Modeling biogeochemical processes of phosphorus for global food supply
Introduction
Despite its vital importance to all life forms and the global scale of its flows, no biogeochemical cycle model exists for phosphorus (P) to quantify the temporal and spatial patterns of its distribution on Earth. Yet, due to the small size of the known P-bearing rock deposits (Jasinski, 2009), concerns are rising about future provision of mineral P fertilizer to agro-ecosystems. At the same time as these concerns are voiced, tens of millions of tons of P harmfully make their way to aquatic systems annually (Liu et al., 2004). While in most ecosystems, P cycles several hundred times from the soil to the biomass to the zoomass back to the soil before finding its way to the aquatic systems (Smil, 2000), most human-managed systems are much less efficient as P cycles rarely more than once. P is a constitutive element of basic cellular processes and structures and as such is a non-substitutable ingredient to plant growth. Finally, P is distributed via global markets, traded in the form of food and mineral, the latter being supplied only by a handful of countries which hold more than ninety percent of the known world terrestrial P-bearing rock reserves (Cordell et al., 2009). In a precautionary perspective, we should investigate the vulnerabilities for global food production that are associated with the usage patterns sketched above. We should also examine the impact on food production, cost and pollution of different scenarios of P supply – from the current extractive model to a potential closed cycle. To achieve this, we need a quantitative understanding of P stores and flows and their dynamics on a global scale.
As a first step towards quantifying the P cycle, the objective of this paper is to present a model of P flows through arable soils and the resulting effect on crop yields. This model is based on substance-flow analyses proposed by other authors (e.g. Liu et al., 2004) but it is dynamic. We seek to develop a simple probabilistic formulation that can be applied at different scales. We argue for a simple solution to the scaling of the complex dynamics of P cycling in soils, usually handled by deterministic models that cannot easily be scaled because of the site-specific parameterization needed to implement them (e.g. Jones et al., 1984). One application of our model will be to simulate the evolution of food production when suppressing the inflow of mineral P fertilizer, as a way to evaluate our level of dependence on P-bearing rocks. The model will have wider applications: for example, to quantify the amount of P fertilizer necessary to transition to a long-term steady-state closed-loop cycle. This paper may contribute to methodologies for integrating LCA and biogeochemistry for the successful management of biogeochemical-cycles.
Section snippets
Formalizing how P cycles through the “human ecosystem”
Evaluating the impact on crop yields is one way to translate different states of the P cycle in terms of units that matter to society. Correspondingly, we built a simple model of P cycling whose output variable is total food production (Fig. 1). The boundaries drawn in Fig. 1 represent a particular agricultural region, typically composed of both cropland and grassland. Although Fig. 1 represents a large number of pathways, the dynamics can be summarized as follows:where y
Discussion: From simple toy-model applications to information-rich simulations
The first application of Eqs. (5), (6), (7) is as a toy model: after making meaningful simplifying assumptions, it can help us answer important questions. Indeed, in the absence of appropriate data on recycling, runoff and erosion fluxes we can meaningfully replace the true values by hypothetical values reflecting management scenarios.
Conclusion
The model presented in this paper suggests how to integrate natural processes with human-managed flows to investigate the long-term consequences, in terms of food production, of various scenarios of P management. Furthermore, it proposes a solution to the challenge of capturing the large-scale effect of multiple micro-scale soil cycling processes. However, this model is only a first step towards being able to assess the sustainability of the P cycle. Indeed, implementation of the model at
Acknowledgments
Thanks to Astrid Oberson, Daniel Lang, Justus Gallati and Julia Brändle for valuable discussions as well as to the Plant Nutrition Group of the ETH for constructive feedbacks in seminar. Thanks to Andrew Sharpley for sharing of data.
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