Dimensional analysis in ecology

Legendre, Pierre; Legendre, Louis

doi:10.1016/b978-0-444-53868-0.50003-4

Cited by 358 publications

(498 citation statements)

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“…Dimensional analysis has lots of intention in ecology studies [19][20][21]. The brief introduction on the theory and process of dimensional analysis are as the following: (3) When the system activity can be expressed by some functional relations, theorem Π can be derived based on the homogeneity conditions of dimension (only identical dimensions can be summed, subtracted or equaled ).…”

Section: B Methodologymentioning

confidence: 99%

Notice of Retraction: Application of dimensional analysis for carrying capacity assessment for cage fish farm in Guangdong coastal waters, China

Huang¹,

Jia²,

Genxi³

et al. 2010

2010 Sixth International Conference on Natural Computation

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A critical independent non-dimension power which control dynamic balance of oxygen in cage fish farming waters is derived from 6 variables of Dissolved oxygen (DO), Saturation of DO, Characteristic depth of fish, Oxygen restoring coefficient and Diffusion coefficient of O 2 based on the method of dimensional analysis. Based on the critical independent non-dimension power, a simple carrying capacity assessing model for cage fish farming is developed. Applying this model in cage fish farms in Zhelin Bay and Baisha Bay in Guangdong coast, China, and the results show that theoretic carrying capacity in the two farm in extreme condition are about 10,791 tones and 329 tones, respectively. While the actual carrying capacity estimated based on data from sampling inquiry to fish men in Zhelin Bay was 14,600 tonnes in August 2008, exceeded 3,089 tonnes of the theoretic carrying capacity value and equal to 12,038 cultured cages, and that actual carrying capacity in Baisha Bay was 370 tonnes in September 2007, exceeded 41 tonnes of the theoretic carrying capacity value and equal to 410 cultured cages. It is obvious that marine fish culture cages are both over density in Zhelin Bay and Baisha Bay.

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Section: B Methodologymentioning

confidence: 99%

Notice of Retraction: Application of dimensional analysis for carrying capacity assessment for cage fish farm in Guangdong coastal waters, China

Huang¹,

Jia²,

Genxi³

et al. 2010

2010 Sixth International Conference on Natural Computation

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“…We first appeal to dimensional analysis 27 . From (2) we see that predation losses C i have the dimensions of biomass density over time, e.g.…”

Section: Functional Responsementioning

confidence: 99%

A macro-ecological approach to predators’ functional response

Barbier

Wojcik

Loreau

2019

Preprint

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Predation often deviates from the law of mass action: many micro-and meso-scale experiments have shown that consumption saturates with resource abundance, and decreases due to interference between consumers. But does this observation hold at macro-ecological scales, spanning many species and orders of magnitude in biomass? If so, what are its consequences for large-scale ecological patterns and dynamics?We perform a meta-analysis of predator-prey pairs of mammals, birds and reptiles, and show that predation losses appear to increase, not as the product of predator and prey densities following the Lotka-Volterra (mass action) model, but rather as the square root of that product. This suggests a phenomenological power-law expression of the effective cross-ecosystem functional response. We consider the possibility that the same power-law holds dynamically within an ecosystem, and explore its consequences in a simple food chain model. The empirical exponents fall close to the boundary between regimes of donor and consumer limitation. Exponents on this boundary are singular in multiple ways. First, they maximize predator abundance and some stability metrics. Second, they create proportionality relations between biomass and productivity, both within and between trophic levels. These intuitive relations do not hold in general in mass action models, but are widely observed empirically.These results provide evidence of mechanisms limiting predation across multiple ecological scales. Some of this evidence was previously associated with donor control, but we show that it supports a wider range of possibilities, including forms of consumer control. Limiting consumption counter-intuitively allows larger populations. It is worthwhile to reconsider whether the observed functional response arises from microscopic mechanisms and constraints, or could hint at selective pressure at the population level.

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“…The Mantel statistic is where d is the distance class from one of the MDDS; z ij is the distance between each pair i and j from the other MDDS; w ij is a weight for the pair: typically 1 if z ij is in d and 0 if it is not. The number of classes d is calculated with the Sturges rule [ 29 ]: where m is the number of distances in the upper-triangular binary model matrix.…”

Section: A Appendix: Multilevel and Multivariate Analyses With The mentioning

confidence: 99%

“…One example of multilevel modeling methods is mixed-effects regression [ 25 – 28 ], which can be implemented to detrend dendroclimatic data by considering random effects from ecological factors. Another example is dissimilarity analysis [ 29 – 32 ], which can be used to compare and organize dendroclimatic fluctuations into common ecological-factor levels. However, the implementation of these methods using statistical environments requires dendroclimatic inputs stored in special formats [ 33 ] such as Multilevel Dendroclimatic Data Series (MDDS), or sequences of observations ordered according to spatial/temporal hierarchies which are the result of sampling schemes, with sample variability confined to ecological factors.…”

Section: Introductionmentioning

confidence: 99%

Multilevel analysis of dendroclimatic series with the R-package BIOdry

Lara

Bogino

Bravo³

2018

PLoS ONE

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The R-package allows to model and compare fluctuations of Tree-ring Width (TRW) and climate, or dendroclimatic fluctuations, while accounting for source variability. The package eases multilevel modeling and multivariate comparison in dendroclimatic analysis using the and packages, respectively. For implementing such libraries, the in-package algorithms transform the dendroclimatic fluctuations into Multilevel Dendroclimatic Data Series and maintain categorical variables and time units in the outputs. The dendroclimatic modeling is developed with two functions: and . The first function binds core-level cumulative TRWs to the processed data sets and subtracts trends in TRWs by fitting multilevel log-linear growth formulas or multilevel linear formulas. can also model within-group fluctuations in dendroclimatic variables other than tree-radial increments such as aridity indices or allometric components of tree growth: e.g. diameters at breast height over bark, tree basal areas, total tree biomass, among other. The second function compares fluctuations in objects that share outermost categorical variable and annual records. Here, we use BIOdry to model dendroclimatic relationships in northern and east-central Spain to illustrate future users in the implementation of the package for modeling ecological relationships in space and time.

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Dimensional analysis in ecology

Cited by 358 publications

References 0 publications

Notice of Retraction: Application of dimensional analysis for carrying capacity assessment for cage fish farm in Guangdong coastal waters, China

Notice of Retraction: Application of dimensional analysis for carrying capacity assessment for cage fish farm in Guangdong coastal waters, China

A macro-ecological approach to predators’ functional response

Multilevel analysis of dendroclimatic series with the R-package BIOdry

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