Sustainability is a key concept in economic and policy debates. Nevertheless, it is usually treated only in a qualitative way and has eluded quantitative analysis. Here, we propose a sustainability index based on the premise that sustainable systems do not lose or gain Fisher Information over time. We test this approach using time series data from the AmeriFlux network that measures ecosystem respiration, water and energy fluxes in order to elucidate two key sustainability features: ecosystem health and stability. A novel definition of ecosystem health is developed based on the concept of criticality, which implies that if a system’s fluctuations are scale invariant then the system is in a balance between robustness and adaptability. We define ecosystem stability by taking an information theory approach that measures its entropy and Fisher information. Analysis of the Ameriflux consortium big data set of ecosystem respiration time series is contrasted with land condition data. In general we find a good agreement between the sustainability index and land condition data. However, we acknowledge that the results are a preliminary test of the approach and further verification will require a multi-signal analysis. For example, high values of the sustainability index for some croplands are counter-intuitive and we interpret these results as ecosystems maintained in artificial health due to continuous human-induced inflows of matter and energy in the form of soil nutrients and control of competition, pests and disease.

We review the concept of ecosystem resilience in its relation to ecosystem integrity from an information theory approach. We summarize the literature on the subject identifying three main narratives: ecosystem properties that enable them to be more resilient; ecosystem response to perturbations; and complexity. We also include original ideas with theoretical and quantitative developments with application examples. The main contribution is a new way to rethink resilience, that is mathematically formal and easy to evaluate heuristically in real-world applications: ecosystem antifragility. An ecosystem is antifragile if it benefits from environmental variability. Antifragility therefore goes beyond robustness or resilience because while resilient/robust systems are merely perturbation-resistant, antifragile structures not only withstand stress but also benefit from it.

if you think you are in control of your behavior, think again. evidence suggests that behavioral modifications, as development and persistence of depression, maybe the consequence of a complex network of communication between macro and micro-organisms capable of modifying the physiological axis of the host. Some parasites cause significant nutritional deficiencies for the host and impair the effectiveness of cognitive processes such as memory, teaching or non-verbal intelligence. Bacterial communities mediate the establishment of parasites and vice versa but this complexity approach remains little explored. We study the gut microbiota-parasite interactions using novel techniques of network analysis using data of individuals from two indigenous communities in Guerrero, Mexico. Our results suggest that Ascaris lumbricoides induce a gut microbiota perturbation affecting its network properties and also subnetworks of key species related to depression, translating in a loss of emergence. Studying these network properties changes is particularly important because recent research has shown that human health is characterized by a dynamic trade-off between emergence and self-organization, called criticality. emergence allows the systems to generate novel information meanwhile selforganization is related to the system's order and structure. in this way, the loss of emergence means a depart from criticality and ultimately loss of health.

Abstract. Combining well-established non-equilibrium thermodynamic principles and a system dynamics approach, we define, for the first time, the concept of planetary antifragility as changes of Fisher information of Earth's entropy production. As a first approximation for entropy production, we propose using shortwave global albedo anomalies and provide a first quantitative example with data for the July months in the Northern Hemisphere from 1982 to 2010. These preliminary results show a net reduction of 47.63 % in albedo's Fisher information. This loss of antifragility implies a compounding problem because human perturbations such as climate or land-use changes are increasing, but at the same time, the planet is losing its capacity to respond to them. We discuss the concept of antifragility in the context of safe operating space for humanity and planetary boundaries. We conclude that not only does interaction among state variables of the boundaries matter, but more importantly the perturbation response capacity dimension is also missing. In conclusion we speculate on improving the operational definition for ecosystems.

The gut microbiota-brain axis is a complex communication network essential for host health. Any long-term disruption can affect higher cognitive functions, or it may even result in several chronic neurological diseases. The type and diversity of nutrients an individual consumes are essential for developing the gut microbiota (GM) and the brain. Hence, dietary patterns might influence networks communication of this axis, especially at the age that both systems go through maturation processes. By implementing Mutual Information and Minimum Spanning Tree (MST); we proposed a novel combination of Machine Learning and Network Theory techniques to study the effect of animal protein and lipid intake on the connectivity of GM and brain cortex activity (BCA) networks in children from 5-to 10 years old from an indigenous community in the southwest of México. Socio-ecological conditions in this nonwestern lifestyle community are very homogeneous among its inhabitants but it shows high individual heterogeneity in the consumption of animal products. Results suggest that MST, the critical backbone of information flow, diminishes under low protein and lipid intake. So, under these nonwestern regimens, deficient animal protein and lipid consumption diets may significantly affect the GM-BCA connectivity in crucial development stages. Finally, MST offers us a metric that unifies biological systems of different nature to evaluate the change in their complexity in the face of environmental pressures or disturbances. Effect of Diet on gut microbiota and brain networks connectivity.