable state when assembly processes are completely deterministic; in LV data set, it is identified by a stable state to which a community composition most frequently converged (if there is more than one such state, it belongs to all of them).Effective boundarycommunity compositions in emulated compositional dynamics having the highest energy during the transition from one stable state to another.Empirical probabilityone of actual features; the ratio of the number of observations of σ(k) to the total number of observations.Emulated compositional dynamicscompositional dynamics constrained by an energy landscape; it is generated by using the heat-bath (also known as Gibbs sampling) method.Energy barrierthe energy level that need to go up during the transition from one stable state to another.Energy landscapea weighted network whose nodes represent unique community compositions and links represent transition path between them; nodes are weighted according to energy E given by eq.(2) or (4); an energy landscape is the approximation of a stability landscape based on the maximum entropy principle given observational data; energy landscape analysis is the analysis of topological and connection attributes of an energy landscape.Energy minimacommunity compositions having the lowest energy compared to all neighboring compositions, and thus constitute end-points when assembly processes are completely deterministic (i.e., when transition of community compositions always go down the energy landscape); we identify energy minima of an energy landscape as stable states of a stability landscape.Extended pairwise maximum entropy modelan extension of the pairwise maximum entropy model (Markov network) including a term representing environmental effects. We referred the two models as the pairwise maximum entropy models all together.Imbalance score (IS)one of actual features; quantifies how stable states to which a community composition in LV data set converges are uniquely determined.LV data seta data set generated by the LV competition model; it is used to calculate actual features.Relative convergence time (RCT)one of actual features; the average number of different community compositions that a community composition undergoes before converging to a stable state; it is normalized to have a value between 0 and 1 and indicates distance from a community composition to a stable state to which it converges.Rescaled energythe energy of a community composition normalized to take 0 at a stable state and 1 at the community composition that has the highest energy within an attractive basin; for σ(k) it is calculated as, where Ek is the energy of σ(k), ESS is the energy of stable state to which basin σ(k) belongs, and Emax is the energy of a community composition that is the highest within the basin of attraction.Stable stategiven a fixed set of species, a community composition that can be an end state of assembly sequences.Stability landscapea structure that governs the overall compositional stability of an ecological community; it can be represented as a graph with a set of community compositions and transition paths between them (Figure 1).Tipping pointthe community composition located at the lowest part of the ridge between two basins of attraction.Transition channelsa fraction of effective boundary that mediates most of the transition between stable states.