Self‐Similarity, the Power Law Form of the Species‐Area Relationship, and a Probability Rule: A Reply to Maddux

2004 ◽  
Vol 163 (4) ◽  
pp. 627-633 ◽  
Author(s):  
Annette Ostling ◽  
John Harte ◽  
Jessica L. Green ◽  
Ann P. Kinzig
Keyword(s):  
Power Law ◽  
Self Similarity ◽  
Species Area ◽  
Species Area Relationship

Scale collapse and the emergence of the power law species-area relationship

2015 ◽  
Vol 24 (8) ◽  
pp. 883-895 ◽  
Author(s):  
Mark Q. Wilber ◽  
Justin Kitzes ◽  
John Harte
Keyword(s):  
Power Law ◽  
Species Area ◽  
Species Area Relationship

THE SPECIES–AREA RELATIONSHIP, SELF-SIMILARITY, AND THE TRUE MEANING OF THEz-VALUE

Ecology ◽  
2008 ◽  
Vol 89 (12) ◽  
pp. 3528-3533 ◽  
Author(s):  
Even Tjørve ◽  
Kathleen M. Calf Tjørve
Keyword(s):  
Self Similarity ◽  
True Meaning ◽  
Species Area ◽  
Species Area Relationship

scholarly journals Extended power-law scaling of air permeabilities measured on a block of tuff

2012 ◽  
Vol 16 (1) ◽  
pp. 29-42 ◽  
Author(s):  
M. Siena ◽  
A. Guadagnini ◽  
M. Riva ◽  
S. P. Neuman
Keyword(s):  
Power Law ◽  
Structure Functions ◽  
Self Similarity ◽  
Scaling Exponents ◽  
Multi Scale ◽  
Sample Structure ◽  
Heavy Tailed ◽  
Non Gaussian ◽  
Nonlinear Fashion ◽  
Extended Power

Abstract. We use three methods to identify power-law scaling of multi-scale log air permeability data collected by Tidwell and Wilson on the faces of a laboratory-scale block of Topopah Spring tuff: method of moments (M), Extended Self-Similarity (ESS) and a generalized version thereof (G-ESS). All three methods focus on q-th-order sample structure functions of absolute increments. Most such functions exhibit power-law scaling at best over a limited midrange of experimental separation scales, or lags, which are sometimes difficult to identify unambiguously by means of M. ESS and G-ESS extend this range in a way that renders power-law scaling easier to characterize. Our analysis confirms the superiority of ESS and G-ESS over M in identifying the scaling exponents, ξ(q), of corresponding structure functions of orders q, suggesting further that ESS is more reliable than G-ESS. The exponents vary in a nonlinear fashion with q as is typical of real or apparent multifractals. Our estimates of the Hurst scaling coefficient increase with support scale, implying a reduction in roughness (anti-persistence) of the log permeability field with measurement volume. The finding by Tidwell and Wilson that log permeabilities associated with all tip sizes can be characterized by stationary variogram models, coupled with our findings that log permeability increments associated with the smallest tip size are approximately Gaussian and those associated with all tip sizes scale show nonlinear variations in ξ(q) with q, are consistent with a view of these data as a sample from a truncated version (tfBm) of self-affine fractional Brownian motion (fBm). Since in theory the scaling exponents, ξ(q), of tfBm vary linearly with q we conclude that nonlinear scaling in our case is not an indication of multifractality but an artifact of sampling from tfBm. This allows us to explain theoretically how power-law scaling of our data, as well as of non-Gaussian heavy-tailed signals subordinated to tfBm, are extended by ESS. It further allows us to identify the functional form and estimate all parameters of the corresponding tfBm based on sample structure functions of first and second orders.

scholarly journals The species–area relationship and evolution

2006 ◽  
Vol 241 (3) ◽  
pp. 590-600 ◽  
Author(s):  
Daniel Lawson ◽  
Henrik Jeldtoft Jensen
Keyword(s):  
Species Area ◽  
Species Area Relationship

Fragmentation, grazing and the species-area relationship

Ecography ◽  
2012 ◽  
Vol 35 (3) ◽  
pp. 224-231 ◽  
Author(s):  
Tiffany L. Bogich ◽  
Gary M. Barker ◽  
Karin Mahlfeld ◽  
Frank Climo ◽  
Rhys Green ◽  
...  
Keyword(s):  
Species Area ◽  
Species Area Relationship
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