{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,19]],"date-time":"2026-03-19T10:35:31Z","timestamp":1773916531358,"version":"3.50.1"},"reference-count":64,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2013,1,24]],"date-time":"2013-01-24T00:00:00Z","timestamp":1358985600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>In the Amazon, the development and paving of roads connects regions and peoples, and over time can form dense and recursive networks, which often serve as nodes for continued development. These developed areas exhibit robust fractal structures that could potentially link their spatial patterns with deforestation processes. Fractal dimension is commonly used to describe the growth trajectory of such fractal structures and their spatial-filling capacities. Focusing on a tri-national frontier region, we applied a  box-counting method to calculate the fractal dimension of the developed areas in the Peruvian state of Madre de Dios, Acre in Brazil, and the department of Pando in Bolivia, from 1986 through 2010. The results indicate that development has expanded in all three regions with declining forest cover over time, but with different patterns and rates in each country. Such differences were summarized within a proposed framework to indicate deforestation progress\/level, which can be used to understand and regulate deforestation and its evolution in time. In addition, the role and influence of scale was also assessed, and we found local fractal dimensions are not invariant at different spatial scales and thus concluded such scale-dependent features of fragmentation patterns are here mainly shaped by the road paving.<\/jats:p>","DOI":"10.3390\/rs5020454","type":"journal-article","created":{"date-parts":[[2013,1,24]],"date-time":"2013-01-24T11:29:13Z","timestamp":1359026953000},"page":"454-472","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":43,"title":["Remote Sensing-Based Fractal Analysis and Scale Dependence Associated with Forest Fragmentation in an Amazon Tri\u2011National Frontier"],"prefix":"10.3390","volume":"5","author":[{"given":"Jing","family":"Sun","sequence":"first","affiliation":[{"name":"Department of Geography, University of Florida, Gainesville, FL 32611, USA"}]},{"given":"Jane","family":"Southworth","sequence":"additional","affiliation":[{"name":"Department of Geography, University of Florida, Gainesville, FL 32611, USA"}]}],"member":"1968","published-online":{"date-parts":[[2013,1,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Lambin, E.F., and Geist, H.J. (2006). Land-Use and Land Cover Change: Local Processes and Global Impacts, Springer.","DOI":"10.1007\/3-540-32202-7"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Gutman, G., Janetos, A., Justice, C., Moran, E., Mustard, J., Rindfuss, R., Skole, D., and Turner, B.L. (2004). Land Change Science: Observing, Monitoring, and Understanding Trajectories of Change on the Earth\u2019s Surface, Kluwer Academic Publishers.","DOI":"10.1007\/978-1-4020-2562-4"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"505","DOI":"10.1038\/19066","article-title":"Large-scale impoverishment of Amazonian forests by logging and fire","volume":"398","author":"Nepstad","year":"1999","journal-title":"Nature"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1016\/S0378-1127(01)00511-4","article-title":"Road paving, fire regime feedbacks, and the future of Amazon forests","volume":"154","author":"Nepstad","year":"2001","journal-title":"Forest Ecol. Manage"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1017\/S0376892901000339","article-title":"Is deforestation accelerating in the Brazilian Amazon?","volume":"28","author":"Laurance","year":"2001","journal-title":"Environ. Conserv"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"737","DOI":"10.1046\/j.1365-2699.2002.00721.x","article-title":"Predictors of deforestation in the Brazilian Amazon","volume":"29","author":"Laurance","year":"2002","journal-title":"J. Biogeogr"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Andersen, L.E., Granger, C.W.J., Reis, E.J., Weinhold, D., and Wunder, S (2002). The Dynamics of Deforestation and Economic Development in the Brazilian Amazon, Cambridge University Press.","DOI":"10.1017\/CBO9780511493454"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"529","DOI":"10.1111\/j.1467-7660.2007.00422.x","article-title":"Socio-spatial process of unofficial road building in the Amazon: Socioeconomic and biophysical explanations","volume":"38","author":"Perz","year":"2007","journal-title":"Dev. Change"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"112","DOI":"10.1017\/S0376892907003827","article-title":"Unofficial road building in the Brazilian Amazon: dilemmas and models of road governance","volume":"34","author":"Perz","year":"2007","journal-title":"Environ. Conserv"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"600","DOI":"10.1016\/j.landusepol.2006.01.003","article-title":"Will buying tropical forest carbon benefit the poor? Evidence from Costa Rica","volume":"24","author":"Pfaff","year":"2007","journal-title":"Land Use Policy"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"575","DOI":"10.1177\/0309133308096755","article-title":"1993: Tropical deforestation and habitat fragmentation in the Amazon: satellite data from 1978 to 1988. Science, 260, 1905\u20131910","volume":"32","author":"Giles","year":"2008","journal-title":"Progr. Phys. Geogr"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1177\/0309133311399492","article-title":"Amazon deforestation: Rates and patterns of land cover change and fragmentation in Pando, northern Bolivia, 1986 to 2005","volume":"35","author":"Marsik","year":"2011","journal-title":"Progr. Phys. Geogr"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1047","DOI":"10.3390\/rs3051047","article-title":"Roads as drivers of change: Trajectories across the Tri-National frontier in MAP, the southwestern Amazon","volume":"3","author":"Southworth","year":"2011","journal-title":"Remote Sens"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1016\/j.ecocom.2012.03.002","article-title":"Spatial complexity in fragmenting Amazonian rainforests: Do feedbacks from edge effects push forests towards an ecological threshold?","volume":"11","author":"Cumming","year":"2012","journal-title":"Ecol. Complex"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1923","DOI":"10.1126\/science.1064397","article-title":"Ecological meltdown in Predator-Free forest fragments","volume":"294","author":"Terborgh","year":"2001","journal-title":"Science"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"879","DOI":"10.1086\/284386","article-title":"Conservation strategy: The effects of fragmentation on extinction","volume":"125","author":"Wilcox","year":"1985","journal-title":"Am. Nat"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1017\/S0376892901000133","article-title":"Tropical deforestation in the Bolivian Amazon","volume":"28","author":"Steininger","year":"2001","journal-title":"Environ. Conserv"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"5686","DOI":"10.1175\/2009JCLI2757.1","article-title":"Amazon deforestation and climate change in a coupled model simulation","volume":"22","author":"Nobre","year":"2009","journal-title":"J. Clim"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"645","DOI":"10.1016\/S0014-2921(00)00043-X","article-title":"Development, ecological resources and their management: A study of complex dynamic systems","volume":"44","year":"2000","journal-title":"Eur. Econ. Rev"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"591","DOI":"10.1038\/35098000","article-title":"Catastrophic shifts in ecosystems","volume":"413","author":"Scheffer","year":"2001","journal-title":"Nature"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1016\/S0065-2504(08)60149-X","article-title":"Positive-feedback Switches in Plant Communities","volume":"23","author":"Wilson","year":"1992","journal-title":"Adv. Ecol. Res"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"753","DOI":"10.2307\/2260864","article-title":"Land-use history (1730\u20131990) and vegetation dynamics in central New England, USA","volume":"80","author":"Foster","year":"1992","journal-title":"J. Ecol"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"305","DOI":"10.2307\/1312380","article-title":"The worldwide extent of land-use change","volume":"44","author":"Houghton","year":"1994","journal-title":"BioScience"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"487","DOI":"10.1093\/wber\/10.3.487","article-title":"Roads, land use, and deforestation: A spatial model applied to Belize","volume":"10","author":"Chomitz","year":"1996","journal-title":"World Bank Econ. Rev"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"667","DOI":"10.1029\/98GB02512","article-title":"Characterizing patterns of global land use: An analysis of global croplands data","volume":"12","author":"Ramankutty","year":"1998","journal-title":"Global Biogeochem. Cy"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"467","DOI":"10.1111\/0004-5608.00205","article-title":"Land-cover-change trajectories in Southern Cameroon","volume":"90","author":"Mertens","year":"2000","journal-title":"Ann. Assoc. Am. Geogr"},{"key":"ref_27","unstructured":"Turner, M., Gardner, R.H., and O\u2019Neill, R.V. (2001). Landscape Ecology in Theory and Practice: Pattern and Process, Springer."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1007\/s10980-006-9013-2","article-title":"Mapping spatial patterns with morphological image processing","volume":"22","author":"Vogt","year":"2007","journal-title":"Lands. Ecol"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"481","DOI":"10.1016\/j.ecolind.2006.11.001","article-title":"Mapping landscape corridors","volume":"7","author":"Vogt","year":"2007","journal-title":"Ecol. Indicat"},{"key":"ref_30","unstructured":"Gunderson, L.H., and Pritchard, L. (2002). Resilience and the Behavior of Large-Scale Systems, Island Press."},{"key":"ref_31","first-page":"27","article-title":"Global-scale patterns of forest fragmentation","volume":"4","author":"Riitters","year":"2000","journal-title":"Conserv. Ecol"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"815","DOI":"10.1007\/s10021-002-0209-2","article-title":"Fragmentation of continental United States forests","volume":"5","author":"Riitters","year":"2002","journal-title":"Ecosystems"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"406","DOI":"10.1111\/j.1467-9272.2006.00578.x","article-title":"Linking spatial and temporal variation at multiple scales in a heterogeneous landscape","volume":"58","author":"Southworth","year":"2006","journal-title":"Prof. Geogr"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1016\/j.ecocom.2005.11.002","article-title":"Disturbance patterns in a socioecological system at multiple scales","volume":"3","author":"Zurlini","year":"2006","journal-title":"Ecol. Complex"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"26","DOI":"10.5751\/ES-02416-130126","article-title":"Source\/sink patterns of disturbance and cross-scale mismatches in a Panarchy of social-ecological landscapes","volume":"13","author":"Zaccarelli","year":"2008","journal-title":"Ecol. Soc"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1146\/annurev.energy.30.050504.164507","article-title":"The role of protected areas in conserving biodiversity and sustaining local livelihoods","volume":"30","author":"Holland","year":"2005","journal-title":"Annu. Rev. Environ. Resour"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"3","DOI":"10.5751\/ES-04349-160403","article-title":"How effective is the buffer zone? Linking institutional processes with satellite images from a case study in the Lore Lindu Forest Biosphere Reserve, Indonesia","volume":"16","author":"Mehring","year":"2011","journal-title":"Ecol. Soc"},{"key":"ref_38","unstructured":"Mandelbrot, B.B. (1977). Fractals, Form, Chance and Dimension, W.H. Freeman and Company."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Mandelbrot, B.B. (1983). The Fractal Geometry of Nature, W.H. Freeman and Company.","DOI":"10.1119\/1.13295"},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Jopp, F., Reuter, H., and Breckling, B. (2011). Modelling Complex Ecological Dynamics, Springer Berlin-Heidelberg.","DOI":"10.1007\/978-3-642-05029-9"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1007\/BF00135076","article-title":"Using fractal analysis to assess how species perceive landscape structure","volume":"9","author":"With","year":"1994","journal-title":"Lands. Ecol"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/j.zool.2003.09.001","article-title":"Fractal analysis of narwhal space use patterns","volume":"107","author":"Laidre","year":"2004","journal-title":"Zoology (Jena)"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"1453","DOI":"10.1007\/s10531-004-9669-3","article-title":"Fractal analysis of plant spatial patters: a monitoring tool for vegetation transition shift","volume":"14","author":"Alados","year":"2005","journal-title":"Biodivers. Conserv"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"838","DOI":"10.1068\/b35078","article-title":"Spatiotemporal evolution of urban form and land use structure in Hangzhou, China: evidence from fractals","volume":"37","author":"Feng","year":"2010","journal-title":"Environ. Plann. B Plann. Des"},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Barabasi, A.L., and Stanley, H.E. (1995). Fractal Concepts in Surface Growth, Cambridge University Press. [1st ed].","DOI":"10.1017\/CBO9780511599798"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1146\/annurev.es.20.110189.001131","article-title":"Landscape ecology: The effect of pattern on process","volume":"20","author":"Turner","year":"1989","journal-title":"Annu. Rev. Ecol. Syst"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"788","DOI":"10.1007\/s00267-004-0110-1","article-title":"Measurement and management of human-induced patterns of forest fragmentation: a case study","volume":"37","author":"Tole","year":"2006","journal-title":"Environ. Manage"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"1055","DOI":"10.1364\/JOSAA.7.001055","article-title":"Estimating fractal dimension","volume":"7","author":"Theiler","year":"1990","journal-title":"J. Opt. Soc.Am. A"},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"Encarna\u00e7\u00e3o, S., Gaudiano, M., Santos, F., Tened\u00f3rio, J., and Jorge, M.P. (2012). Fractal cartography of urban areas. Scientific Reports.","DOI":"10.1038\/srep00527"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1111\/j.1467-8306.1987.tb00158.x","article-title":"The Fractal nature of geographic phenomena","volume":"77","author":"Goodchild","year":"1978","journal-title":"Ann. Assoc. Am. Geogr"},{"key":"ref_51","unstructured":"Batty, M., and Longley, P. (1994). Fractal Cities, Academic Press."},{"key":"ref_52","doi-asserted-by":"crossref","unstructured":"Sol\u00e9, R.V., and Bascompte, J. (2006). Self-Organization in Complex Ecosystems, Princeton University Press.","DOI":"10.1515\/9781400842933"},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"1889","DOI":"10.1098\/rstb.2007.0017","article-title":"Road building, land use and climate change: Prospects for environmental governance in the Amazon","volume":"363","author":"Perz","year":"2008","journal-title":"Phil. Trans. Biol. Sci"},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1016\/j.cities.2003.10.007","article-title":"Planning just-in-time versus Planning just-in-case","volume":"21","author":"Alfasi","year":"2004","journal-title":"Cities"},{"key":"ref_55","doi-asserted-by":"crossref","unstructured":"Chen, Y. (2010). Exploring the fractal parameters of urban growth and form with wave-spectrum analysis. Discrete Dynam. Nat. Soc.","DOI":"10.1155\/2010\/974917"},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1016\/j.chaos.2011.10.007","article-title":"Fractal dimension evolution and spatial replacement dynamics of urban growth","volume":"45","author":"Chen","year":"2012","journal-title":"Chaos, Soliton. Fract"},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1016\/j.foreco.2005.02.061","article-title":"Population structure and nut yield of a bertholletia excelsa stand in southwestern Amazonia","volume":"211","author":"Wadt","year":"2005","journal-title":"Forest Ecol. Manage"},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"853","DOI":"10.1038\/35002501","article-title":"Biodiversity hotspots for conservation priorities","volume":"403","author":"Myers","year":"2000","journal-title":"Nature"},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"975","DOI":"10.1007\/s10021-005-0129-z","article-title":"An exploratory framework for the empirical measurement of resilience","volume":"8","author":"Cumming","year":"2005","journal-title":"Ecosystems"},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"2555","DOI":"10.1080\/01431160050110179","article-title":"An analysis of deforestation patterns in the extractive reserves of acre, Amazonia from satellite imagery: A landscape ecological approach","volume":"21","author":"Peralta","year":"2000","journal-title":"Int. J. Remote Sens"},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1016\/S0924-2716(02)00154-5","article-title":"Scale dependence in multitemporal mapping of forest fragmentation in Bolivia: implications for explaining temporal trends in landscape ecology and applications to biodiversity conservation","volume":"57","author":"Millington","year":"2003","journal-title":"ISPRS J. Photogramm"},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"2221","DOI":"10.1080\/01431160500396550","article-title":"Spatial and temporal scale issues in determining biomass burning regimes in Bolivia and Peru","volume":"27","author":"Bradley","year":"2006","journal-title":"Int. J. Remote Sens"},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"103","DOI":"10.2307\/1941764","article-title":"Orchestrating environmental research assessment","volume":"2","author":"Levin","year":"1992","journal-title":"Ecol. Appl"},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"769","DOI":"10.1126\/science.1151419","article-title":"The size, scale, and shape of cities","volume":"319","author":"Batty","year":"2008","journal-title":"Science"}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/5\/2\/454\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:44:31Z","timestamp":1760219071000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/5\/2\/454"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,1,24]]},"references-count":64,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2013,2]]}},"alternative-id":["rs5020454"],"URL":"https:\/\/doi.org\/10.3390\/rs5020454","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,1,24]]}}}