Driven by the global discussion about global climate change and adaptation, CMM has generated during the last decade, through different projects and national and international associations, a corpus of knowledge and scientific questions that motivate many of the actions we develop today. In all these questions, the use of mathematics in interdisciplinary projects plays a fundamental role, as the complexity of the problems relating biodiversity and climate imposes the need to introduce and develop novel mathematical techniques in order to understand them. Challenges in this area require combining areas of expertise ranging from PDEs to data analysis. We divide our efforts in two dimensions, which are intimately related.
Biodiversity and its environment
Mathematical Systems Biology was born as a response to the analysis of massive and heterogeneous data in the era of omics sciences. A fundamental current challenge is to understand causality, that is, to establish chains of implications determining a biological process from data. Our proposal aims to develop methods combining machine learning, bioinformatics, dynamical systems and mathematical modeling to analyze massive data about microbial diversity in extreme environments efficiently. Among other themes, we work on identifying environmental niches (in particular those modulated by temperature) directly from data, and on quantitatively predicting changes in them from environmental changes. The availability of genetic material enable to tackle questions that have always surrounded the theory, many of them coming from ecology and biodiversity. In particular: (i) Why are species found together, forming interacting sets in a given environment? This is the long-standing question regarding what drives community assembly; and (ii) How do communities evolve following changes in their environments? To test our methods, we are inspired by data collected from two sources. The first one is the Atacama Desert, which provides a unique opportunity to test to what extent microbial communities are resistant to strong environmental gradients and what are the drivers of change. The second is data from the different TARA-Océan expeditions from the last ten years, in the context of the CNRS Federation GO-SEE project of which we are part since 2018. In this regard, we co-coordinate the expedition TARA-Mission Microbiome 2021-2023 in its Chilean trajectory (program Ceodos). This effort is complemented with the recently attributed project OcéanIA, to be developed with INRIA-Chile and other French institutions. Other applications concern the study of environmental changes in the context of new human diseases and new ideas in Smart Agro.
More information: Mathomics website
Climate extremes and social-physical systems
The most noticeable and profound manifestation of anthropogenic climate impact in human society and natural systems are the changes in frequency and intensity of extreme climate events. This refers not only to the evident changes in weather variables such as temperature extremes or intense precipitation events, but also to more complex event-driven effects: droughts, higher frequency of floods, heat waves, forest fires, climate-induced extinctions, emergence and redistribution of species/diseases, and the corresponding economic and social losses. We use sophisticated mathematical dynamical systems methods for analyzing climate extremes and the so-called tipping points for a more robust detection, attribution and sensitivity of causal links between climate forcing and observed responses. Validation comes from available data in a complementary effort with other research actors in our region. These are: (i) the study of regional paleoclimate data using immersed topological data analysis; (ii) data assimilation and model-based detection and attribution from the development of dynamical social-physical climate systems; and (iii) data-PDE driven machine learning methods to enhance quality and resolution of atmospheric/ocean distributed signals. These topics allow for developing new models and algorithms for analyzing extreme events in the past and present climate and the introduction of modern mathematical and simulation tools for the geographical and temporal distribution of climate-driven propagation of climate extremes.