<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> <html> <head> <title>UTas ePrints - Stability in paradigm biological systems</title> <script type="text/javascript" src="http://eprints.utas.edu.au/javascript/auto.js"><!-- padder --></script> <style type="text/css" media="screen">@import url(http://eprints.utas.edu.au/style/auto.css);</style> <style type="text/css" media="print">@import url(http://eprints.utas.edu.au/style/print.css);</style> <link rel="icon" href="/images/eprints/favicon.ico" type="image/x-icon" /> <link rel="shortcut icon" href="/images/eprints/favicon.ico" type="image/x-icon" /> <link rel="Top" href="http://eprints.utas.edu.au/" /> <link rel="Search" href="http://eprints.utas.edu.au/cgi/search" /> <meta content="Rixon, Andrew J." name="eprints.creators_name" /> <meta content="Johnson, Craig R." name="eprints.creators_name" /> <meta content="Jones, Alan S." name="eprints.creators_name" /> <meta name="eprints.creators_id" /> <meta content="Craig.Johnson@utas.edu.au" name="eprints.creators_id" /> <meta name="eprints.creators_id" /> <meta content="article" name="eprints.type" /> <meta content="2007-06-24" name="eprints.datestamp" /> <meta content="2008-02-04T06:03:58Z" name="eprints.lastmod" /> <meta content="show" name="eprints.metadata_visibility" /> <meta content="Stability in paradigm biological systems" name="eprints.title" /> <meta content="pub" name="eprints.ispublished" /> <meta content="239901" name="eprints.subjects" /> <meta content="270702" name="eprints.subjects" /> <meta content="restricted" name="eprints.full_text_status" /> <meta content="A discrete spatial model of a multi-species environment is formulated, and the behaviour of the system is studied. The model is used to explore stability and resilience of biological systems and discuss how they are dependent on spatial scale chosen. " name="eprints.abstract" /> <meta content="1998-07" name="eprints.date" /> <meta content="published" name="eprints.date_type" /> <meta content="Journal of the Australian Mathematical Society - Series B" name="eprints.publication" /> <meta content="40" name="eprints.volume" /> <meta content="1" name="eprints.number" /> <meta content="23-34" name="eprints.pagerange" /> <meta content="UNSPECIFIED" name="eprints.thesis_type" /> <meta content="TRUE" name="eprints.refereed" /> <meta content="0334-2700" name="eprints.issn" /> <meta content="http://www.austms.org.au/Publ/Jamsb/V40P1/abs/1500/" name="eprints.official_url" /> <meta content="[1] W. Brown, "Cheat thy neighbour -a recipe for success", New Scientist 9 (1993) 19-20. [2] H. N. Commins, R. M. May and M. P. Hassel, "Spatial structure and chaos in insect population dynamics", Nature 353 (1991) 255-258. [3] J. H. Connel andW. P. Sousa, "On the evidence needed to judge ecological stability or persistence", American Naturalist 121 (1983) 789-824. [4] P. Davis, "Order in evolutionary chaos", Guardian Weekly 23 Jan (1994) . [5] H. T. Dublin, A. R. E. Sinclair and J. McGlade, "Elephants and fire as causes of multiple stable states in SerengetiMara woodlands", J. Animal Ecology 59 (1990) 1147-1164. [6] M. J. Feigenbaum, "Universal behaviour in nonlinear systems", Physica 7D (1983) 16-39. [7] B. S. Goh, "Global stability in two species interactions", J. Math. Biol. 3 (1976) 313 - 318. [8] A. Hastings, "Food web theory and stability", Ecology 69 (1988) 1665-1668. [9] A. Hastings and K. Higgins, "Persistence of transients in spatially structured ecological models", Science 263 (1994) 1133-1136. [10] R. H. G. Helleman, G. Iooss and R. Stora, "Chaotic behaviour of deterministic systems", Les Houches 85-134. [11] P. Hogeweg, "Cellular automata as paradigm for ecological modelling", Appl. Math. Comp. 27 (1988) 81-100. [12] A. V. Holden, Chaos (Manchester University Press Publications, 1987). [13] C. S. Holling, "Resilience and stability of ecological systems", A. Rev. Ecol. Syst. 4 (1973) 1-23. [14] N. Knowlton, "Thresholds and multiple stable states in coral reef dynamics", Amer. Zool. 32 (1990) 674-682. [15] C. G. Langton, "Studying artificial life with cellular automata", Physica 22D (1986) 120-149. [16] R. C. Lewontin, "The meaning of stability", Brookhaven Symp. Biol. 22 (1969) 13 - 23. [17] R. M. May, "Stability and complexity in model ecosystems", Nature 238 (1972) 413-414. [18] R. M. May, "Will a large complex system be stable?", Nature 238 (1972) 413-414. [19] R. M. May, "Simple mathematical models with very complicated dynamics", Nature 261 (1976) 459-466. [20] R. M. May, "Thresholds and breakpoints in ecosystems with a multiplicity of stable states", Nature 269 (1977) 471-477. [21] R. M. May and M. A. Novak, "Evolutionary games and spatial chaos", Nature 359 (1992) 826-829. [22] R. M. May and M. A. Novak, "Spatial dilemmas of evolution", Int. J. Bifurcation and Chaos in applied Sciences and Engineering 3 (1993) 35-78. [23] C. H. Peterson, "Does a rigorous criterion for environmental identity preclude the existence of multiple stable points?", Am. Nat. 132 (1984) 652-661. [24] S. L. Pimm, "Food web design and the effect of species deletion", OIKOS 35 (1980) 139-149. [25] I. Stewart, Does God Play Dice? (Penguin Publications, 1989). [26] J. P. Sutherland, "Perturbations, resistance, and alternative views of the existence of multiple stable points in nature", Am. Nat. 136 (1990) 270-275. [27] S. Wolfram, "Cellular automata as models of complexity", Nature 311 (1984) 419-424." name="eprints.referencetext" /> <meta content="Rixon, Andrew J. and Johnson, Craig R. and Jones, Alan S. (1998) Stability in paradigm biological systems. 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border: solid 1px #ccc; padding: 3px"><tr> <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> <td align="right" style="white-space: nowrap"> <form method="get" accept-charset="utf-8" action="http://eprints.utas.edu.au/cgi/search" style="display:inline"> <input class="ep_tm_searchbarbox" size="20" type="text" name="q" /> <input class="ep_tm_searchbarbutton" value="Search" type="submit" name="_action_search" /> <input type="hidden" name="_order" value="bytitle" /> <input type="hidden" name="basic_srchtype" value="ALL" /> <input type="hidden" name="_satisfyall" value="ALL" /> </form> </td> </tr></table></td></tr> <tr> <td class="toplinks"><!-- InstanceBeginEditable name="content" --> <div align="center"> <table width="720" class="ep_tm_main"><tr><td align="left"> <h1 class="ep_tm_pagetitle">Stability in paradigm biological systems</h1> <p style="margin-bottom: 1em" class="not_ep_block"><span class="person_name">Rixon, Andrew J.</span> and <span class="person_name">Johnson, Craig R.</span> and <span class="person_name">Jones, Alan S.</span> (1998) <xhtml:em>Stability in paradigm biological systems.</xhtml:em> Journal of the Australian Mathematical Society - Series B, 40 (1). pp. 23-34. ISSN 0334-2700</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/1208/1/rixon-johnson-jones.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/1208/1/rixon-johnson-jones.pdf"><span class="ep_document_citation">PDF</span></a> - Full text restricted - Requires a PDF viewer<br />56Kb</td><td><form method="get" accept-charset="utf-8" action="http://eprints.utas.edu.au/cgi/request_doc"><input value="1552" 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://www.austms.org.au/Publ/Jamsb/V40P1/abs/1500/">http://www.austms.org.au/Publ/Jamsb/V40P1/abs/1500/</a></p><div class="not_ep_block"><h2>Abstract</h2><p style="padding-bottom: 16px; text-align: left; margin: 1em auto 0em auto">A discrete spatial model of a multi-species environment is formulated, and the behaviour of the system is studied. The model is used to explore stability and resilience of biological systems and discuss how they are dependent on spatial scale chosen. </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">Subjects:</th><td valign="top" class="ep_row"><a href="http://eprints.utas.edu.au/view/subjects/239901.html">230000 Mathematical Sciences > 239900 Other Mathematical Sciences > 239901 Biological Mathematics</a><br /><a href="http://eprints.utas.edu.au/view/subjects/270702.html">270000 Biological Sciences > 270700 Ecology and Evolution > 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">1208</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">24 Jun 2007</td></tr><tr><th valign="top" class="ep_row">Last Modified:</th><td valign="top" class="ep_row">04 Feb 2008 17:03</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=1208;">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&eprintid=1208">item control page</a></p> </td></tr></table> </div> <!-- InstanceEndEditable --></td> </tr> <tr> <td><!-- #BeginLibraryItem "/Library/footer_eprints.lbi" --> <table width="795" border="0" align="left" cellpadding="0" class="footer"> <tr valign="top"> <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> </tr> <tr><td colspan="2"><p><img src="/images/eprints/footerline.gif" width="100%" height="4" /></p></td></tr> <tr valign="top"> <td width="68%" class="footer">Authorised by the University Librarian<br /> © University of Tasmania ABN 30 764 374 782<br /> <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 & 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> <td width="32%"><div align="right"> <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> <p align="right" class="NoPrint"><a href="http://www.utas.edu.au/"><br /> </a></p> </div></td> </tr> <tr valign="top"> <td><p> </p></td> <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> </tr> </table> <!-- #EndLibraryItem --> <div align="center"></div></td> </tr> </table> </body> </html>