Nonlinearities and Alternative States of Biogeochemical Cycling in Terrestrial Ecosystems

• Applicant: Dr. Carlos A. Sierra
• Subject Area: Ecology and Biodiversity of Plants and Ecosystems
• Term: from 2014 to 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 257784447

• Final Report Year: 2021

Final Report Abstract

The Theoretical Ecosystem Ecology Group of the Max Planck Institute for Biogeochemistry, funded by the DFG Emmy Noether Programme, was established in 2015 with the aim to study ecosystems using the mathematical theory of dynamical systems, and explore potential critical transitions in the timescales of element cycling. The group made significant progress on these two topics, 1) establishing and formalizing a general mathematical representation of ecosystems as compartmental dynamical systems, and 2) developing general mathematical formulas for timescales of element cycling, further expanding the theory of ages and transit times in compartmental systems. On the topic of mathematical generalization, the group has shown in a series of publications that a) biogeochemical cycling in ecosystems can be reduced to a set of six basic ecological principles, which results in a general mathematical representation of ecosystems as non-autonomous nonlinear compartmental systems, b) the mathematical properties and overall behavior of different ecosystem models are directly linked to the properties of linearity and autonomy. Stability properties for linear autonomous systems are well defined and in these conditions tipping points cannot occur. For nonlinear systems tipping points can only occur between oscillatory and non-oscillatory systems. Other type of non-stable tipping points are not possible because the system would violate the principle of mass conservation. On the topic of timescales, we have made important progress in d) developing formulas for the computation of age and transit time distributions for compartmental systems, and e) applying these formulas to problems of carbon allocation in vegetation, and studying the persistence of soil organic matter. Another important contribution was f) obtaining a general characteristic of the terrestrial carbon cycle: carbon fixed during photosynthesis passes very quickly through ecosystems, staying only a few years or maybe some decades, but some carbon stays for very long times. Therefore the age of carbon stored in terrestrial ecosystems can be centuries years old, and is in general much older than the transit time. This basic understanding of the carbon cycle in ecosystems, allowed us to g) develop new concepts to quantify carbon sequestration and the climate benefit of carbon sequestration. The group made innovative theoretical work in ecosystem science, and this work is expected to lead to new advances in the understanding of terrestrial ecosystems, how they respond to changes in climate, and how can humans manage ecosystems to mitigate climate change.

Publications

• (2015). A general mathematical framework for representing soil organic matter dynamics. Ecological Monographs, 85:505–524
  Sierra, C. A. and Müller, M.
  
• (2017). Application of input to state stability to reservoir models. Theoretical Ecology, 10:451–475
  Müller, M. and Sierra, C. A.
  
• (2017). The muddle of ages, turnover, transit, and residence times in the carbon cycle. Global Change Biology, 23(5):1763–1773
  Sierra, C. A., Müller, M., Metzler, H., Manzoni, S., and Trumbore, S. E.
  
• (2018). Ages and transit times as important diagnostics of model performance for predicting carbon dynamics in terrestrial vegetation models. Biogeosciences, 15(5):1607–1625
  Ceballos-Nunez, V., Richardson, A. D., and Sierra, C. A.
  
• (2018). Linear autonomous compartmental models as continuoustime Markov chains: Transit-time and age distributions. Mathematical Geosciences, 50(1):1– 34
  Metzler, H. and Sierra, C. A.
  
• (2018). Soil organic matter persistence as a stochastic process: Age and transit time distributions of carbon in soils. Global Biogeochemical Cycles, 32(10):1574–1588
  Sierra, C. A., Hoyt, A. M., He, Y., and Trumbore, S. E.
  
• (2018). Transit-time and age distributions for nonlinear time-dependent compartmental systems. Proceedings of the National Academy of Sciences, 115(6):1150–1155
  Metzler, H., Müller, M., and Sierra, C. A.
  
• (2020). Mathematical reconstruction of land carbon models from their numerical output: Computing soil radiocarbon from C dynamics. Journal of Advances in Modeling Earth Systems, 12(1):e2019MS001776
  Metzler, H., Zhu, Q., Riley, W., Hoyt, A., Müller, M., and Sierra, C. A.
  
• (2020). Towards better representations of carbon allocation in vegetation: a conceptual framework and mathematical tool. Theoretical Ecology, 13(3):317–332
  Ceballos-Nunez, V., Müller, M., and Sierra, C. A.
  
• (2021). The climate benefit of carbon sequestration. Biogeosciences
  Sierra, C. A., Crow, S. E., Heimann, M., Metzler, H., and Schulze, E.-D.