Beyond species area curves: application of a scale‐free measure for spatial variability of species richness

Laurie, Henri; Perrier, Edith

doi:10.1111/j.1600-0706.2010.19134.x

Cited by 13 publications

(13 citation statements)

References 41 publications

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“…The symmetric pattern was not observed in the regular cases (Fig. ) because the negative part ( q < 0) analyses numbers close to 0, and the logarithm (eqn ) enhances the differences between small numbers (Laurie & Perrier ). Thus, the difference ∆ D q = ¦ D q – D 0 ¦ is greater for q < 0.…”

Section: Resultsmentioning

confidence: 89%

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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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Section: Resultsmentioning

confidence: 89%

“…Ranges of q between −10 and 10 or narrower are generally used (Yakimov et al . ; Laurie & Perrier ; Saravia, Giorgi & Momo ; Wei et al . ), but sometimes the applied range has been wider (Saravia, Giorgi & Momo ).…”

Section: Resultsmentioning

confidence: 99%

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

Saravia

2015

Methods Ecol Evol

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“…For the uniform SAD we expected D SAD 0 to be around 0.5, following a symmetric pattern around q = 0, as all species have the same abundance and occupy the same area. The symmetric pattern was not observed in the regular cases ( Figure 2) because the negative part (q < 0) analyzes numbers close to 0 and the logarithm (equation 5) enhances the differences between small numbers (Laurie & Perrier 2011). Thus the difference…”

Section: Calculation Of Power and Type I Errormentioning

confidence: 87%

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

Saravia

2015

Preprint

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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 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 species abundance distribution. A generalized dimension ($D_q$) 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 analyzed using $D_q$. Thus there is an old $D_q$ based on SAR ($D_q^{SAD}$), and a new one based on SRS ($D_q^{SRS}$). I perform spatial simulations to examine the relationship of $D_q$ 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, $D_q^{SAD}$ and $D_q^{SRS}$ all had good performance in detecting models with contrasting mechanisms. $D_q^{SRS}$, 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 $D_q^{SRS}$ could be interesting methods to study community or macroecological patterns.

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“…When q is larger in its absolute value, For the uniform SAD we expected D SAD 0 to be around 0.5, with a symmetric pattern with small deviations around this value, as all species have the same abundance and occupy the same area. The symmetric pattern was not observed in the regular cases ( Figure 2) because the negative part (q < 0) analyzes numbers close to 0 and the logarithm enhances the differences between small numbers (Laurie & Perrier 2011). Thus the…”

Section: Resultsmentioning

confidence: 87%

“…I talk of high power when its value is 0.75 or higher, and low power when it is 0.5 or lower. between -10 and 10 or narrower are generally used (Yakimov et al 2008;Laurie & Perrier 2011;Wei et al 2013) but sometimes the applied range has been wider . I started using a q range of -24 to 24, and found that for this range type I error rates were, in all cases, higher than the nominal significance level α = 0.5 (Appendix table 4).…”

Section: Statistical Power and Type I Errorsmentioning

confidence: 99%

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Supplemental Information 1: Apendices

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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.

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Beyond species area curves: application of a scale‐free measure for spatial variability of species richness

Cited by 13 publications

References 41 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

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

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