Exploring noise, degeneracy, and determinism in biological networks with the einet package

Connections between soil microbes, land use and European climate: Insights for management practices

Soil microbial biomass and activity strongly depend on land use, vegetation cover, climate, and soil physicochemical properties. In most cases, this dependence was assessed by one-to-one correlations while by employing network analysis, information about network robustness and the balance between stochasticity and determinism controlling connectivity, was revealed. In this study, we further elaborated on the hypothesis of Smith et al. (2021) that cropland soils depended more on climate variables and therefore are more vulnerable to climate change. We used the same dataset with that of Smith et al. (2021) that contains seasonal microbial, climate and soil variables collected from 881 soil points representing the main land uses in Europe: forests, grassland, cropland. We examined complete (both direct and indirect relationships) and incomplete networks (only direct relationships) and recorded higher robustness in the former. Partial Least Square results showed that on average more than 45% of microbial attributes' variability was predicted by climate and habitat drivers denoting medium to strong effect of habitat filtering. Network architecture slightly affected by season or land use type; it followed the core/periphery structure with positive and negative interactions and no hub nodes. Microbial attributes (biomass, activity and their ratio) mostly belong to core block together with Soil Organic Carbon (SOC), while climate and soil variables to periphery block with the exception of cropland networks, denoting the higher dependence between microbial and climate variables in these latter. All complete networks appeared robust except for cropland and forest in summer, a finding that disagrees with our initial hypothesis about cropland. Networks' connectivity was controlled stronger by stochasticity in forest than in croplands. The lack of human interventions in forest soils increase habitat homogeneity enhancing the influence of stochastic agents such as microbial unlimited dispersal and/or stochastic extinction. The increased stochasticity implies the necessity for proactive management actions.

Emergence and Causality in Complex Systems: A Survey of Causal Emergence and Related Quantitative Studies

Emergence and causality are two fundamental concepts for understanding complex systems. They are interconnected. On one hand, emergence refers to the phenomenon where macroscopic properties cannot be solely attributed to the cause of individual properties. On the other hand, causality can exhibit emergence, meaning that new causal laws may arise as we increase the level of abstraction. Causal emergence (CE) theory aims to bridge these two concepts and even employs measures of causality to quantify emergence. This paper provides a comprehensive review of recent advancements in quantitative theories and applications of CE. It focuses on two primary challenges: quantifying CE and identifying it from data. The latter task requires the integration of machine learning and neural network techniques, establishing a significant link between causal emergence and machine learning. We highlight two problem categories: CE with machine learning and CE for machine learning, both of which emphasize the crucial role of effective information (EI) as a measure of causal emergence. The final section of this review explores potential applications and provides insights into future perspectives.

Fire and Rhizosphere Effects on Bacterial Co-Occurrence Patterns

Fires are common in Mediterranean soils and constitute an important driver of their evolution. Although fire effects on vegetation dynamics are widely studied, their influence on the assembly rules of soil prokaryotes in a small-scale environment has attracted limited attention. In the present study, we reanalyzed the data from Aponte et al. (2022) to test whether the direct and/or indirect effects of fire are reflected in the network of relationships among soil prokaryotes in a Chilean sclerophyllous ecosystem. We focused on bacterial (genus and species level) co-occurrence patterns in the rhizospheres and bulk soils in burned and unburned plots. Four soils were considered: bulk-burnt (BB), bulk-unburnt (BU), rhizosphere-burnt (RB), and rhizosphere-unburnt (RU). The largest differences in network parameters were recorded between RU and BB soils, while RB and BU networks exhibited similar values. The network in the BB soil was the most compact and centralized, while the RU network was the least connected, with no central nodes. The robustness of bacterial communities was enhanced in burnt soils, but this was more pronounced in BB soil. The mechanisms mainly responsible for bacterial community structure were stochastic in all soils, whether burnt or unburnt; however, communities in RB were much more stochastic than in RU.

Neural Information Squeezer for Causal Emergence

Conventional studies of causal emergence have revealed that stronger causality can be obtained on the macro-level than the micro-level of the same Markovian dynamical systems if an appropriate coarse-graining strategy has been conducted on the micro-states. However, identifying this emergent causality from data is still a difficult problem that has not been solved because the appropriate coarse-graining strategy can not be found easily. This paper proposes a general machine learning framework called Neural Information Squeezer to automatically extract the effective coarse-graining strategy and the macro-level dynamics, as well as identify causal emergence directly from time series data. By using invertible neural network, we can decompose any coarse-graining strategy into two separate procedures: information conversion and information discarding. In this way, we can not only exactly control the width of the information channel, but also can derive some important properties analytically. We also show how our framework can extract the coarse-graining functions and the dynamics on different levels, as well as identify causal emergence from the data on several exampled systems.