Newer
Older
Digital_Repository / Misc / Mass downloads / UTas / 1049.html
  1. <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"
  2. "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
  3. <html>
  4. <head>
  5. <title>UTas ePrints - Determining natural scales of ecological systems</title>
  6. <script type="text/javascript" src="http://eprints.utas.edu.au/javascript/auto.js"><!-- padder --></script>
  7. <style type="text/css" media="screen">@import url(http://eprints.utas.edu.au/style/auto.css);</style>
  8. <style type="text/css" media="print">@import url(http://eprints.utas.edu.au/style/print.css);</style>
  9. <link rel="icon" href="/images/eprints/favicon.ico" type="image/x-icon" />
  10. <link rel="shortcut icon" href="/images/eprints/favicon.ico" type="image/x-icon" />
  11. <link rel="Top" href="http://eprints.utas.edu.au/" />
  12. <link rel="Search" href="http://eprints.utas.edu.au/cgi/search" />
  13. <meta content="Habeeb, Rebecca L." name="eprints.creators_name" />
  14. <meta content="Trebilco, Jessica" name="eprints.creators_name" />
  15. <meta content="Wotherspoon, Simon" name="eprints.creators_name" />
  16. <meta content="Johnson, Craig R." name="eprints.creators_name" />
  17. <meta name="eprints.creators_id" />
  18. <meta name="eprints.creators_id" />
  19. <meta name="eprints.creators_id" />
  20. <meta content="craig.johnson@utas.edu.au" name="eprints.creators_id" />
  21. <meta content="article" name="eprints.type" />
  22. <meta content="2007-05-18" name="eprints.datestamp" />
  23. <meta content="2008-02-04T05:18:40Z" name="eprints.lastmod" />
  24. <meta content="show" name="eprints.metadata_visibility" />
  25. <meta content="Determining natural scales of ecological systems
  26. " name="eprints.title" />
  27. <meta content="pub" name="eprints.ispublished" />
  28. <meta content="270702" name="eprints.subjects" />
  29. <meta content="restricted" name="eprints.full_text_status" />
  30. <meta content="attractor reconstruction; characteristic length scale; community dynamics; ecosystem; nonlinear dynamics; spatial and temporal dynamics; spatial scale; spatiotemporal models" name="eprints.keywords" />
  31. <meta content="Copyright by the Ecological Society of America." name="eprints.note" />
  32. <meta content="A key issue in ecology is to identify the appropriate scale(s) at which to observe trends in ecosystem behavior. The characteristic length scale (CLS) is a natural scale of a system at which the underlying deterministic dynamics are most clearly observed. Any approach to estimating CLSs of a natural system must be able to accommodate complex nonlinear dynamics and must have realistic requirements for data. Here, we compare the robustness of two methods to estimate CLSs of dynamical systems, both of which use attractor reconstruction to account for the complex oscillatory dynamics of ecological systems. We apply these techniques to estimate CLSs of spatial multispecies systems of varying complexity, and show that both methods are robust for the simplest system, but as model complexity increases, the Pascual and Levin metric is more robust than that of Keeling et al. Both methods demonstrate some sensitivity to the choice of species used in the analysis, with closely connected species producing more similar CLSs than loosely
  33. connected species. In this context, connectivity is determined both by the topology of the interaction network and spatial organization in the system. Notably, systems showing complex spatial self-organization can yield multiple CLSs, with larger length scales indicating the emergent dynamics of interactions between patches. While the prediction r to the power of 2 metric of Pascual and Levin is suitable to estimate CLSs of complex systems, their method is not
  34. suitable to apply to most real ecosystems because of the requirement of long time series for attractor reconstruction. We offer two alternatives, both based on prediction r to the power of 2, but where repetition in space is largely (the &quot;short time series&quot; method) or wholly (the &quot;sliding
  35. window&quot; method) substituted for repetition in time in attractor reconstruction. Both methods, and in particular the short time series based on only three or four sequential observations of a system, are robust in detecting the primary length scale of complex systems. We conclude that the modified techniques are suitable for application to natural systems. Thus they offer, for the first time, an opportunity to estimate natural scales of real ecosystems,
  36. providing objectivity in important decisions about scaling in ecology." name="eprints.abstract" />
  37. <meta content="2005-11" name="eprints.date" />
  38. <meta content="published" name="eprints.date_type" />
  39. <meta content="Ecological Monographs" name="eprints.publication" />
  40. <meta content="75" name="eprints.volume" />
  41. <meta content="4" name="eprints.number" />
  42. <meta content="467-487" name="eprints.pagerange" />
  43. <meta content="10.1890/04-1415" name="eprints.id_number" />
  44. <meta content="UNSPECIFIED" name="eprints.thesis_type" />
  45. <meta content="TRUE" name="eprints.refereed" />
  46. <meta content="http://dx.doi.org/10.1890/04-1415" name="eprints.official_url" />
  47. <meta content="Abarbanel, H. 1996. Analysis of observed chaotic data.
  48. Springer-Verlag, New York, New York, USA.
  49. Allain, C., and M. Cloitre. 1991. Characterizing the lacunarity
  50. of random and deterministic fractal sets. Physical
  51. Review A 44:3552-3558.
  52. Bishop, M. J., A. J. Underwood, and P. Archambault. 2002.
  53. Sewage and environmental impacts on rocky shores: necessity
  54. of identifying relevant spatial scales. Marine Ecology
  55. Progress Series 236:121-128.
  56. Buzug, T., and G. Pfister. 1992. Comparison of algorithms
  57. calculating optimal embedding parameters for delay time
  58. coordinates. Physica D 58:127-137.
  59. Carlile, D., J. Skalski, J. Batker, J. Thomas, and V. Cullinan.
  60. 1989. Determination of ecological scale. Landscape Ecology
  61. 2:203-213.
  62. Casdagli, M. 1989. Nonlinear prediction of chaotic time series.
  63. Physica D 35:335-356.
  64. De Roos, A., E. McCauley, and W. Wilson. 1991. Mobility
  65. versus density-limited predator-prey dynamics on different
  66. spatial scales. Proceedings of the Royal Society of London
  67. B 246:117-122.
  68. Dieckmann, U., R. Law, and J. A. J. Metz, editors. 2000.
  69. The geometry of ecological interactions: simplifying spatial
  70. complexity. Cambridge University Press, Cambridge,
  71. UK.
  72. Dunstan, P. K., and C. R. Johnson. 2005. Predicting global
  73. dynamics from local interactions: individual-based models
  74. predict complex features of marine epibenthic communities.
  75. Ecological Modelling, 186:221-233.
  76. Durrett, R., and S. A. Levin. 2000. Lessons on pattern formation
  77. from planet WATOR. Journal of Theoretical Biology
  78. 205:201-214.
  79. Ellner, S., and P. Turchin. 1995. Chaos in a noisy world: new
  80. methods and evidence from time-series analysis. American
  81. Naturalist 145:343-375.
  82. Farmer, J. 1982. Chaotic attractors of an infinite-dimensional
  83. dynamical system. Physica D 4:366-393.
  84. Greig-Smith, P. 1952. The use of random and contiguous
  85. quadrats in the study of the structure of plant communities.
  86. Annals of Botany 16:293-316.
  87. Hastings, A., C. L. Hom, S. Ellner, P. Turchin, and H. C. J.
  88. Godfray. 1993. Chaos in ecology: is mother nature a
  89. strange attractor? Annual Review of Ecology and Systematics
  90. 24:1-33.
  91. Johnson, C. R. 1997. Self-organising in spatial competition
  92. systems. Pages 245-263 in N. Klomp and I. Lunt, editors.
  93. Frontiers in ecology: building the links. Elsevier, Oxford,
  94. UK.
  95. Johnson, C. R., D. Klumpp, J. Field, and R. Bradbury. 1995.
  96. Carbon flux on coral reefs: effects of large shifts in community
  97. structure. Marine Ecology Progress Series 126:123-
  98. 143.
  99. Johnson, C. R., and K. H. Mann. 1988. Diversity, patterns
  100. of adaptation, and stability of Nova Scotian kelp beds. Ecological
  101. Monographs 58:129-154.
  102. Johnson, C. R., and I. Seinen. 2002. Selection for restraint
  103. in competitive ability in spatial competition systems. Proceedings
  104. of the Royal Society of London B 269:655-663.
  105. Kantz, H., and T. Schreiber. 1997. Nonlinear time series analysis.
  106. Cambridge University Press, Cambridge, UK.
  107. Kaplan, D., and L. Glass. 1995. Understanding nonlinear
  108. dynamics. Springer-Verlag, New York, New York, USA.
  109. Keeling, M. J., I. Mezic, R. Hendry, J. Mcglade, and D. Rand.
  110. 1997. Characteristic length scales of spatial models in ecology
  111. via fluctuation analysis. Philisophical Transactions of
  112. the Royal Society of London B 352:1589-1601.
  113. Kennel, M. B., R. Brown, and H. D. I. Abarbanel. 1994.
  114. Determining embedding dimension for phase-space reconstruction
  115. using a geometrical construction. Physics Review
  116. A 45:3403-3411.
  117. Kershaw, K. A. 1957. The use of cover and frequency in the
  118. detection of pattern in plant communities. Ecology 38:291-
  119. 299.
  120. Levin, S. A. 1992. The problem of pattern and scale in ecology.
  121. Ecology 73:1943-1967.
  122. Levin, S. A. 2000. Multiple scales and the maintenance of
  123. biodiversity. Ecosystems 3:498-506.
  124. Levin, S. A., B. Grenfell, A. Hastings, and A. S. Perelson.
  125. 1997. Mathematical and computational challenges in population
  126. biology and ecosystems science. Science 275:334-
  127. 343.
  128. Liebert, W., and H. Schuster. 1989. Proper choice of the time
  129. delay for the analysis of chaotic time series. Physics Letters
  130. A 142:107-111.
  131. Little, S., S. Ellner, M. Pascual, M. Neubert, D. Kaplan, T.
  132. Sauer, H. Caswell, and A. Solow. 1996. Detecting nonlinear
  133. dynamics in spatio-temporal systems, examples from
  134. ecological models. Physica D 96:321-333.
  135. Marcos-Nikolaus, P., J. M. Martin-Gonzalez, and R. V. Sole.
  136. 2002. Spatial forecasting: detecting determinism from single
  137. snapshots. International Journal of Bifurcation and Chaos
  138. 12:369-376.
  139. Molofsky, J., J. Bever, J. Antonovics, and T. Newmaan. 2002.
  140. Negative frequency dependence and the importance of spatial
  141. scale. Ecology 83:21-27.
  142. Nichols, J. M., and J. D. Nichols. 2001. Attractor reconstruction
  143. for non-linear systems: a methodological note. Mathematical
  144. Biosciences 171:21-32 ™Neill, R. V., D. L. DeAngelis, J. B. Waide, and T. F. H.
  145. Allen. 1986. A hierarchical concept of ecosystems. Princeton
  146. University Press, Princeton, New Jersey, USA.
  147. Pascual, M., and S. Ellner. 2000. Linking ecological patterns
  148. to environmental forcing via nonlinear time series models.
  149. Ecology 81:2767-2780.
  150. Pascual, M., and S. A. Levin. 1999. From individuals to
  151. population densities: searching for the intermediate scale
  152. of nontrivial determinism. Ecology 80:2225-2236.
  153. Plotnick, R. E., R. H. Gardner, W. W. Hargrove, K. Prestegaard,
  154. and M. Perlmutter. 1996. Lacunarity analysis: a general
  155. technique for the analysis of spatial patterns. Physical
  156. Review E 53:5461-5468.
  157. Rand, D. 1994. Measuring and characterizing spatial patterns,
  158. dynamics and chaos in spatially extended dynamical
  159. systems and ecologies. Philisophical Transactions of the
  160. Royal Society of London A 348:497-514.
  161. Rand, D., and H. Wilson. 1995. Using spatio-temporal chaos
  162. and intermediate-scale determinism to quantify spatially
  163. extended ecosystems. Proceedings of the Royal Society of
  164. London B 259:111-117.
  165. Schneider, D. C. 1994. Quantitative ecology: spatial and temporal
  166. scaling. Academic Press, San Diego.
  167. Schreiber, T. 1995. Efficient neighbor searching in nonlinear
  168. time series analysis. International Journal of Bifurcation
  169. and Chaos 5:349-358.
  170. Schreiber, T. 1999. Interdisciplinary application of nonlinear
  171. time series methods. Physics Reports 308:2-64.
  172. Sole, R. V., and J. Bascompte. 1995. Measuring chaos from
  173. spatial information. Journal of Theoretical Biology 175:
  174. 139-147.
  175. Sugihara, G., B. Grenfell, and R. M. May. 1990. Distinguishing
  176. error from chaos in ecological time series. Philisophical
  177. Transactions of the Royal Society of London B
  178. 330:235-251.
  179. Takens, F. 1981. Detecting strange attractors in turbulence.
  180. Pages 366-381 in D. Rand and L. Young, editors. Dynamical
  181. systems and turbulence, Warwick 1980. Lecture notes
  182. in mathematics. Springer-Verlag, New York, New York,
  183. USA.
  184. Tilman, D., and P. Kareiva, editors. 1997. Spatial ecology:
  185. the role of space in population dynamics and interspecific
  186. interactions. Princeton University Press, Princeton, New
  187. Jersey, USA.
  188. Turner, S., R. V. ™Neill, W. Conley, M. Conley, and H.
  189. Humphries. 1991. Pattern and scale: Statistics for landscape
  190. ecology. Pages 17-47 in S. J. Turner and R. H. Gardner,
  191. editors. Quantitative methods in landscape ecology.
  192. Springer Verlag, New York, New York, USA.
  193. Tyre, A. J., H. P. Possingham, and C. M. Bull. 1997. Characteristic
  194. scales in ecology: fact, fiction or futility. Pages
  195. 233-243 in N. Klomp and I. Lunt, editors. Frontiers in
  196. ecology. Elsevier Science, New York, New York, USA.
  197. Wiens, J. 1989. Spatial scaling in ecology. Functional Ecology
  198. 3:385-397.
  199. Wilson, H. B., and M. J. Keeling. 2000. Spatial scales and
  200. low dimensional deterministic dynamics. Pages 209-226
  201. in U. Dieckmann, R. Law, and J. A. J. Metz, editors. The
  202. geometry of ecological interactions: simplifying spatial
  203. complexity. Cambridge University Press, Cambridge, UK." name="eprints.referencetext" />
  204. <meta content="Habeeb, Rebecca L. and Trebilco, Jessica and Wotherspoon, Simon and Johnson, Craig R. (2005) Determining natural scales of ecological systems. Ecological Monographs, 75 (4). pp. 467-487." name="eprints.citation" />
  205. <meta content="http://eprints.utas.edu.au/1049/1/2005_Habeeb%2C_Trebilco%2C_Wotherspoon_%26_Johnson_Ecol_Monogr.pdf" name="eprints.document_url" />
  206. <link rel="schema.DC" href="http://purl.org/DC/elements/1.0/" />
  207. <meta content="Determining natural scales of ecological systems
  208. " name="DC.title" />
  209. <meta content="Habeeb, Rebecca L." name="DC.creator" />
  210. <meta content="Trebilco, Jessica" name="DC.creator" />
  211. <meta content="Wotherspoon, Simon" name="DC.creator" />
  212. <meta content="Johnson, Craig R." name="DC.creator" />
  213. <meta content="270702 Marine and Estuarine Ecology (incl. Marine Ichthyology)" name="DC.subject" />
  214. <meta content="A key issue in ecology is to identify the appropriate scale(s) at which to observe trends in ecosystem behavior. The characteristic length scale (CLS) is a natural scale of a system at which the underlying deterministic dynamics are most clearly observed. Any approach to estimating CLSs of a natural system must be able to accommodate complex nonlinear dynamics and must have realistic requirements for data. Here, we compare the robustness of two methods to estimate CLSs of dynamical systems, both of which use attractor reconstruction to account for the complex oscillatory dynamics of ecological systems. We apply these techniques to estimate CLSs of spatial multispecies systems of varying complexity, and show that both methods are robust for the simplest system, but as model complexity increases, the Pascual and Levin metric is more robust than that of Keeling et al. Both methods demonstrate some sensitivity to the choice of species used in the analysis, with closely connected species producing more similar CLSs than loosely
  215. connected species. In this context, connectivity is determined both by the topology of the interaction network and spatial organization in the system. Notably, systems showing complex spatial self-organization can yield multiple CLSs, with larger length scales indicating the emergent dynamics of interactions between patches. While the prediction r to the power of 2 metric of Pascual and Levin is suitable to estimate CLSs of complex systems, their method is not
  216. suitable to apply to most real ecosystems because of the requirement of long time series for attractor reconstruction. We offer two alternatives, both based on prediction r to the power of 2, but where repetition in space is largely (the &quot;short time series&quot; method) or wholly (the &quot;sliding
  217. window&quot; method) substituted for repetition in time in attractor reconstruction. Both methods, and in particular the short time series based on only three or four sequential observations of a system, are robust in detecting the primary length scale of complex systems. We conclude that the modified techniques are suitable for application to natural systems. Thus they offer, for the first time, an opportunity to estimate natural scales of real ecosystems,
  218. providing objectivity in important decisions about scaling in ecology." name="DC.description" />
  219. <meta content="2005-11" name="DC.date" />
  220. <meta content="Article" name="DC.type" />
  221. <meta content="PeerReviewed" name="DC.type" />
  222. <meta content="application/pdf" name="DC.format" />
  223. <meta content="http://eprints.utas.edu.au/1049/1/2005_Habeeb%2C_Trebilco%2C_Wotherspoon_%26_Johnson_Ecol_Monogr.pdf" name="DC.identifier" />
  224. <meta content="http://dx.doi.org/10.1890/04-1415" name="DC.relation" />
  225. <meta content="Habeeb, Rebecca L. and Trebilco, Jessica and Wotherspoon, Simon and Johnson, Craig R. (2005) Determining natural scales of ecological systems. Ecological Monographs, 75 (4). pp. 467-487." name="DC.identifier" />
  226. <meta content="http://eprints.utas.edu.au/1049/" name="DC.relation" />
  227. <link rel="alternate" href="http://eprints.utas.edu.au/cgi/export/1049/BibTeX/epprod-eprint-1049.bib" title="BibTeX" type="text/plain" />
  228. <link rel="alternate" href="http://eprints.utas.edu.au/cgi/export/1049/ContextObject/epprod-eprint-1049.xml" title="OpenURL ContextObject" type="text/xml" />
  229. <link rel="alternate" href="http://eprints.utas.edu.au/cgi/export/1049/ContextObject::Dissertation/epprod-eprint-1049.xml" title="OpenURL Dissertation" type="text/xml" />
  230. <link rel="alternate" href="http://eprints.utas.edu.au/cgi/export/1049/ContextObject::Journal/epprod-eprint-1049.xml" title="OpenURL Journal" type="text/xml" />
  231. <link rel="alternate" href="http://eprints.utas.edu.au/cgi/export/1049/DC/epprod-eprint-1049.txt" title="Dublin Core" type="text/plain" />
  232. <link rel="alternate" href="http://eprints.utas.edu.au/cgi/export/1049/DIDL/epprod-eprint-1049.xml" title="DIDL" type="text/xml" />
  233. <link rel="alternate" href="http://eprints.utas.edu.au/cgi/export/1049/EndNote/epprod-eprint-1049.enw" title="EndNote" type="text/plain" />
  234. <link rel="alternate" href="http://eprints.utas.edu.au/cgi/export/1049/HTML/epprod-eprint-1049.html" title="HTML Citation" type="text/html; charset=utf-8" />
  235. <link rel="alternate" href="http://eprints.utas.edu.au/cgi/export/1049/METS/epprod-eprint-1049.xml" title="METS" type="text/xml" />
  236. <link rel="alternate" href="http://eprints.utas.edu.au/cgi/export/1049/MODS/epprod-eprint-1049.xml" title="MODS" type="text/xml" />
  237. <link rel="alternate" href="http://eprints.utas.edu.au/cgi/export/1049/RIS/epprod-eprint-1049.ris" title="Reference Manager" type="text/plain" />
  238. <link rel="alternate" href="http://eprints.utas.edu.au/cgi/export/1049/Refer/epprod-eprint-1049.refer" title="Refer" type="text/plain" />
  239. <link rel="alternate" href="http://eprints.utas.edu.au/cgi/export/1049/Simple/epprod-eprint-1049text" title="Simple Metadata" type="text/plain" />
  240. <link rel="alternate" href="http://eprints.utas.edu.au/cgi/export/1049/Text/epprod-eprint-1049.txt" title="ASCII Citation" type="text/plain; charset=utf-8" />
  241. <link rel="alternate" href="http://eprints.utas.edu.au/cgi/export/1049/XML/epprod-eprint-1049.xml" title="EP3 XML" type="text/xml" />
  242.  
  243. </head>
  244. <body bgcolor="#ffffff" text="#000000" onLoad="loadRoutine(); MM_preloadImages('images/eprints/ePrints_banner_r5_c5_f2.gif','images/eprints/ePrints_banner_r5_c7_f2.gif','images/eprints/ePrints_banner_r5_c8_f2.gif','images/eprints/ePrints_banner_r5_c9_f2.gif','images/eprints/ePrints_banner_r5_c10_f2.gif','images/eprints/ePrints_banner_r5_c11_f2.gif','images/eprints/ePrints_banner_r6_c4_f2.gif')">
  245. <div class="ep_noprint"><noscript><style type="text/css">@import url(http://eprints.utas.edu.au/style/nojs.css);</style></noscript></div>
  246.  
  247.  
  248.  
  249.  
  250. <table width="795" border="0" cellspacing="0" cellpadding="0">
  251. <tr>
  252. <td><script language="JavaScript1.2">mmLoadMenus();</script>
  253. <table border="0" cellpadding="0" cellspacing="0" width="795">
  254. <!-- fwtable fwsrc="eprints_banner_final2.png" fwbase="ePrints_banner.gif" fwstyle="Dreamweaver" fwdocid = "1249563342" fwnested="0" -->
  255. <tr>
  256. <td><img src="/images/eprints/spacer.gif" width="32" height="1" border="0" alt="" /></td>
  257. <td><img src="/images/eprints/spacer.gif" width="104" height="1" border="0" alt="" /></td>
  258. <td><img src="/images/eprints/spacer.gif" width="44" height="1" border="0" alt="" /></td>
  259. <td><img src="/images/eprints/spacer.gif" width="105" height="1" border="0" alt="" /></td>
  260. <td><img src="/images/eprints/spacer.gif" width="41" height="1" border="0" alt="" /></td>
  261. <td><img src="/images/eprints/spacer.gif" width="16" height="1" border="0" alt="" /></td>
  262. <td><img src="/images/eprints/spacer.gif" width="68" height="1" border="0" alt="" /></td>
  263. <td><img src="/images/eprints/spacer.gif" width="68" height="1" border="0" alt="" /></td>
  264. <td><img src="/images/eprints/spacer.gif" width="68" height="1" border="0" alt="" /></td>
  265. <td><img src="/images/eprints/spacer.gif" width="82" height="1" border="0" alt="" /></td>
  266. <td><img src="/images/eprints/spacer.gif" width="69" height="1" border="0" alt="" /></td>
  267. <td><img src="/images/eprints/spacer.gif" width="98" height="1" border="0" alt="" /></td>
  268. <td><img src="/images/eprints/spacer.gif" width="1" height="1" border="0" alt="" /></td>
  269. </tr>
  270. <tr>
  271. <td colspan="12"><img name="ePrints_banner_r1_c1" src="/images/eprints/ePrints_banner_r1_c1.gif" width="795" height="10" border="0" alt="" /></td>
  272. <td><img src="/images/eprints/spacer.gif" width="1" height="10" border="0" alt="" /></td>
  273. </tr>
  274. <tr>
  275. <td rowspan="6"><img name="ePrints_banner_r2_c1" src="/images/eprints/ePrints_banner_r2_c1.gif" width="32" height="118" border="0" alt="" /></td>
  276. <td rowspan="5"><a href="http://www.utas.edu.au/"><img name="ePrints_banner_r2_c2" src="/images/eprints/ePrints_banner_r2_c2.gif" width="104" height="103" border="0" alt="" /></a></td>
  277. <td colspan="10"><img name="ePrints_banner_r2_c3" src="/images/eprints/ePrints_banner_r2_c3.gif" width="659" height="41" border="0" alt="" /></td>
  278. <td><img src="/images/eprints/spacer.gif" width="1" height="41" border="0" alt="" /></td>
  279. </tr>
  280. <tr>
  281. <td colspan="3"><a href="http://eprints.utas.edu.au/"><img name="ePrints_banner_r3_c3" src="/images/eprints/ePrints_banner_r3_c3.gif" width="190" height="31" border="0" alt="" /></a></td>
  282. <td rowspan="2" colspan="7"><img name="ePrints_banner_r3_c6" src="/images/eprints/ePrints_banner_r3_c6.gif" width="469" height="37" border="0" alt="" /></td>
  283. <td><img src="/images/eprints/spacer.gif" width="1" height="31" border="0" alt="" /></td>
  284. </tr>
  285. <tr>
  286. <td colspan="3"><img name="ePrints_banner_r4_c3" src="/images/eprints/ePrints_banner_r4_c3.gif" width="190" height="6" border="0" alt="" /></td>
  287. <td><img src="/images/eprints/spacer.gif" width="1" height="6" border="0" alt="" /></td>
  288. </tr>
  289. <tr>
  290. <td colspan="2"><img name="ePrints_banner_r5_c3" src="/images/eprints/ePrints_banner_r5_c3.gif" width="149" height="1" border="0" alt="" /></td>
  291. <td rowspan="2" colspan="2"><a href="/information.html" onMouseOut="MM_swapImgRestore();MM_startTimeout()" onMouseOver="MM_showMenu(window.mm_menu_0821132634_0,0,25,null,'ePrints_banner_r5_c5');MM_swapImage('ePrints_banner_r5_c5','','/images/eprints/ePrints_banner_r5_c5_f2.gif',1);"><img name="ePrints_banner_r5_c5" src="/images/eprints/ePrints_banner_r5_c5.gif" width="57" height="25" border="0" alt="About" /></a></td>
  292. <td rowspan="2"><a href="/view/" onMouseOut="MM_swapImgRestore();MM_startTimeout()" onMouseOver="MM_showMenu(window.mm_menu_0821133021_1,0,25,null,'ePrints_banner_r5_c7');MM_swapImage('ePrints_banner_r5_c7','','/images/eprints/ePrints_banner_r5_c7_f2.gif',1);"><img name="ePrints_banner_r5_c7" src="/images/eprints/ePrints_banner_r5_c7.gif" width="68" height="25" border="0" alt="Browse" /></a></td>
  293. <td rowspan="2"><a href="/perl/search/simple" onMouseOut="MM_swapImgRestore();MM_startTimeout()" onMouseOver="MM_showMenu(window.mm_menu_0821133201_2,0,25,null,'ePrints_banner_r5_c8');MM_swapImage('ePrints_banner_r5_c8','','/images/eprints/ePrints_banner_r5_c8_f2.gif',1);"><img name="ePrints_banner_r5_c8" src="/images/eprints/ePrints_banner_r5_c8.gif" width="68" height="25" border="0" alt="Search" /></a></td>
  294. <td rowspan="2"><a href="/perl/register" onMouseOut="MM_swapImgRestore();MM_startTimeout();" onMouseOver="MM_showMenu(window.mm_menu_1018171924_3,0,25,null,'ePrints_banner_r5_c9');MM_swapImage('ePrints_banner_r5_c9','','/images/eprints/ePrints_banner_r5_c9_f2.gif',1);"><img name="ePrints_banner_r5_c9" src="/images/eprints/ePrints_banner_r5_c9.gif" width="68" height="25" border="0" alt="register" /></a></td>
  295. <td rowspan="2"><a href="/perl/users/home" onMouseOut="MM_swapImgRestore();MM_startTimeout()" onMouseOver="MM_showMenu(window.mm_menu_0821133422_4,0,25,null,'ePrints_banner_r5_c10');MM_swapImage('ePrints_banner_r5_c10','','/images/eprints/ePrints_banner_r5_c10_f2.gif',1);"><img name="ePrints_banner_r5_c10" src="/images/eprints/ePrints_banner_r5_c10.gif" width="82" height="25" border="0" alt="user area" /></a></td>
  296. <td rowspan="2"><a href="/help/" onMouseOut="MM_swapImgRestore();MM_startTimeout()" onMouseOver="MM_showMenu(window.mm_menu_0821133514_5,0,25,null,'ePrints_banner_r5_c11');MM_swapImage('ePrints_banner_r5_c11','','/images/eprints/ePrints_banner_r5_c11_f2.gif',1);"><img name="ePrints_banner_r5_c11" src="/images/eprints/ePrints_banner_r5_c11.gif" width="69" height="25" border="0" alt="Help" /></a></td>
  297. <td rowspan="3" colspan="4"><img name="ePrints_banner_r5_c12" src="/images/eprints/ePrints_banner_r5_c12.gif" width="98" height="40" border="0" alt="" /></td>
  298. <td><img src="/images/eprints/spacer.gif" width="1" height="1" border="0" alt="" /></td>
  299. </tr>
  300. <tr>
  301. <td rowspan="2"><img name="ePrints_banner_r6_c3" src="/images/eprints/ePrints_banner_r6_c3.gif" width="44" height="39" border="0" alt="ePrints home" /></td>
  302. <td><a href="/" onMouseOut="MM_swapImgRestore()" onMouseOver="MM_swapImage('ePrints_banner_r6_c4','','/images/eprints/ePrints_banner_r6_c4_f2.gif',1);"><img name="ePrints_banner_r6_c4" src="/images/eprints/ePrints_banner_r6_c4.gif" width="105" height="24" border="0" alt="ePrints home" /></a></td>
  303. <td><img src="/images/eprints/spacer.gif" width="1" height="24" border="0" alt="" /></td>
  304. </tr>
  305. <tr>
  306. <td><img name="ePrints_banner_r7_c2" src="/images/eprints/ePrints_banner_r7_c2.gif" width="104" height="15" border="0" alt="" /></td>
  307. <td colspan="8"><img name="ePrints_banner_r7_c4" src="/images/eprints/ePrints_banner_r7_c4.gif" width="517" height="15" border="0" alt="" /></td>
  308. <td><img src="/images/eprints/spacer.gif" width="1" height="15" border="0" alt="" /></td>
  309. </tr>
  310. </table></td>
  311. </tr>
  312. <tr><td><table width="100%" style="font-size: 90%; border: solid 1px #ccc; padding: 3px"><tr>
  313. <td align="left"><a href="http://eprints.utas.edu.au/cgi/users/home">Login</a> | <a href="http://eprints.utas.edu.au/cgi/register">Create Account</a></td>
  314. <td align="right" style="white-space: nowrap">
  315. <form method="get" accept-charset="utf-8" action="http://eprints.utas.edu.au/cgi/search" style="display:inline">
  316. <input class="ep_tm_searchbarbox" size="20" type="text" name="q" />
  317. <input class="ep_tm_searchbarbutton" value="Search" type="submit" name="_action_search" />
  318. <input type="hidden" name="_order" value="bytitle" />
  319. <input type="hidden" name="basic_srchtype" value="ALL" />
  320. <input type="hidden" name="_satisfyall" value="ALL" />
  321. </form>
  322. </td>
  323. </tr></table></td></tr>
  324. <tr>
  325. <td class="toplinks"><!-- InstanceBeginEditable name="content" -->
  326.  
  327.  
  328. <div align="center">
  329. <table width="720" class="ep_tm_main"><tr><td align="left">
  330. <h1 class="ep_tm_pagetitle">Determining natural scales of ecological systems</h1>
  331. <p style="margin-bottom: 1em" class="not_ep_block"><span class="person_name">Habeeb, Rebecca L.</span> and <span class="person_name">Trebilco, Jessica</span> and <span class="person_name">Wotherspoon, Simon</span> and <span class="person_name">Johnson, Craig R.</span> (2005) <xhtml:em>Determining natural scales of ecological systems.</xhtml:em> Ecological Monographs, 75 (4). pp. 467-487.</p><p style="margin-bottom: 1em" class="not_ep_block"></p><table style="margin-bottom: 1em" class="not_ep_block"><tr><td valign="top" style="text-align:center"><a href="http://eprints.utas.edu.au/1049/1/2005_Habeeb%2C_Trebilco%2C_Wotherspoon_%26_Johnson_Ecol_Monogr.pdf"><img alt="[img]" src="http://eprints.utas.edu.au/style/images/fileicons/application_pdf.png" border="0" class="ep_doc_icon" /></a></td><td valign="top"><a href="http://eprints.utas.edu.au/1049/1/2005_Habeeb%2C_Trebilco%2C_Wotherspoon_%26_Johnson_Ecol_Monogr.pdf"><span class="ep_document_citation">PDF</span></a> - Full text restricted - Requires a PDF viewer<br />2396Kb</td><td><form method="get" accept-charset="utf-8" action="http://eprints.utas.edu.au/cgi/request_doc"><input value="1229" name="docid" accept-charset="utf-8" type="hidden" /><div class=""><input value="Request a copy" name="_action_null" class="ep_form_action_button" onclick="return EPJS_button_pushed( '_action_null' )" type="submit" /> </div></form></td></tr></table><p style="margin-bottom: 1em" class="not_ep_block">Official URL: <a href="http://dx.doi.org/10.1890/04-1415">http://dx.doi.org/10.1890/04-1415</a></p><div class="not_ep_block"><h2>Abstract</h2><p style="padding-bottom: 16px; text-align: left; margin: 1em auto 0em auto">A key issue in ecology is to identify the appropriate scale(s) at which to observe trends in ecosystem behavior. The characteristic length scale (CLS) is a natural scale of a system at which the underlying deterministic dynamics are most clearly observed. Any approach to estimating CLSs of a natural system must be able to accommodate complex nonlinear dynamics and must have realistic requirements for data. Here, we compare the robustness of two methods to estimate CLSs of dynamical systems, both of which use attractor reconstruction to account for the complex oscillatory dynamics of ecological systems. We apply these techniques to estimate CLSs of spatial multispecies systems of varying complexity, and show that both methods are robust for the simplest system, but as model complexity increases, the Pascual and Levin metric is more robust than that of Keeling et al. Both methods demonstrate some sensitivity to the choice of species used in the analysis, with closely connected species producing more similar CLSs than loosely&#13;
  332. connected species. In this context, connectivity is determined both by the topology of the interaction network and spatial organization in the system. Notably, systems showing complex spatial self-organization can yield multiple CLSs, with larger length scales indicating the emergent dynamics of interactions between patches. While the prediction r to the power of 2 metric of Pascual and Levin is suitable to estimate CLSs of complex systems, their method is not&#13;
  333. suitable to apply to most real ecosystems because of the requirement of long time series for attractor reconstruction. We offer two alternatives, both based on prediction r to the power of 2, but where repetition in space is largely (the "short time series" method) or wholly (the "sliding&#13;
  334. window" method) substituted for repetition in time in attractor reconstruction. Both methods, and in particular the short time series based on only three or four sequential observations of a system, are robust in detecting the primary length scale of complex systems. We conclude that the modified techniques are suitable for application to natural systems. Thus they offer, for the first time, an opportunity to estimate natural scales of real ecosystems,&#13;
  335. providing objectivity in important decisions about scaling in ecology.</p></div><table style="margin-bottom: 1em" border="0" cellpadding="3" class="not_ep_block"><tr><th valign="top" class="ep_row">Item Type:</th><td valign="top" class="ep_row">Article</td></tr><tr><th valign="top" class="ep_row">Additional Information:</th><td valign="top" class="ep_row">Copyright by the Ecological Society of America.</td></tr><tr><th valign="top" class="ep_row">Keywords:</th><td valign="top" class="ep_row">attractor reconstruction; characteristic length scale; community dynamics; ecosystem; nonlinear dynamics; spatial and temporal dynamics; spatial scale; spatiotemporal models</td></tr><tr><th valign="top" class="ep_row">Subjects:</th><td valign="top" class="ep_row"><a href="http://eprints.utas.edu.au/view/subjects/270702.html">270000 Biological Sciences &gt; 270700 Ecology and Evolution &gt; 270702 Marine and Estuarine Ecology (incl. Marine Ichthyology)</a></td></tr><tr><th valign="top" class="ep_row">Collections:</th><td valign="top" class="ep_row">UNSPECIFIED</td></tr><tr><th valign="top" class="ep_row">ID Code:</th><td valign="top" class="ep_row">1049</td></tr><tr><th valign="top" class="ep_row">Deposited By:</th><td valign="top" class="ep_row"><span class="ep_name_citation"><span class="person_name">Professor Craig R. Johnson</span></span></td></tr><tr><th valign="top" class="ep_row">Deposited On:</th><td valign="top" class="ep_row">18 May 2007</td></tr><tr><th valign="top" class="ep_row">Last Modified:</th><td valign="top" class="ep_row">04 Feb 2008 16:18</td></tr><tr><th valign="top" class="ep_row">ePrint Statistics:</th><td valign="top" class="ep_row"><a target="ePrintStats" href="/es/index.php?action=show_detail_eprint;id=1049;">View statistics for this ePrint</a></td></tr></table><p align="right">Repository Staff Only: <a href="http://eprints.utas.edu.au/cgi/users/home?screen=EPrint::View&amp;eprintid=1049">item control page</a></p>
  336. </td></tr></table>
  337. </div>
  338.  
  339.  
  340.  
  341. <!-- InstanceEndEditable --></td>
  342. </tr>
  343. <tr>
  344. <td><!-- #BeginLibraryItem "/Library/footer_eprints.lbi" -->
  345. <table width="795" border="0" align="left" cellpadding="0" class="footer">
  346. <tr valign="top">
  347. <td colspan="2"><div align="center"><a href="http://www.utas.edu.au">UTAS home</a> | <a href="http://www.utas.edu.au/library/">Library home</a> | <a href="/">ePrints home</a> | <a href="/contact.html">contact</a> | <a href="/information.html">about</a> | <a href="/view/">browse</a> | <a href="/perl/search/simple">search</a> | <a href="/perl/register">register</a> | <a href="/perl/users/home">user area</a> | <a href="/help/">help</a></div><br /></td>
  348. </tr>
  349. <tr><td colspan="2"><p><img src="/images/eprints/footerline.gif" width="100%" height="4" /></p></td></tr>
  350. <tr valign="top">
  351. <td width="68%" class="footer">Authorised by the University Librarian<br />
  352. © University of Tasmania ABN 30 764 374 782<br />
  353. <a href="http://www.utas.edu.au/cricos/">CRICOS Provider Code 00586B</a> | <a href="http://www.utas.edu.au/copyright/copyright_disclaimers.html">Copyright &amp; Disclaimers</a> | <a href="http://www.utas.edu.au/accessibility/index.html">Accessibility</a> | <a href="http://eprints.utas.edu.au/feedback/">Site Feedback</a>  </td>
  354. <td width="32%"><div align="right">
  355. <p align="right" class="NoPrint"><a href="http://www.utas.edu.au/"><img src="http://www.utas.edu.au/shared/logos/unioftasstrip.gif" alt="University of Tasmania Home Page" width="260" height="16" border="0" align="right" /></a></p>
  356. <p align="right" class="NoPrint"><a href="http://www.utas.edu.au/"><br />
  357. </a></p>
  358. </div></td>
  359. </tr>
  360. <tr valign="top">
  361. <td><p>  </p></td>
  362. <td><div align="right"><span class="NoPrint"><a href="http://www.eprints.org/software/"><img src="/images/eprintslogo.gif" alt="ePrints logo" width="77" height="29" border="0" align="bottom" /></a></span></div></td>
  363. </tr>
  364. </table>
  365. <!-- #EndLibraryItem -->
  366. <div align="center"></div></td>
  367. </tr>
  368. </table>
  369.  
  370. </body>
  371. </html>