Nonconcavity of mass exponents’ spectrum in multifractal analysis of community spatial structure: The problem and possible solutions

Yakimov, Basil N.; Gelashvili, D. B.; Solntsev, L. A.; Иудин, Д. И.; Розенберг, Г. С.

doi:10.1016/j.ecocom.2014.07.003

Cited by 6 publications

(3 citation statements)

References 45 publications

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“…A partial solution has been proposed (Yakimov et al . ), but the anomalies observed may be related to the mathematical assumptions needed for D q to be non‐increasing, in which case, a new mathematical proof should be developed for

D_{q}^{SAD}

. Thus, as long as the linear relationship is reasonable, I take

D_{q}^{SAD}

as a useful technique of analysis.…”

Section: Methodsmentioning

confidence: 99%

A new method to analyse species abundances in space using generalized dimensions

Saravia

2015

Methods Ecol Evol

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Summary Species–area relationships (SAR) and species‐abundance distributions (SAD) are among the most studied patterns in ecology, due to their application to both theoretical and conservation issues. One problem with these general patterns is that different theories can generate the same predictions, and for this reason, they cannot be used to detect different mechanisms of community assembly. A solution is to search for more sensitive patterns, for example by extending the SAR to the whole SAD. A generalized dimension (Dq) approach has been proposed to study the scaling of SAD, but to date, there has been no evaluation of the ability of this pattern to detect different mechanisms. An equivalent way to express SAD is the rank‐abundance distribution (RAD). Here I introduce a new way to study SAD scaling using a spatial version of RAD: the species‐rank surface (SRS), which can be analysed using Dq. Thus, there is an old Dq based on SAR (DqSAD), and a new one based on SRS (DqSRS). I perform spatial simulations to examine the relationship of Dq with SAD, spatial patterns and number of species. Finally, I compare the power of both Dq, SAD, SAR exponent and the fractal information dimension to detect different community patterns using a continuum of hierarchical and neutral spatially explicit models. The SAD, DqSAD and DqSRS all had good performance in detecting models with contrasting mechanisms. DqSRS, however, had a better fit to data and allowed comparisons between hierarchical communities where the other methods failed. The SAR exponent and information dimension had low power and should not be used. SRS and DqSRS could be interesting methods to study community or macroecological patterns.

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D_{q}^{SAD}

. Thus, as long as the linear relationship is reasonable, I take

D_{q}^{SAD}

as a useful technique of analysis.…”

Section: Methodsmentioning

confidence: 99%

A new method to analyse species abundances in space using generalized dimensions

Saravia

2015

Methods Ecol Evol

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show abstract

“…[36~38] 和土壤动物类群 [39] 会存在一定的多重分形特征, 其可能通过养分输入的方式影响着地上森林群落物种多样性, 进而使得地上森林群落物种多样性格局也呈现出多重分形特征. 尽管多重分形谱函数ƒ(α)的负值在物理学中并未有实际意义 [40] , 但是在生态学中的研究表明负值具有生态学意义, 其表征了特定种组丰富度的减少 [41] . 可能是植物功能性状差异所致, 先前的研究表明优势种组的叶干物质含量、叶面积、叶片厚度和最大高度的群落加权均值均显著高于稀有种组 [43] .…”

Section: 仍具有多重分形特征研究表明土壤理化性质unclassified

南亚热带常绿阔叶林物种多样性与谱系多样性的多重分形分析

Yin,

Li,

Wei

et al. 2024

Chin. Sci. Bull.

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“…PrePrintsoriginal definition, equation 1, is over boxes, and this changes the way in which the mathematical limits are taken and also the computation method of D SAD q . A partial solution has been proposed[35], but the anomalies observed may be related to the mathematical assumptions needed for D q to be non-increasing, in…”

mentioning

confidence: 99%

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Supplemental Information 1: Appendices: Text, Tables and Figures

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• Species-area relationships (SAR) and species abundance distributions (SAD) are among the most studied patterns in ecology, due to their application in both theoretical and conservation issues. One problem with these general patterns is that different theories can generate the same predictions, and for this reason they can not be used to detect different mechanisms. • A solution for this is to search for more sensitive patterns. One possibility is to extend the SAR to the whole species abundance distribution. A generalized dimension (D q) approach has been proposed to study the scaling of SAD, but there has been no evaluation of the ability of this pattern to detect different mechanisms. • An equivalent way to express SAD is the rank abundance distribution (RAD). Here I introduce a new way to study scaling of SAD using a spatial version of RAD: the species-rank surface (SRS), which can be analyzed using D q. Thus there is an old D q based on SAR (D SAD q), and a new one based on SRS (D SRS q). I perform spatial simulations to relate both D q with SAD, spatial patterns and number of species. Finally I compare the power of both D q , SAD, SAR exponent, and the fractal information dimension to detect different community patterns using a continuum of hierarchical and neutral spatially explicit models. • The SAD, D SAD q and D SRS q all had good performance in detecting models with contrasting mechanisms. D SRS q had a better fit to data and a strong ability to compare between hierarchical communities where the other methods failed. The SAR exponent and information dimension had low power and should not be used.

show abstract

Nonconcavity of mass exponents’ spectrum in multifractal analysis of community spatial structure: The problem and possible solutions

Cited by 6 publications

References 45 publications

A new method to analyse species abundances in space using generalized dimensions

A new method to analyse species abundances in space using generalized dimensions

南亚热带常绿阔叶林物种多样性与谱系多样性的多重分形分析

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