Fig 1.
The narrative surrounding ecosystem health has shifted from a very disciplinary framework, through multi, inter and transdisciplinarity, before finally being defined in terms of complex systems.
Fig 2.
Our proposal for measuring the dynamic dimension of ecosystemic health is based on the idea of criticality as the combination of scale invariance and balance between adaptability and robustness (pink noise).
By combining a scale invariance index based on BIC values with the value of the scalar coefficients (beta) in power spectra, we propose an Ecosystemic Health Index, whose maximum for beta values equals 1, and that is associated with a balance between adaptability and robustness. In this way, an ecosystem may lose health by losing robustness and exhibiting white-noise dynamics, or by losing adaptability leading to Brownian-noise dynamics.
Fig 3.
In this figure we show the land condition variable used as validation in terms of noise type.
Color scale corresponds to ecosystem types in the IGBP nomenclature gaia.agraria.unitus.it/IGBPdesignations.pdf.
Fig 4.
As expected, most ecosystems fall into pink noise.
In general, we found that ecosystems out of criticality are older forests or have been altered by human activity or events such as wildfires.
Fig 5.
Values of our Ecosystemic Health Index for all ecosystem types (IGBP).
The color of each data point corresponds to the type of noise (white, pink and brown).
Fig 6.
Permutation entropy boxplot in terms of noise color.
Fig 7.
Permutation entropy scatter plot in terms of β value.
Entropy reaches highest values around the beta values range for which pink noise is defined.
Fig 8.
Complexity as a quadratic function of Permutation Entropy.
Fig 9.
Evolution of Fisher information for the Harvard Forest site (US-Ha1) from 1991 to 2003.
Pink points are 1 year time series with a pink noise kind of dynamics (0.5 < β < 1.5) and blue point correspond to 1 year time series with a white noise dynamics (β ≤ 0.5).
Fig 10.
Since criticality (pink noise) appears to be the most healthy and stable (sustainable) type of dynamics, we use it as a leaf variable in a classification tree using the C4.5 algorithm in WEKA.
Fig 11.
In this map we represent the type of noise in a color scale, and land condition as size of the circles.
Fig 12.
Here, ecosystem stability (Permutation Entropy) is shown in a color scale and ecosystem health (as the square root of scale invariance indicator times the criticality indicator) as the size of the circles.