Individual-based modelling of carbon and nitrogen dynamics in soils: Parameterization and sensitivity analysis of microbial components

Abstract

The fate of soil carbon and nitrogen compounds in soils in response to climate change is currently the object of significant research. In particular, there is much interest in the development of a new generation of micro-scale models of soil ecosystems processes. Crucial to the elaboration of such models is the ability to describe the growth and metabolism of small numbers of individual microorganisms, distributed in a highly heterogeneous environment. In this context, the key objective of the research described in this article was to further develop an individual-based soil organic matter model, INDISIM-SOM, first proposed a few years ago, and to assess its performance with a broader experimental data set than previously considered. INDISIM-SOM models the dynamics and evolution of carbon and nitrogen associated with organic matter in soils. The model involves a number of state variables and parameters related to soil organic matter and microbial activity, including growth and decay of microbial biomass, temporal evolutions of easily hydrolysable N, mineral N in ammonium and nitrate, CO₂ and O₂. The present article concentrates on the biotic components of the model. Simulation results demonstrate that the model can be calibrated to provide good fit to experimental data from laboratory incubation experiments performed on three different types of Mediterranean soils. In addition, analysis of the sensitivity toward its biotic parameters shows that the model is far more sensitive to some parameters, i.e., the microbial maintenance energy and the probability of random microbial death, than to others. These results suggest that, in the future, research should focus on securing better measurements of these parameters, on environmental determinants of the switch from active to dormant states, and on the causes of random cell death in soil ecosystems.

Introduction

In the last few years, a number of critical reviews of the literature have highlighted the fact that current models of C and N dynamics in soils fail to reproduce observed measurements in a wide range of situations in which the temperature, the hydrological regime of soils, or both, vary significantly (Kirschbaum, 2006, Baveye, 2007, Gras et al., 2010). One perspective on this poor performance of models is that they are not describing processes at an appropriate scale, or at least do not contain upscaled information that is appropriate to satisfactorily account for the macroscopic emergence of microheterogeneous processes. From that viewpoint, a novel type of mathematical model is needed, which combines a pore-scale description of water and solute transport (e.g., via the Lattice-Boltzmann method), with a detailed account of microbial growth and metabolism.

A difficulty in trying to combine these two components is that the type of unstructured, population-level biokinetic equation (like Tessier's or Monod's) traditionally used to describe microbial growth in soils (e.g., Baveye and Valocchi, 1989, Seki et al., 2004, Thullner and Baveye, 2008) is not in principle applicable to the generally limited numbers of bacteria present in small pores. Therefore a different kind of microbial growth kinetic model is required, which accounts statistically for behavioural differences that may exist among individual microorganisms in a soil pore. Models with that scope have been the object of considerable research in general microbiology and population biology in the last decade (Bousquet and Le Page, 2004). In particular, individual-based models (IBMs) have received a lot of attention and met with considerable success in the description of microbial growth and metabolism under a wide range of conditions (Grimm, 1999, Ferrer et al., 2008, Prats et al., 2008, Prats et al., 2010, Hellweger and Bucci, 2009, Ginovart et al., 2011).

The IBM INDISIM-SOM stems from an earlier model called INDISIM (for INdividual DIscrete SIMulations) and described in detail by Ginovart et al. (2002). INDISIM resulted from the merging of a discrete approach to ecosystems through individual-based modelling with the formalism used to model molecular dynamics in fluids (Ferrer et al., 2008). In a nutshell, INDISIM settles and controls a group of microbial cells in a discrete space—a regular lattice consisting of a set of spatial units, subjected to appropriate boundary conditions. Then, INDISIM models the global evolution of the group of microbial cells by determining the individual behaviour of each bacterium and spatial unit in discrete events (time steps). The model uses stochastic rules and allows variability within the microbial population. Ginovart et al. (2005) were the first to adopt the IBM perspective to describe the fate of soil organic matter (SOM) with the model called INDISIM-SOM, describing in detail the many abiotic and biotic reactions controlling the dynamics of C and N. INDISIM-SOM encompasses a wide range of physical, chemical, and microbiological processes that regulate the short-term dynamics of soil C and N, namely decomposition, mineralization or immobilization of C and N, nitrification, and humification. In particular, in terms of microbiology, the model describes explicitly the uptake, metabolism, reproduction, death and lysis of microbial cells belonging to two broad metabolic groups, heterotrophic microorganisms (ammonifiers or decomposers), and nitrifying bacteria or autotrophs. Further details on the microbiological component of the model are provided by Ginovart et al. (2005) and Gras and Ginovart, 2004, Gras and Ginovart, 2006.

Since Ginovart et al.’s (Ginovart et al., 2005) first implementation of an IBM in connection with soil microorganisms, significant additional research has been done in the area. Knudsen et al. (2006) developed a model of the hyphal growth of a biocontrol fungus, in which records of spatial location and branching hierarchy are maintained for individual hyphal nodes, so that the entire spatial structure of a fungal colony (hyphal network) can be explicitly reconstructed at any time. Masse et al. (2007) developed an IBM to analyze the effect of the spatial distribution of organic matter and microbial decomposers on soil carbon and nitrogen dynamics. With this model, two scenarios were tested according to the degrees of clustering of organic matter and microorganisms. The results of simulations highlighted the effect of the ratio of accessible organic carbon to microbial carbon on the dynamics of microbial biomass and CO₂ release. This ratio was determined by the number of contacts between one object representing the microbial decomposers and the surrounding objects representing the labile or soluble organic substrates. More recently, Falconer et al. (2008) presented an IBM of the growth and propagation of fungal hyphae, and with this model, demonstrated that the spatial heterogeneity of the pore space in soils could affect the level of interaction of distinct fungal colonies.

In this general context, a primary objective of this article is to analyze in detail the calibration of the parameters of the microbial submodel of the current implementation of the INDISIM-SOM model (involving several new features and model components, compared to the original model), using a larger soil data set than that used by Ginovart et al. (2005), and to determine if the fit of model outputs to experimental data of C and N dynamics is satisfactory. Because of the large number of parameters involved, and clear conceptual differences among abiotic and biotic ones, the analysis is carried out here only for the biotic components of the model, related to heterotrophic and nitrifier microorganisms. A parallel treatment for the abiotic parameters is provided by Gras et al. (2010). A second objective of this article is to assess the sensitivity of the model toward its biotic parameters, specifically the C to N microbial biomass ratio for the heterotrophs, maintenance energy and death probability for the two prototypes of microorganisms, and the ratio of nitrifier C to microbial C. Such a sensitivity analysis should prove particularly useful in the near future, in two different ways. The first will be when INDISIM-SOM will be integrated in a pore-scale, Lattice-Boltzmann model of water and solute transport in soils. A combined model of that sort is likely to be computationally demanding. Initial integration and calculations would be greatly facilitated if it turned out that, under some conditions, model predictions are far less sensitive to some components than to others. In this case, as a first approximation, a “lighter” version of INDISIM-SOM could be implemented, with only the most sensitive components, leaving the integration of the full model formulation to a later stage. In addition, and perhaps more importantly, by indicating which parameters of the model are most sensitive, the analysis carried out in the following suggests clearly where emphasis should be placed in experimental research.