The Return of von Liebig's “Law of the Minimum”

Paris, Quirino

doi:10.2134/agronj1992.00021962008400060025x

Cited by 60 publications

(31 citation statements)

References 8 publications

(14 reference statements)

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“…to the more complex (e.g., Fisher et al 2008), without a concomitant increase in accuracy. One reason that simple models work as well as multifactor models is that plant productivity (and transpiration) tend to be limited by a single factor at a given time and place (Liebig's law of the minimum) (Paris 1992), although at the community level co-limiting factor might operate (Danger et al 2008).…”

Section: Limitations Of VI Methodsmentioning

confidence: 99%

Vegetation Index Methods for Estimating Evapotranspiration by Remote Sensing

2010

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Evapotranspiration (ET) is the largest term after precipitation in terrestrial water budgets. Accurate estimates of ET are needed for numerous agricultural and natural resource management tasks and to project changes in hydrological cycles due to potential climate change. We explore recent methods that combine vegetation indices (VI) from satellites with ground measurements of actual ET (ET a ) and meteorological data to project ET a over a wide range of biome types and scales of measurement, from local to global estimates. The majority of these use time-series imagery from the Moderate Resolution Imaging Spectrometer on the Terra satellite to project ET over seasons and years. The review explores the theoretical basis for the methods, the types of ancillary data needed, and their accuracy and limitations. Coefficients of determination between modeled ET a and measured ET a are in the range of 0.45-0.95, and root mean square errors are in the range of 10-30% of mean ET a values across biomes, similar to methods that use thermal infrared bands to estimate ET a and within the range of accuracy of the ground measurements by which they are calibrated or validated. The advent of frequent-return satellites such as Terra and planed replacement platforms, and the increasing number of moisture and carbon flux tower sites over the globe, have made these methods feasible. Examples of operational

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Section: Limitations Of VI Methodsmentioning

confidence: 99%

Vegetation Index Methods for Estimating Evapotranspiration by Remote Sensing

2010

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“…The final criterion for choosing the Mitscherlich functional form is based on a theoretical viewpoint. It has been shown that this functional form accords best with the von Liebig hypothesis known as the "Law of the Minimum" (Paris 1992a, b, Sumelius 1993 1 .…”

Section: Results and Discussion N-response For Maizementioning

confidence: 56%

Marginal abatement costs for reducing leaching of nitrates in Croatian agriculture

Sumelius¹,

Mešić²,

Grgić³

2008

AFSci

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The aim of this paper is to estimate marginal abatement costs (MAC) of N-fertiliser tax policies which aim to prevent NO 3 levels from rising. Estimates of MAC provide information on how large reductions in Nfertilisation rates should be before other measures are considered. Based on N-response experiments from Croatian field trials with maize, N-response curves were estimated and profit maximising N-doses were derived. Values of NO 3 -N concentration in lysimeter water from the same treatments were used to estimate an NO 3 -leaching function. A sample of 20 Croatian family farms was used to obtain records of producer and input prices as well as actual N-doses. Abatement costs and MAC for an N-tax, a product tax and an Nquota were estimated. The MAC for all the instruments are non-constant and increase at an accelerating rate. The MAC for N-taxes are positive for N-taxes lower than 60%, indicating a net return to society. Reduction rates in fertilisation up to this level should be achieved before considering governmental support for other measures. The N-tax has the lowest abatement cost and the lowest MAC for a particular level of reduction while the N-quota has a lower MAC than the product tax when total reduction levels are below 20 mg NO 3 l -1 .

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“…13 where we can observe a high number of secondary users as compared to primary users at the equilibrium position. These results are analogous with the law of minimum, where the less resource demanding species can grow and the equilibrium position is determined based on the most scarcest resource [19]. Figure 14 shows the region of mutual co-existence for both primary and secondary users, and the region where one type of users is competitively excluded from the bandwidth resource competition.…”

Section: The Varying Bandwidth Cooperative Cognitive Modelmentioning

confidence: 65%

“…The fitness is directly proportional to the maximum percapita growth rate of any species. According to [19], the fitness function can be described by the multiplication of each resource response to each other and the growth rate. So the fitness of primary and secondary users in term of the law of minimum, can be described as follow:…”

Section: Fitness Functionmentioning

confidence: 99%

Bandwidth Resource Competition in Cooperative Cognitive Wireless Communications

Nazir

Rajatheva

2011

Int J Wireless Inf Networks

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In this paper, we analyze the behavior of Cooperative Cognitive Wireless nodes for the bandwidth resource competition using the ecological models of mutualism. We transform our cooperative cognitive wireless communication (CCWC) system as mutually interacting species. The two types of species are primary and secondary users. The Primary users have under-utilized licensed bandwidth to be shared with the secondary users. On the other hand, secondary users are willing to behave as possible relays for cognitive primary users, in exchange of shared licensed bandwidth. So, instead of pricing model, the proposed system is analyzed with the traditional barter system (exchange of commodities). We analyzed our proposed system based on three ecological models. Our first model is based on the coalitional form of Lotka-Volterra equations, where predator-prey role of mobile nodes are replaced with cooperation as in symbiosis. The second model deals with the population dynamism of strategically interacting partner for conflicting bandwidth resource. The third model adds the dynamism for the varying amount of bandwidth to be shared among the individual mobile users. For each type, a mathematical model is derived and then simulated for the equilibrium position analysis. The obtained results show that sharing of bandwidth resource is essential for the existence of CCWC systems.

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The Return of von Liebig's “Law of the Minimum”

Cited by 60 publications

References 8 publications

Vegetation Index Methods for Estimating Evapotranspiration by Remote Sensing

Vegetation Index Methods for Estimating Evapotranspiration by Remote Sensing

Marginal abatement costs for reducing leaching of nitrates in Croatian agriculture

Bandwidth Resource Competition in Cooperative Cognitive Wireless Communications

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