Multifractal estimation using a standard box-counting algorithm
Software used to determine multifractal spectra: Generalized dimensions Dq and spectrum of singularities f(alfa), the software is described in the paper:
- Saravia LA (2014) mfSBA: Multifractal analysis of spatial patterns in ecological communities [v2; ref status: indexed, http://f1000r.es/347]. F1000Research 3: 14. doi:10.12688/f1000research.3-14.v2.
mfSBA estimate both spectra and outputs data to evaluate the fits. A more detailed description is in the file mfSBA_README.
mfSBArnz estimate the Dq spectrun and randomize the original image N times to calculate a confidence interval to test the hipothesis that the original distribution was random.
multiSpeciesSBA estimates the multifractal spectra of a 2D species distribution assuming that each position is one individual and that each value represents a different specie. The species can be analyzed as a spatial rank surface (SRS) or as a generalization of species area distribution which I call multifractal SAD (species abundance distribution).
sed2grad transforms a sed file using a discrete gradient transformation.
R Functions and scripts
There are two scripts to test and demonstrate the software:
testMFA.r: Test and demostration of functions for standard, SRS and SAD multifractal analysis
Fun_MFA.r: R Functions for multifractal analysis,
The output should be compared with the same files in folder testOut
Several ".sed" files ".tif" are used as examples
The q21.sed is a file with q values used to estimate spectra.
These programs were used in the following papers:
Saravia LA. (2105) A new method to analyse species abundances in space using generalized dimensionss. Methods in Ecology and Evolution. doi: 10.1111/2041-210X.12417
Saravia LA, Giorgi A, Momo FR (2012) Multifractal Spatial Patterns and Diversity in an Ecological Succession. PLoS One 7: e34096.
Saravia LA, Giorgi A, Momo F (2012) Multifractal growth in periphyton communities. Oikos 121: 1810–1820.
Please leave an Issue on github if you have some trouble.
Copyright 2011 Leonardo A. Saravia This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program. If not, see <http://www.gnu.org/licenses/>.