Liebig's Law of the Minimum in Relation to General Biological Problems

Hooker, Henry Daggett

doi:10.1126/science.46.1183.197

Cited by 28 publications

(11 citation statements)

References 2 publications

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“…In addition to previously studied nonlinear tracking models we propose a stochastic version of Liebig's law of the minimum (SLLM) (Hooker, 1917; Farrior et al, 2013) (Table 1). This may reduce the PEA for populations that are limited by multiple limiting resources by changing the limiting resource each year, breaking the autocorrelation that would be present in a single limiting resource.…”

Section: Introductionmentioning

confidence: 99%

An updated perspective on the role of environmental autocorrelation in animal populations

et al. 2015

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Ecological theory predicts that the presence of temporal autocorrelation in environments can considerably affect population extinction risk. However, empirical estimates of autocorrelation values in animal populations have not decoupled intrinsic growth and density feedback processes from environmental autocorrelation. In this study we first discuss how the autocorrelation present in environmental covariates can be reduced through nonlinear interactions or by interactions with multiple limiting resources. We then estimated the degree of environmental autocorrelation present in the Global Population Dynamics Database using a robust, model-based approach. Our empirical results indicate that time series of animal populations are affected by low levels of environmental autocorrelation, a result consistent with predictions from our theoretical models. Claims supporting the importance of autocorrelated environments have been largely based on indirect empirical measures and theoretical models seldom anchored in realistic assumptions. It is likely that a more nuanced understanding of the effects of autocorrelated environments is necessary to reconcile our conclusions with previous theory. We anticipate that our findings and other recent results will lead to improvements in understanding how to incorporate fluctuating environments into population risk assessments.

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Section: Introductionmentioning

confidence: 99%

An updated perspective on the role of environmental autocorrelation in animal populations

et al. 2015

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“…Finally, a comprehensive evaluation model was built based on the geometric mean method of the unique area and arc length to synthetically and simultaneously analyze the functionality and inhomogeneity of the evaluation objects. [22], a scientific evaluation system should not only accurately describe the functional size of the evaluation object from all aspects but also objectively reflect the inhomogeneity between the indices. In other words, a scientific and reasonable evaluation method involves the unification of the functionality and inhomogeneity of the evaluation system.…”

Section: New Methods Based On Unit Circlementioning

confidence: 99%

“…According to the Leaky Bucket Theory and Liebig's Law of the Minimum [22], that is, the performance of an evaluation system mainly depends on its minimum index value. If the indicators of two evaluation objects take values of (1,2,3) and (2,2,2), then the former object has a relatively weaker score than the latter although they have the same total scores [23].…”

Section: Introductionmentioning

confidence: 99%

A Novel Comprehensive Evaluation Method of Forest State Based on Unit Circle

Zhang¹,

Gao²,

Zhang³

et al. 2018

Forests

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Comprehensive evaluation of forest state is the precondition and critical step for forest management. To solve the problem that the radar plot and unit circle only focus on the value of each the evaluation index, this paper proposes a novel method for comprehensively and simultaneously evaluating the functionality and inhomogeneity of forest state based on the modified unit circle method. We evaluated the forest state of the Quercus aliena BL. var. acuteserrata Maxim. ex Wenz. broad-leaved mixed forest in the Xiaolong Mountains Forest Area of Gansu Province and the Pinus koraiensis Sieb. et Zucc. broad-leaved mixed forest in Jilin Province in China. According to the principle of comprehensive, scientific and operability, 10 evaluation indices on forest structure and vitality were selected to construct the evaluation indicator system. Each index was normalized based on the assignment method and ensured to be strictly positive based on reciprocal transformation method. The areas and arc length of the closed graph, formed by connecting every two adjacent indicators, in the radar plot and unit circle were extracted. Based on the isoperimetric theorem (isoperimetric inequality), a comprehensive evaluation model was constructed. Compared with radar chart and unit circle method, each index in the newly proposed unit circle method is represented by an independent sector region, reflecting the contribution of the index to the overall evaluation result. Each index has the same relative importance weight, contributing to the estimation the relative sizes of each aspect of forest state. The unique area and arc length of the closed graph help summarize the overall performance with a global score. The expression effect of improved unit circle has been enhanced, and as an English proverb put it, “A picture is worth a thousand words.” The new proposed method simultaneously evaluates the functionality and inhomogeneity of the forest state and it is a powerful tool for the diagnosis of forest state problems and the decision-making of forest management.

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“…Two types of nutrient addition scenarios were considered: if nitrogen were limiting, and if phosphorus were limiting. Dosing increments for each scenario are listed in Table , where one nutrient was set at nonlimiting levels so the other could be evaluated ( sensu Liebig's Law; Hooker, ). This was done because different control strategies may be needed to address each nutrient in the future.…”

Section: Methodsmentioning

confidence: 99%

Model‐Based Nitrogen and Phosphorus (Nutrient) Criteria for Large Temperate Rivers: 2. Criteria Derivation

Suplee

Flynn

Chapra

2014

J American Water Resour Assoc

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Nitrogen and phosphorus criteria were developed for 233 km of the Yellowstone River, one of the first cases where a mechanistic model has been used to derive large river numeric nutrient criteria. A water quality model and a companion model which simulates lateral algal biomass across transects were used to simulate effects of increasing nutrients on five variables (dissolved oxygen, total organic carbon, total dissolved gas, pH, and benthic algal biomass in depths ≤1 m). Incremental increases in nutrients were evaluated relative to their impact on predefined thresholds for each variable; the first variable to exceed a threshold set the nutrient criteria. Simulations were made at a low flow, the 14Q5 (lowest average 14 consecutive day flow, July-September, recurring one in five years), which was derived using benthic algae growth curves and EPA guidance on excursion frequency. An extant climate dataset with an annual recurrence was used, and tributary water quality and flows were coincident with the river's 10 lowest flow years. The river had different sensitivities to nutrients longitudinally, pH being the most sensitive variable in the upstream reach and algal biomass in the lower. Model-based criteria for the Yellowstone River are as follows: between the Bighorn and Powder river confluences, 55 lg TP/l and 655 lg TN/l; from the Powder River confluence to Montana state line, 95 lg TP/l and 815 lg TN/l. Pros and cons of using steady-state models to derive river nutrient criteria are discussed.(KEY TERMS: algae; large river; nutrients; water quality criteria; model; environmental impacts; environmental regulations; QUAL2K; Yellowstone River; eutrophication.) Suplee, Michael W., Kyle F. Flynn, and Steven C. Chapra, 2015. Model-Based Nitrogen and Phosphorus (Nutrient) Criteria for Large Temperate Rivers: 2. Criteria Derivation.

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Liebig's Law of the Minimum in Relation to General Biological Problems

Abstract: W. GOODSPEED 219 MSS. intended for publication and books, etc., intended Tor review should be sent to Professor J. McKeen Cattell, Garrisonon-Hudson. N. Y.

Cited by 28 publications

References 2 publications

An updated perspective on the role of environmental autocorrelation in animal populations

An updated perspective on the role of environmental autocorrelation in animal populations

A Novel Comprehensive Evaluation Method of Forest State Based on Unit Circle

Model‐Based Nitrogen and Phosphorus (Nutrient) Criteria for Large Temperate Rivers: 2. Criteria Derivation

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