Soil organic carbon (SOC) represents nearly 80% of the total C stored in terrestrial systems. Therefore, understanding its dynamics and response to human actions is crucial for developing effective climate change mitigation strategies. Such dynamics depend on the C coming into the soil through photosynthesis and the C leaving the soil through decomposition. The easiest way to maximize soil C through management is to increase C inputs to the soil, and there are several possible ways. For example, we can plant crops with deeper roots, use trees or other perennials in combination with annual crops, and so on. But all these agronomical approaches will need to be compared quantitatively in terms of their potential to increase C storage. We must accurately model an ecosystem's C balance and organic matter decomposition to do that.
At least in aerobic conditions, which we find in most soils globally, organic matter decomposition follows relatively simple kinetics over time, influenced mainly by temperature and soil water content which drive microbial activity. Although decomposition is a complex process with many biochemical steps, ecosystems tend naturally to maximize resource utilization efficiency, and the process usually follows its upper limits (the fundamental constraints of microbial growth). We can already describe most of the variation over time of soil C with a combination of relationships discovered long ago.
For example, the temperature limits to chemical reactions described by Svante Arrhenius already in 1889 are still in use in many models. The fundamental equation used by almost any SOC model was developed in the 1960's (when ecologists had no access to computers) and was just an application of an exponential decay function. That same function is still the theoretical foundation upon which most SOC decomposition models are built and still does a decent job.
This fundamental "law" of decomposition assumes that microbial biomass will always grow to saturate the available resources, limited by the speed at which organic matter can decompose over time. So the decomposition rate of organic matter at any time will only be defined by the amount of organic matter available and the proportion that can decompose in a specific unit of time. The latter is the decomposition rate, usually denoted as k. This defines a linear relationship: the decomposition flux is proportional to the mass of organic matter times its decomposition rate. This relationship emerges from a highly complex ecosystem with thousands of microbial species cooperating and competing.
Reality is more complex, and this relationship cannot describe all the variance of the process over time (although it comes pretty close). In the last two decades, the scientific community working on the problem started to focus on the limits of such a theory.
For example, the assumption that microbial growth is limited by a constant decomposition rate of organic matter implies that microbes cannot modify such a rate, but this is not always true. Experiments have shown that if we feed an energetic substrate to microbes, they can "invest" more metabolic energy in enzymes to modify the overall decomposition rate. Another assumption of linear decomposition is redundancy, the idea that all the functions needed for decomposition will always be present in the soil and expressed when needed, and the variation over time of microbial communities would not impact decomposition. But in some cases, microbial communities do matter. For example, in systems dominated by fungi, we recently realized that the microbial community's ecological succession has a noticeable impact on decomposition. And over short-term time scales, we find seasonal or even daily variations in decomposition that linear models cannot explain, possibly due to variations in microbial metabolism.
Questioning the linear decomposition assumption has led to experimenting with nonlinear decomposition models, where the decomposition rate or kinetic k is no longer constant but varies over time as a function of different variables.
These models are far more complex objects to deal with than linear ones and have different characteristics. While linear decomposition models always present one steady state, a nonlinear model can have none or multiple ones, making such states difficult, if not plainly impossible, to calculate. Small inexactness in the model calibration or the representation of some processes can have consequences amplified by the nonlinearities, leading to artifacts or unrealistic behavior. More briefly, they are wilder beasts than linear models and more challenging to tame.
The scientific debate in the field of SOC decomposition models is nowadays exciting, continuously oscillating between these two paradigms: linear or nonlinear decomposition. Both paradigms have pros and cons and are more suited to different purposes.
This lecture aims at highlighting, after briefly describing the field's history and the two paradigms, the virtues and limitations of each in different applications.