Exploring the spontaneous contribution of Claude E. Shannon to eco-evolutionary theory

Mathematical bounds on Shannon entropy given the abundance of the ith most abundant taxon

The measurement of diversity is a central component of studies in ecology and evolution, with broad uses spanning multiple biological scales. Studies of diversity conducted in population genetics and ecology make use of analogous concepts and even employ equivalent mathematical formulas. For the Shannon entropy statistic, recent developments in the mathematics of diversity in population genetics have produced mathematical constraints on the statistic in relation to the frequency of the most frequent allele. These results have characterized the ways in which standard measures depend on the highest-frequency class in a discrete probability distribution. Here, we extend mathematical constraints on the Shannon entropy in relation to entries in specific positions in a vector of species abundances, listed in decreasing order. We illustrate the new mathematical results using abundance data from examples involving coral reefs and sponge microbiomes. The new results update the understanding of the relationship of a standard measure to the abundance vectors from which it is calculated, potentially contributing to improved interpretation of numerical measurements of biodiversity.

Vegetation Monitoring of Protected Areas in Rugged Mountains Using an Improved Shadow-Eliminated Vegetation Index (SEVI)

It is significant to study the vegetation of protected areas in rugged mountains where the vegetation grows naturally with minimal eco-society environmental stress from anthropogenic activities. The shadow-eliminated vegetation index (SEVI) was used to monitor the vegetation of protected areas, since it successfully removes topographic shadow effects. In order to auto achieve the best adjustment factor for SEVI calculation from regional area images, we developed a new calculation algorithm using block information entropy (BIE-algorithm). The BIE-algorithm auto-detected typical blocks (subareas) from slope images and achieved the best adjustment factor from a block where the SEVI obtained the highest information entropy in an entire scene. Our obtained regional SEVI result from two scenes of Landsat 8 OLI images using the BIE-algorithm exhibited an overall flat feature with the impression of the relief being drastically removed. It achieved balanced values among three types of samples: Sunny area, self-shadow, and cast shadow, with SEVI means of 0.73, 0.77, and 0.75, respectively, and the corresponding SEVI relative errors of self-shadow and cast shadow were only 4.99% and 1.84%, respectively. The linear regression of SEVI vs. the cosine of the solar incidence angle was nearly horizontal, with an inclination of −0.0207 and a coefficient of determination of 0.0042. The regional SEVI revealed that the vegetation growth level sequence of three protected areas was Wuyishan National Park (SEVI mean of 0.718) > Meihuashan National Nature Reserve (0.672) > Minjiangyuan National Nature Reserve (0.624) > regional background (0.572). The vegetation growth in the protected areas was influenced by the terrain slope and years of establishment of the protected area and by the surrounding buffer zone. The homogeneous distribution of vegetation in a block is influenced by many factors, such as the actual vegetation types, block size, and shape, which need consideration when the proposed BIE-algorithm is used.

Spatial Heterogeneity Analysis: Introducing a New Form of Spatial Entropy

Distinguishing and characterizing different landscape patterns have long been the primary concerns of quantitative landscape ecology. Information theory and entropy-related metrics have provided the deepest insights in complex system analysis, and have high relevance in landscape ecology. However, ideal methods to compare different landscape patterns from an entropy view are still lacking. The overall aim of this research is to propose a new form of spatial entropy (H_s) in order to distinguish and characterize different landscape patterns. H_s is an entropy-related index based on information theory, and integrates proximity as a key spatial component into the measurement of spatial diversity. Proximity contains two aspects, i.e., total edge length and distance, and by including both aspects gives richer information about spatial pattern than metrics that only consider one aspect. Thus, H_s provides a novel way to study the spatial structures of landscape patterns where both the edge length and distance relationships are relevant. We compare the performances of H_s and other similar approaches through both simulated and real-life landscape patterns. Results show that H_s is more flexible and objective in distinguishing and characterizing different landscape patterns. We believe that this metric will facilitate the exploration of relationships between landscape patterns and ecological processes.

Ecology: Science or philately? An interdisciplinary analysis of sustainability by exploring if it is possible to get more and more information by reducing collateral environmental damages

We herein explore the connections between the current condition of ecology concerning to sustainable development and the statement of Rutherford regarding the importance of physics to understand sustainability and biological conservation. The recent emergence of organic biophysics of ecosystems (OBEC) may constitute a feasible alternative to fill the gap between conventional ecological thinking and physics, especially thermodynamics. However, our comprehension of sustainability and biological conservation is influenced by the interactions between information and entropy, because we tend to exclude parts of the biosphere as well as their relationships among them. We explore the use of a holistic analysis of sustainability and biological conservation using physics, and also establish a parallelism between Maxwell's demons and human beings. Lastly, the ecological meaning of the hypothetical feasibility of Maxwell's demon at the anthroposphere scale is analyzed starting from the objections of von Smoluchowski, Szilard and Bennet.