In my past and current work I have always followed an ideal of innovation, addressing various topics such as modeling anomalous diffusion processes in Ecology (Boyer & López-Corona, 2009), groundwater flow (López-Corona, 2011), mining data (López-Corona et al., 2013a), optimization with Evolutionary Computation (López-Corona et al., 2012) and modeling with agents (López-Corona et al., 2013d, c). In the mathematical part I have developed together with my collaborators a set of non-classical underground flow equations (López-Corona et al., 2013b) that in turn used a new method to arrive at a continuous formulation (for differential equation systems) partial) of discrete agent problems (López-Corona et al., 2013d).

Full graduate and undergraduate dissertations inhere

My current line of work is all about:

What does Theoretical Physics tell us about Ecosystem Health?

Physics in general seeks to recognize universal patterns within the processes that occur in nature, however, it has been until very recently with the advent of Complexity Sciences that its methods are being used with great success in various subjects that were not traditionally associated with the discipline, such as health in general or the health of ecosystems. in particular, by incorporating two dimensions not explicitly considered, dynamics and response to shocks. Thus we have arrived at a new concept in the scientific literature, ecosystem antifragility.

Key Ideas:

Health is not only a state but also a type of dynamics and the way in which systems react to disturbances in their environment.

A system (human, animal, ecosystem or the planet) is healthy if its dynamics are critical, where there is a balance between robustness and flexibility.

A system is healthy if it is able to benefit from the volatility of its environment, we call this antifragility.


Like other important modern terms in science, the health of ecosystems is a fuzzy concept that has been defined several times since the late 1980s (Rapport et al., 1998). This conceptual diversity has given rise to different ways of measuring it, which in turn has generated a wide range of narratives related to the health of ecosystems (O’Brien et al., 2016). Ultimately, it has become a constant priority for government, scientists, and decision makers worldwide (Burger et al., 2006).

The ecological literature has tended to identify the health of ecosystems with their ecological integrity understood as an underlying attribute in the constitution of ecosystems that produce specific manifestations in their structural characteristics, development processes and acquired composition. The integrity of ecosystems (see Fig. 1) arises from self-organization processes derived from thermodynamic mechanisms that operate through locally existing living organisms (biota), as well as from the energy and materials at their disposal, until reaching operational points “optimal” that are not fixed, but vary according to variations in physical conditions or changes in the biota or the environment. In a collaboration between CONABIO and INECOL, a three-layer model for the integrity of ecosystems has been developed, with which an Ecosystem Integrity Index has been developed using environmental Big Data and Machine Learning algorithms, at a scale of 1Km ^ 2 of the entire country (see


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Fig. 1: Three-layer ecosystem integrity model. The internal level is hidden from the observer, but its status can be inferred from the information available at the instrumental or observation level where measurements of the structure (including composition or other characteristics of biodiversity) and function are obtained, taking into account, of course, the context in which the ecosystem develops. The tips of the arrows indicate the direction of the supposed mechanical influence, although the information can go in any direction. Taken from

Incorporating the dynamics: criticality

When you enter as a CONACyT Chair researcher at CONABIO, quickly identify that this line of research was quite similar to the one that had been developing in the group of Alexander Frank in the Center of Sciences of the Complexity (C3) of the UNAM, with which we have been studying health through the analysis of physiological time series. Various studies have accumulated empirical evidence that indicates that systemic physiological processes such as cardiac activity are in what is medically identified as health when the time series of its fluctuations follows a pattern defined as criticality.

Several authors have found evidence of dynamic criticality in physiological processes such as cardiac activity, and have postulated that it may be a key feature of a healthy state (Kiyono, 2001; Goldberger, 2002). In a recent document reviewing criticality in the brain (Cocchi, 2017) it is stated that i) criticality is a widespread phenomenon in natural systems that provides a unifying framework that can be used to model and understand brain activity and function cognitive, and ii) that there is substantial evidence supporting the hypothesis that the brain works close to criticality. In this sense, what has been called the Criticality Hypothesis affirms that systems in a dynamic regime in balance between self-organization (order) and emergence (randomness), reach the highest level of computing capacity. and they achieve an optimal balance between robustness and flexibility. This hypothesis is supported by various recent results in cell biology, evolutionary and neurosciences, highlighting its role as a viable candidate general law in the field of complex adaptive systems (see Roli, 2018 and its internal references).

Our interest in the subject arose because this state of criticality is characteristic of phase transitions like the one that occurs in magnetic materials when passing from a non-magnetic state to a magnetized one. This type of process can be described using the famous Ising model with which it can be shown that the maximum complexity of the system is reached in the phase transition. In other words, in a certain way, criticality is a digital fingerprint of complexity.

Using these ideas we begin to think that perhaps we could use these same ideas in ecosystems by identifying some type of environmental physiological processes, such as the case of ecosystem respiration. For this we use data from hundreds of monitoring sites of the international consortium Ameriflux for the forests of North America (Ramírez-Carrillo, 2018). With this we begin to expand the idea of ​​ecosystem health from a description of its state (integrity), including also its dynamics (criticality).

Incorporating the response to disturbances: Antifragility

However, returning to the human health part, my colleagues from the Institute of Nuclear Sciences and C3 of UNAM, Rubén Fossion with his colleague Ana Leonor Rivera, along with doctor Bruno Estañol; they began to study another important aspect, homeostasis. Or seen from a broader perspective, the way systems respond to disturbances, a topic that had interested me in my study of the statistical consequences of long-tail distributions (Taleb, 2020). In their work, my colleagues found that when the human body needs to maintain some homeostatic physiological process (keep it within a defined range of values) such as blood pressure, this is only achieved by coupling it with another process that absorbs variability. from the environment, which in the case of blood pressure is the heart rate. In their work they show that healthy people have a blood pressure that is normally distributed, while heart rate has a long tail to the right. Whereas when there is a chronic disease such as diabetes, blood pressure is no longer Gaussian and generates a long tail to the left, while heart rate is now normally distributed. That a process is normally distributed means that there is a well-defined characteristic scale around which all values ​​are grouped, with very few extreme values. Conversely, having long tails means that there are many extreme events, which in fact dominate the phenomenon to the degree that the characteristic scale can be lost.

The similarity between the results of Fossion and collaborators with the ideas of Nassim Nicholas Taleb, made me think that in fact homeostasis or resilience, as it is generally identified in ecology, are actually a particular case of the Taleb conceptual framework in which a system can be fragile, robust or antifragile, depending on how it responds to disturbances in its environment (see Fig. 2). What Taleb realized (2012) is that the opposite of a system that is harmed by the variability of its environment, such as a crystal glass, is not how a system that is insensitive or that recovers from disturbances is commonly thought. (robustness or resilience). The opposite of losing to volatility is winning, not being insensitive. Taleb named these types of systems antifragile systems. Of course the best example of antifragility is the life phenomenon. The application of these ideas has been reviewed in detail in a recent publication ( that incorporates for the first time in the specialized literature the concept of ecosystem antifragility. Of course Taleb in his work deals with the subject we have only formalized it. These ideas have recently started to be used by colleagues of mine with whom I collaborate, in the characterization of the human intestinal microbiota and in how it affects the functioning of the brain (Ramírez-Carrillo, 2020).

In this way, in our comings and goings between empiricism and theoretical physics, we went from characterizing health only by its state (integrity) to also consider its dynamics (criticality) and the way in which they respond to disturbances (antifragility). We believe that through our work we are showing that this complex way of looking at health applies to different types of systems (human, animal, ecosystem) and at very different scales.

Thus, as far-fetched as it may sound at first, theoretical physics (specifically Complexity) has a lot to say about the health of ecosystems, traditionally understood; but also seeing the organisms themselves as ecosystems (López-Corona 2019); or even to Earth as the planetary ecosystem (López-Corona & Magallanes-Guijón, 2020).


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Fig. 2: Basic characteristics of the systems in terms of antifragility, which is the property of a system to respond convexly to disturbances or variability. (AC) are examples of fragile, robust / resistant and antifragile systems, respectively; (DF) are examples of profile responses to shocks; (JL) are examples of typical probability distributions; and (MO) are the characteristic values ​​obtained with the metric based on the change in complexity. Taken from


Burger JR, Allen CD, Brown JH, Burnside WR, Davidson AD, Fristoe TS, et al. The Macroecology of Sustainability. PLoS Biology. 2012; 10 (6): e1001345. Pmid: 22723741

Cocchi L, Gollo LL, Zalesky A, Breakspear M. Criticality in the brain: A synthesis of neurobiology, models and cognition; 2017

Equihua M, Espinosa Aldama M, Gershenson C, López-Corona O, Munguía M, Pérez-Maqueo O, Ramírez-Carrillo E. 2020. Ecosystem antifragility: beyond integrity and resilience. PeerJ 8: e8533

Fossion, R., Rivera, AL, & Estañol, B. (2018). A physicist’s view of homeostasis: how time series of continuous monitoring reflect the function of physiological variables in regulatory mechanisms. Physiological measurement39(8), 084007.

Goldberger AL, Peng CK, Lipsitz LA. What is physiologic complexity and how does it change with aging and disease ?; 2002.

Kiyono K, Struzik ZR, Aoyagi N, Togo F, Yamamoto Y. Phase transition in a healthy human heart rate. Physical review letters. 2005; 95 (5): 58101.

López-Corona, O, Elvia Ramírez-Carrillo and Gustavo Magallanes-Guijón (2019). The rise of the technobionts: toward a new ontology to understand current planetary crisis. RESEARCHERS.ONE,

López-Corona, O. and Magallanes-Guijón, G .: ESD Ideas: It is not an Anthropocene; it is really the Technocene: names matter in decision making under Planetary Crisis, Earth Syst. Dynam. Discuss., Https://, in review, 2019.

Nassim Nicholas Taleb (2020). Statistical Consequences of Fat Tails: Real World Preasymptotics, Epistemology, and Applications. RESEARCHERS.ONE,

Taleb, NN (2012). Antifragile: Things that gain from disorder (Vol. 3). Random House Incorporated.

O’Brien A, Townsend K, Hale R, Sharley D, Pettigrove V. How is ecosystem health defined and measured? A critical review of freshwater and estuarine studies. Ecological Indicators. 2016; 69: 722–729.

Ramírez-Carrillo E, López-Corona O, Toledo-Roy JC, Lovett JC, de León-González F, Osorio-Olvera L, et al. (2018) Assessing sustainability in North America’s ecosystems using criticality and information theory. PLoS ONE 13 (7): e0200382.

Rapport DJ, Costanza R, McMichael AJ. Assessing ecosystem health. Trends in ecology & evolution. 1998; 13 (10): 397–402.

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Publications full list on Google Scholar