Beyond direct neighbourhood effects: higher-order interactions improve modelling and predicting tree survival and growth

Detecting Nonadditive Biotic Interactions and Assessing Their Biological Relevance among Temperate Rainforest Trees

AbstractInteractions between and within abiotic and biotic processes generate nonadditive density-dependent effects on species performance that can vary in strength or direction across environments. If ignored, nonadditivities can lead to inaccurate predictions of species responses to environmental and compositional changes. While there are increasing empirical efforts to test the constancy of pairwise biotic interactions along environmental and compositional gradients, few assess both simultaneously. Using a nationwide forest inventory that spans broad ambient temperature and moisture gradients throughout New Zealand, we address this gap by analyzing the diameter growth of six focal tree species as a function of neighbor densities and climate, as well as neighbor × climate and neighbor × neighbor statistical interactions. The most complex model featuring all interaction terms had the highest predictive accuracy. Compared with climate variables, biotic interactions typically had stronger effects on diameter growth, especially when subjected to nonadditivities from local climatic conditions and the density of intermediary species. Furthermore, statistically strong (or weak) nonadditivities could be biologically irrelevant (or significant) depending on whether a species pair typically interacted under average or more extreme conditions. Our study highlights the importance of considering both the statistical potential and the biological relevance of nonadditive biotic interactions when assessing species performance under global change.

Multitrophic Higher-Order Interactions Modulate Species Persistence

AbstractEcologists increasingly recognize that interactions between two species can be affected by the density of a third species. How these higher-order interactions (HOIs) affect species persistence remains poorly understood. To explore the effect of HOIs stemming from multiple trophic layers on a plant community composition, we experimentally built a mesocosm with three plants and three pollinator species arranged in a fully nested and modified network structure. We estimated pairwise interactions among plants and between plants and pollinators, as well as HOIs initiated by a plant or a pollinator affecting plant species pairs. Using a structuralist approach, we evaluated the consequences of the statistically supported HOIs on the persistence probability of each of the three competing plant species and their combinations. HOIs substantially redistribute the strength and sign of pairwise interactions between plant species, promoting the opportunities for multispecies communities to persist compared with a non-HOI scenario. However, the physical elimination of a plant-pollinator link in the modified network structure promotes changes in per capita pairwise interactions and HOIs, resulting in a single-species community. Our study provides empirical evidence of the joint importance of HOIs and network structure in determining species persistence within diverse communities.

Warming-induced phenological mismatch between trees and shrubs explains high-elevation forest expansion

Despite the importance of species interaction in modulating the range shifts of plants, little is known about the responses of coexisting life forms to a warmer climate. Here, we combine long-term monitoring of cambial phenology in sympatric trees and shrubs at two treelines of the Tibetan Plateau, with a meta-analysis of ring-width series from 344 shrubs and 575 trees paired across 11 alpine treelines in the Northern Hemisphere. Under a spring warming of +1°C, xylem resumption advances by 2-4 days in trees, but delays by 3-8 days in shrubs. The divergent phenological response to warming was due to shrubs being 3.2 times more sensitive than trees to chilling accumulation. Warmer winters increased the thermal requirement for cambial reactivation in shrubs, leading to a delayed response to warmer springs. Our meta-analysis confirmed such a mechanism across continental scales. The warming-induced phenological mismatch may give a competitive advantage to trees over shrubs, which would provide a new explanation for increasing alpine treeline shifts under the context of climate change.

Higher-Order Interactions and Their Duals Reveal Synergy and Logical Dependence beyond Shannon-Information

Information-theoretic quantities reveal dependencies among variables in the structure of joint, marginal, and conditional entropies while leaving certain fundamentally different systems indistinguishable. Furthermore, there is no consensus on the correct higher-order generalisation of mutual information (MI). In this manuscript, we show that a recently proposed model-free definition of higher-order interactions among binary variables (MFIs), such as mutual information, is a Möbius inversion on a Boolean algebra, except of surprisal instead of entropy. This provides an information-theoretic interpretation to the MFIs, and by extension to Ising interactions. We study the objects dual to mutual information and the MFIs on the order-reversed lattices. We find that dual MI is related to the previously studied differential mutual information, while dual interactions are interactions with respect to a different background state. Unlike (dual) mutual information, interactions and their duals uniquely identify all six 2-input logic gates, the dy- and triadic distributions, and different causal dynamics that are identical in terms of their Shannon information content.

Ecology: Lifting the curtain on higher-order interactions

Higher-order interactions - the modification of interactions between a species pair by a third - remain poorly understood in nature. A new study manipulates pairwise and higher-order interactions in the field, offering exciting new insights into how higher-order interactions contribute to coexistence.

Disentangling key species interactions in diverse and heterogeneous communities: A Bayesian sparse modelling approach

Modelling species interactions in diverse communities traditionally requires a prohibitively large number of species-interaction coefficients, especially when considering environmental dependence of parameters. We implemented Bayesian variable selection via sparsity-inducing priors on non-linear species abundance models to determine which species interactions should be retained and which can be represented as an average heterospecific interaction term, reducing the number of model parameters. We evaluated model performance using simulated communities, computing out-of-sample predictive accuracy and parameter recovery across different input sample sizes. We applied our method to a diverse empirical community, allowing us to disentangle the direct role of environmental gradients on species' intrinsic growth rates from indirect effects via competitive interactions. We also identified a few neighbouring species from the diverse community that had non-generic interactions with our focal species. This sparse modelling approach facilitates exploration of species interactions in diverse communities while maintaining a manageable number of parameters.

A system model of three-body interactions in complex networks: consensus and conservation

Networked complex systems in a wide range of physics, biology and social sciences involve synergy among multiple agents beyond pairwise interactions. Higher-order mathematical structures such as hypergraphs have been increasingly popular in modelling and analysis of complex dynamical behaviours. Here, we study a simple three-body consensus model, which favourably incorporates higher-order network interactions, higher-order dimensional states, the group reinforcement effect and the social homophily principle. The model features asymmetric roles of acting agents using modulating functions. We analytically establish sufficient conditions for nonlinear consensus and conservation of states for agents with both discrete-time and continuous-time dynamics. We show that higher-order interactions encoded in three-body edges give rise to consensus and conservation for systems with gravity-like and Heaviside-like modulating functions. Furthermore, we illustrate our theoretical results with numerical simulations and examine the system convergence time through a network depreciation process.

Effects of Soil Heterogeneity and Species on Plant Interactions

Plant interactions are central in driving the composition and structure of plant populations and communities. Soil heterogeneity and species identity can modulate such interactions, yet require more studies. Thus, a manipulative experiment was done where three soil heterogeneity levels were developed by mixing local soil and sand in three different ratios (i.e., soil:sand ratio = 2:8, 5:5, and 8:2), and three typical species (i.e., Festuca elata, Bromus inermis, and Elymus breviaristatus) were used in different combinations. Soil heterogeneity was assumed to affect plant interactions, which were in turn modified by species. Plant height was applied as an indicator for plant interactions. Relative competition intensity (RCI) was used to quantify plant interactions, where RCI was applied as a ratio of monoculture and mixture performance. Results showed that soil heterogeneity and soil heterogeneity × species significantly affected the RCI in mixtures compared with plant individuals growing alone (i.e., RCI1). However, species as a single factor did not affect RCI1. Moreover, species and soil heterogeneity × species significantly affected the RCI in mixtures compared with two individuals growing together (i.e., RCI2), and the difference between RCI1 and RCI2 (i.e., RCIdiff). Soil heterogeneity significantly affected RCI2 of F. elata. This study suggests that soil heterogeneity could buffer the stability of plant populations by modifying plant interactions, which would subsequently drive plant establishment. To explore the underlying mechanisms of such patterns, further studies considering more species and plant traits are needed.