Order and disorder in ecological time-series: Introducing normalized spectral entropy

Information theory and entropy measures have been extensively applied in ecology in different areas like biodiversity assessment, evolution, species interactions, spatial dynamics or landscape analysis. Ecological applications of entropy measures have been primarily focused on structural and functional complexity of systems and less attention has been paid to temporal evolution and dynamics. The aim of this paper is to present “normalized spectral entropy” (Hsn), an entropy related index able to measure part of the structural complexity of an ecological time series. Hsn quantifies the degree of order and predictability derived by the series’ power spectrum. The index sensitivity to data attributes is investigated by means of time-series surrogates of known properties (i.e., time-series length, power spectrum shape, and time-series values distribution). A procedure to calculate confidence intervals is outlined as a preliminary statistical tool to assess differences among values. Three examples of possible application are described using time series of meteorological variables, vegetation physiological responses and remote sensing images. Results show how Hsn is able to contribute to the ongoing debate on how to estimate spatio-temporal complexity of ecological systems, thus making a step forward in the proposed use of complexity as an ecological orientor.