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mfSBA: Multifractal Analysis of Spatial Patterns in Ecological Communities


mfSBA: Multifractal Analysis of Spatial Patterns in Ecological Communities

Leonardo A Saravia. F1000Res.


Multifractals have been applied to characterize complex communities in a spatial context. They were developed for nonlinear systems and are particularly suited to capture multiplicative processes observed in ecological systems. Multifractals characterize variability in a scale-independent way within an experimental range. I have developed an open-source software package to estimate multifractals using a box-counting algorithm (available from and permanently available at doi: 10.5281/zenodo.8481). The software is specially designed for two dimensional (2D) images such as the ones obtained from remote sensing, but other 2D data types can also be analyzed. Additionally I developed a new metric to analyze MULTISPECIES SPATIAL PATTERNS WITH MULTIFRACTALS: spatial rank surface, which is included in the software.

Conflict of interest statement

Competing interests: No competing interests were disclosed.


Figure 1.
Figure 1.. Plot of the linear regressions for different q used to estimate the D q multifractal spectrum.
Figure 2.
Figure 2.. D q multifractal spectrum calculated from species spatial distributions.
If the multispecies distribution is analyzed unordered (with species numbers assigned by the simulation software) the D q is almost flat corresponding to a uniform plus random noise distribution. But when the species rank surface (SRS) is used the D q spectrum has a wide range of values, corresponding with a highly heterogeneous distribution, formed of valleys for the most abundant species and peaks for rare species. The error bars are the standard deviation obtained from the linear regressions used to estimate D q.
Supplementary Figure 1.
Supplementary Figure 1.. Comparison of a multiespecies spatial distribution generated by a neutral model with 64 possible species.
Both figures represent the same species distribution but with diferent numeric values assigned to species. ( a) The values are assigned by the simulation program. The most abundant species have higher values and the range 1–64 represents all posible species. ( b) Spatial Rank Surface: each species is assigned to its rank as explained in the main text: the most abundant species has the lowest value and represent valleys, rare species represent peaks. The range is lower because some species did not appear.

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The author(s) declared that no grants were involved in supporting this work.

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