Multifractal analysis of neutral community spatial structure

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

doi:10.1016/j.jtbi.2013.10.011

Cited by 17 publications

(9 citation statements)

References 48 publications

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“…Hence multifractals do for densities what fractals do for shapes: a multifractal shows contrast at all scales. Multifractals have previously been applied to ecological data (Laurie and Perrier, 2011;Savaria et al, 2012;Savaria, 2014;Dal Bello et al, 2015) and in ecological theory (Yakimov et al, 2014); here for the first time we apply them to macrobenthic faunal assemblages. Prigarin et al (2013) provide a useful summary of fractal and multifractal concepts and the numerical techniques that may be used to estimate the fractal and multifractal dimensions (note that they use the term "Rényi entropy" for the function ( ) below, more generally, as here, termed Rényi dimensions).…”

Section: Multifractal Analysesmentioning

confidence: 99%

Seagrass macrofaunal abundance shows both multifractality and scale-invariant patchiness

Barnes

Laurie

2018

Marine Environmental Research

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Spatial patterns of abundance of the whole macrobenthic assemblage and of its 10 most numerous species were examined across hierarchically nested scales within a 0.85 ha area of intertidal seagrass in subtropical Moreton Bay, Queensland. Multifractality characterised the assemblage and all ten dominant species across those scales (c. 33, 130, 530 & 2115 m), with patchiness of assemblage numbers and those of at least some dominants exhibiting scale-invariance. The system displayed several abundance peaks, 12% of stations accounting for 88% of total variance, with many individual dominants showing a series of non-overlapping 'hot-spots'. Scale invariance and multifractality occurred notwithstanding low levels of species interaction consequent on maintenance at very low density. This suggests that critical self-organisation cannot be responsible for such patterning. Contrary to received wisdom, coefficient β of Taylor's power-law cannot form an index of aggregation, although it does indicate direction of change in dispersion pattern with changing numbers.

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Section: Multifractal Analysesmentioning

confidence: 99%

Seagrass macrofaunal abundance shows both multifractality and scale-invariant patchiness

Barnes

Laurie

2018

Marine Environmental Research

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“…In addition, generalized dimensions have been applied to a spatially explicit neutral model (Yakimov et al . ) and used in open source software for ecological multifractal analysis (Saravia ).…”

Section: Introductionmentioning

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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“…Moreover, the presence of multiplicative process is argued to produce the log-normal-like shape of speciesabundance distributions 16 . Also, random processes with spatial correlations can generate multifractals 14 ; these kind of processes are part of neutral community models 17,18 and are observed in natural communities 19 . Thus there are a priori reasons to think that multifractals can be applied to spatial ecological data.…”

Section: Introductionmentioning

confidence: 99%

mfSBA: Multifractal analysis of spatial patterns in ecological communities

Saravia

2014

F1000Res

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Multifractal analysis of neutral community spatial structure

Cited by 17 publications

References 48 publications

Seagrass macrofaunal abundance shows both multifractality and scale-invariant patchiness

Seagrass macrofaunal abundance shows both multifractality and scale-invariant patchiness

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

mfSBA: Multifractal analysis of spatial patterns in ecological communities

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