From simple rules to cycling in community assembly

358.Simulation studies of community assembly have frequently observed two relatedphenomena: (1) the humpty dumpty effect in which communities can not bereconstructed by ‘‘sequential’’ invasions (i.e. single species invasions separated bylong intervals of time) and (2) cycling between sub-communities. To better understandthe mechanisms underlying these phenomena, we analyze a system consisting of twopredators and two prey competing for a shared resource. We show how simpledominance rules (i.e. R

[1]  James P. Grover,et al.  Assembly Rules for Communities of Nutrient-Limited Plants and Specialist Herbivores , 1994, The American Naturalist.

[2]  G. Kirlinger.  Two predators feeding on two prey species: a result on permanence. , 1989, Mathematical biosciences.

[3]  David Tilman,et al.  Resources: A Graphical-Mechanistic Approach to Competition and Predation , 1980, The American Naturalist.

[4]  Richard Law,et al.  PERMANENCE AND THE ASSEMBLY OF ECOLOGICAL COMMUNITIES , 1996 .

[5]  L. Milne,et al.  The Balance of Nature , 1953, Oryx.

[6]  W. Post,et al.  Community assembly and food web stability , 1983 .

[7]  W. L..  The Balance of Nature , 1870, Nature.

[8]  James B. Grace,et al.  Perspectives on Plant Competition , 1991 .

[9]  G. Wolkowicz,et al.  Successful invasion of a food web in a chemostat. , 1989, Mathematical biosciences.

[10]  M. Longair.  The Theoretical Framework , 1998 .

[11]  Richard Law,et al.  Alternative Permanent States of Ecological Communities , 1993 .

[12]  Chad L. Hewitt,et al.  Invasion Success and Community Resistance in Single and Multiple Species Invasion Models: Do the Models Support the Conclusions? , 2002, Biological Invasions.

[13]  T. Case,et al.  Invasion resistance arises in strongly interacting species-rich model competition communities. , 1990, Proceedings of the National Academy of Sciences of the United States of America.

[14]  R. Holt.  Predation, apparent competition, and the structure of prey communities. , 1977, Theoretical population biology.

[15]  J. Gupta.  THEORETICAL FRAMEWORK , 2018, The Cultic Life of Trees in the Prehistoric Aegean, Levant, Egypt and Cyprus.

[16]  Julie L. Lockwood,et al.  Assembling Ecological Communities in Time and Space , 1997 .

[17]  B. Pavlik.  Species Diversity in Ecological Communities: Historical and Geographical Perspectives by R. E. Ricklefs, D. Schluter , 1995 .

[18]  S. Pimm,et al.  The assembly of ecological communities: a minimalist approach , 1993 .

[19]  John H. Lawton,et al.  The Ecological Consequences of Shared Natural Enemies , 1994 .

[20]  Josef Hofbauer,et al.  Heteroclinic cycles in ecological differential equations , 1994 .

[21]  Dolph Schluter,et al.  Species diversity in ecological communities: historical and geographical perspectives. , 1993 .

[22]  R D Holt,et al.  Intraguild predation: The dynamics of complex trophic interactions. , 1992, Trends in ecology & evolution.

[23]  James A. Drake,et al.  The mechanics of community assembly and succession , 1990 .

[24]  J. Lancaster,et al.  Assembly rules within a contingent ecology , 1999 .

[25]  Josef Hofbauer,et al.  A general cooperation theorem for hypercycles , 1981 .

[26]  Richard Law,et al.  On models for assembling ecological communities , 1996 .

[27]  Robert D. Holt,et al.  A Theoretical Framework for Intraguild Predation , 1997, The American Naturalist.

[28]  Jerry C. Blackford,et al.  Self-assembling food webs : a global viewpoint of coexistence of species in Lotka-Volterra communities , 1992 .

[29]  M. Krupa.  Robust heteroclinic cycles , 1997 .

[30]  Sze-Bi Hsu,et al.  A Mathematical Theory for Single-Nutrient Competition in Continuous Cultures of Micro-Organisms , 1977 .

[31]  James A. Drake,et al.  Community-Assembly Mechanics and the Structure of an Experimental Species Ensemble , 1991, The American Naturalist.

[32]  J. Grace,et al.  Mechanisms of plant competition for nutrients: the elements of a predictive theory of competition. , 1990 .

[33]  Melbourne,et al.  Asymptotic stability of heteroclinic cycles in systems with symmetry , 1995, Ergodic Theory and Dynamical Systems.

[34]  James P. Grover,et al.  Simple Rules for Interspecific Dominance in Systems with Exploitative and Apparent Competition , 1994, The American Naturalist.

[35]  Werner Brannath,et al.  Heteroclinic networks on the tetrahedron , 1994 .