Metrics based on information entropy applied to evaluate complexity of landscape patterns

Landscape is an ecological category represented by a complex system formed by interactions between society and nature. Spatial patterns of different land uses present in a landscape reveal past and present processes responsible for its dynamics and organisation. Measuring the complexity of these patterns (in the sense of their spatial heterogeneity) allows us to evaluate the integrity and resilience of these complex environmental systems. Here, we show how landscape metrics based on information entropy can be applied to evaluate the complexity (in the sense of spatial heterogeneity) of patches patterns, as well as their transition zones, present in a Cerrado conservation area and its surroundings, located in south-eastern Brazil. The analysis in this study aimed to elucidate how changes in land use and the consequent fragmentation affect the complexity of the landscape. The scripts CompPlex HeROI and CompPlex Janus were created to allow calculation of information entropy (He), variability (He/Hmax), and López-Ruiz, Mancini, and Calbet (LMC) and Shiner, Davison, and Landsberg (SDL) measures. CompPlex HeROI enabled the calculation of these measures for different regions of interest (ROIs) selected in a satellite image of the study area, followed by comparison of the complexity of their patterns, in addition to enabling the generation of complexity signatures for each ROI. CompPlex Janus made it possible to spatialise the results for these four measures in landscape complexity maps. As expected, both for the complexity patterns evaluated by CompPlex HeROI and the complexity maps generated by CompPlex Janus, the areas with vegetation located in a region of intermediate spatial heterogeneity had lower values for the He and He/Hmax measures and higher values for the LMC and SDL measurements. So, these landscape metrics were able to capture the behaviour of the patterns of different types of land use present in the study area, bringing together uses linked to vegetation with increased canopy coverage and differentiating them from urban areas and transition areas that mix different uses. Thus, the algorithms implemented in these scripts were demonstrated to be robust and capable of measuring the variability in information levels from the landscape, not only in terms of spatial datasets but also spectrally. The automation of measurement calculations, owing to informational entropy provided by these scripts, allows a quick assessment of the complexity of patterns present in a landscape, and thus, generates indicators of landscape integrity and resilience.

-"Reviewer 1: 3. The introduction should further highlight what is the motivation of the paper." and "Reviewer 2: 1. In the "Introduction" section, "information entropy" is simply mentioned, but as the main content of the research, the background and current related researches of information entropy should be added.": Action(s) performed: We include in the 8 th paragraph of the 'Introduction' background and more current related researches of information entropy (references 25-35).
We have also modified the 9 th (last) paragraph of the 'Introduction' to give more emphasis to our objective ("From the case study presented, this article aims to show how such measures can be used to evaluate and indicate how changes in land use and fragmentation affect the complexity of the landscape, and consequently, to indicate how measures based on entropy information can be used as indicators of its integrity and resilience.") -"Journal Requirements: 2. In your Methods section, please provide additional location information, including geographic coordinates of your field collection site if available.": Action(s) performed: We add to the text the geographic coordinates of the Itirapina Ecological and Experimental Parks -"Reviewer 1: 8. The picture pixels in the manuscript are too low." and "Reviewer 2: 5.The clarity of pictures in the manuscript needs to be further improved.": Action(s) performed: We improved the quality of the images.
-"Reviewer 2: 2. In the "Material and Methods" section, López-Ruiz, Mancini, and Calbet (LMC) and Shiner, Davison, and Landsberg(SDL), as key measures, have not been explained clearly, and need to be further clarified.": ???? Action(s) performed: In item "2.2.1) Application of complexity measures based on information entropy of remote sensing images", we added two paragraphs (4th and 5th paragraphs) explaining in more detail about the LMC and SDL measures.
-"Journal Requirements: 3. We note that Figures 1 and 7 (CC BY 4.0), which means that the manuscript, images, and Supporting Information files will be freely available online, and any third party is permitted to access, download, copy, distribute, and use these materials in any way, even commercially, with proper attribution. For these reasons, we cannot publish previously copyrighted maps or satellite images created using proprietary data, such as Google software (Google Maps, Street View, and Earth). For more information, see our copyright guidelines: http://journals.plos.org/plosone/s/licenses-and-copyright. We require you to either (1) present written permission from the copyright holder to publish these figures specifically under the CC BY 4.0 license, or (2)   -"Reviewer 1: 5. Results and discussion: The results should be better described, discussed and justified using references" and "Reviewer 2: 6. Results and discussion are expressed together in the manuscript, but the content expressed is mostly the description of the results, which lacks indepth discussion. It is suggested that the discussion be set up as a separate part to discuss some key issues, such as:(1) What are the reasons for the differences in the complexity of different landscapes? How changes in landuse and the consequent fragmentation affect the complexity of the landscape? (2) The manuscript mentioned that "the complexity algorithms are robust", https://yout.com/youtube-mp3/?lang=ptbut how to prove it?(3) What are the limitations of the research?": ???? Action(s) performed: We seek to describe, discuss and justify the results by giving more details about them, explaining their meanings and using references to support our justifications. Therefore, we chose to leave the discussions together with the results and, in this way, better clarify the three questions raised by the second reviewer.
-"Reviewer 2: 3. The names of ROIs are inconsistent in the text, Figure 7, Table 2 and Table 3, so it is suggested to unify them." and "Reviewer 2: 4.In Table 2 and Table3, the meanings of different colors are best explained in the legend.": Action(s) performed: We unify the names of ROIs in the text, Figure 7 and Tables 1-3.
-"Reviewer 1: 6. Conclusion mostly looks like a summary of the work done and the results obtained. No interpretation of the results in given as well as no recommendation for the government and policy makers as to how the results could be used. Also, there should be some content in the conclusion regarding the limitations of the current research and future work possibilities.": Action(s) performed: We modified the text of the conclusions, seeking to highlight the most important results achieved and their relevance for research in Landscape Ecology and for its use in environmental planning and management. We also added issues related to possible limitations of the measures used, as well as the possibility of future studies in which they can be used.

Action(s) performed:
We appreciate the literature suggestions, which were included in our text.

Sincerely yours
The authors