ArticleEcological applications : a publication of the Ecological Society of America2021
Finding Liebig's law of the minimum.
Article in Ecological applications : a publication of the Ecological Society of America, 2021. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 15 papers.
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Who cites it
15 citing papers in PubMed.
- Article
- Applying Liebig's law of the minimum for variable rate soybean seeding based on CEC-nutrient fertility index.Scientific reports · 2026Article
- Global constraint principle for microbial growth laws.Proceedings of the National Academy of Sciences of the United States of America · 2025Article
- Exploring the crop suitability of first-contact tribal lands in the eastern United States: impacts of past and near-future climate conditions.Scientific reports · 2025Article
- Solar Radiation Drives the Plant Species Distribution in Urban Built-Up Areas.Plants (Basel, Switzerland) · 2025Article
- Multiple Dimensions Define Thresholds for Population Resilience of the Eastern Oyster,Ecology and evolution · 2025Article
- Nutrient colimitation is a quantitative, dynamic property of microbial populations.Proceedings of the National Academy of Sciences of the United States of America · 2024Article
- A New Proposal for Soybean Plant Stand: Variation Based on the Law of the Minimum.Plants (Basel, Switzerland) · 2024Article
- The Evolutionary Transition of the RNA World to Obcells to Cellular-Based Life.Journal of molecular evolution · 2024Article
- Understanding stoichiometric constraints on growth using resource use efficiency imbalances.Proceedings of the National Academy of Sciences of the United States of America · 2024Article
- Adaptation Strategies of Seedling Root Response to Nitrogen and Phosphorus Addition.Plants (Basel, Switzerland) · 2024Article
- The space-for-time gambit fails a robust test.Proceedings of the National Academy of Sciences of the United States of America · 2024Article
- Article
- Interacting Bioenergetic and Stoichiometric Controls on Microbial Growth.Frontiers in microbiology · 2022Article
- Finding Liebig's law of the minimum.Ecological applications : a publication of the Ecological Society of America · 2021Article
Corrections and comments
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Authors and funding
2 authors.
Funding
No grant is acknowledged in the PubMed record.
Abstract
Liebig's law of the minimum (LLM) is often used to interpret empirical biological growth data and model multiple substrates co-limited growth. However, its mechanistic foundation is rarely discussed, even though its validity has been questioned since its introduction in the 1820s. Here we first show that LLM is a crude approximation of the law of mass action, the state of art theory of biochemical reactions, and the LLM model is less accurate than two other approximations of the law of mass action: the synthesizing unit model and the additive model. We corroborate this conclusion using empirical data sets of algae and plants grown under two co-limiting substrates. Based on our analysis, we show that when growth is modeled directly as a function of substrate uptake, the LLM model improperly restricts the organism to be of fixed elemental stoichiometry, making it incapable of consistently resolving biological adaptation, ecological evolution, and community assembly. When growth is modeled as a function of the cellular nutrient quota, the LLM model may obtain good results at the risk of incorrect model parameters as compared to those inferred from the more accurate synthesizing unit model. However, biogeochemical models that implement these three formulations are needed to evaluate which formulation is acceptably accurate and their impacts on predicted long-term ecosystem dynamics. In particular, studies are needed that explore the extent to which parameter calibration can rescue model performance when the mechanistic representation of a biogeochemical process is known to be deficient.
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