Effects of predation pressure on species packing on a resource gradient: insights from nonlinear dynamics.

The classical case of three competitors arranged on a resource gradient such that the central competitor will be excluded due to competition from the other two is studied from the point of view of the effects of added predators. The basic formulation is motivated by a desire to understand the effects of asymmetries in multidimensional Lotka-Volterra systems. We first study the effects of perfectly specialist predators and find a rich collection of possible behaviors of the system including (1) extinction of all predators and subsequent extinction of the subordinate competitor, (2) dominant competitors and their predators coexist but the subdominant competitor goes extinct, (3) all species except the predator of the subordinate competitor coexist in coordinated phase-reversed chaos, (4) exclusion of one or more species occurs through an expanding heteroclinic cycle, and (5) all species coexist in an uncoordinated chaos. We then study the effects of five qualitatively distinct forms of polyphagy. In one case, corresponding to the well-known vulnerability to predation versus competitive ability trade-off, it is possible to have the subordinate competitor be the only survivor in the system. The other three cases of polyphagy lead to distortions in the basic pattern seen in the previously analyzed specialist case. Studying this case of ecologically motivated asymmetries in the basic Lotka-Volterra formulation is a step in the direction of fully understanding interacting populations.

[1]  K. Fujii,et al.  Complexity-stability relationship of two-prey-one-predator species system model: local and global stability. , 1977, Journal of theoretical biology.

[2]  S. Hsu.  Predator-mediated coexistence and extinction☆ , 1981 .

[3]  M. Pascual,et al.  Competitive coexistence through intermediate polyphagy , 2006 .

[4]  Contributions to the global analysis of 3-D Lotka-Volterra equations: Dynamic boundedness and indirect interactions in the case of one predator and two prey , 1991 .

[5]  William G. Wilson,et al.  Mobility versus density-limited predator-prey dynamics on different spatial scales , 1991, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[6]  J. Harper.  The role of predation in vegetational diversity. , 1969, Brookhaven symposia in biology.

[7]  S. Schreiber.  Generalist and specialist predators that mediate permanence in ecological communities , 1997 .

[8]  T. Höök,et al.  Increased competition may promote species coexistence , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[9]  M. Leibold.  Similarity and local co-existence of species in regional biotas , 2004, Evolutionary Ecology.

[10]  R. Macarthur,et al.  The Limiting Similarity, Convergence, and Divergence of Coexisting Species , 1967, The American Naturalist.

[11]  H. Olff,et al.  Impact of different-sized herbivores on recruitment opportunities for subordinate herbs in grasslands , 2003 .

[12]  R. Macarthur.  Species packing and competitive equilibrium for many species. , 1970, Theoretical population biology.

[13]  E. Berlow,et al.  The Keystone Species Concept: Variation in Interaction Strength in a Rocky Intertidal Habitat , 1994 .

[14]  Peter A. Abrams,et al.  IS PREDATOR‐MEDIATED COEXISTENCE POSSIBLE INUNSTABLE SYSTEMS? , 1999 .

[15]  G. T. Vickers,et al.  A criterion for permanent coexistence of species, with an application to a two-prey one-predator system , 1983 .

[16]  R. Holt,et al.  The impact of consumer-resource cycles on the coexistence of competing consumers. , 2002, Theoretical population biology.

[17]  Mathew A. Leibold,et al.  A Graphical Model of Keystone Predators in Food Webs: Trophic Regulation of Abundance, Incidence, and Diversity Patterns in Communities , 1996, The American Naturalist.

[18]  R. Paine,et al.  Intertidal community structure , 1974, Oecologia.

[19]  H. Howe,et al.  Forest fragmentation severs mutualism between seed dispersers and an endemic African tree , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[20]  T. Schoener,et al.  Lizards reduce food consumption by spiders: mechanisms and consequences , 1990, Oecologia.

[21]  G. Tullock,et al.  Competitive Exclusion. , 1960, Science.

[22]  R. May,et al.  Interspecific competition, predation and species diversity: a comment. , 1972, Journal of theoretical biology.

[23]  G. Kirlinger,et al.  Permanence in Lotka-Volterra equations: Linked prey-predator systems , 1986 .

[24]  Hal L. Smith,et al.  Periodic coexistence of four species competing for three essential resources. , 2003, Mathematical biosciences.

[25]  John Vandermeer,et al.  Coupled Oscillations in Food Webs: Balancing Competition and Mutualism in Simple Ecological Models , 2004, The American Naturalist.

[26]  W. Wilson,et al.  Pattern Formation and the Spatial Scale of Interaction between Predators and Their Prey. , 1998, Theoretical population biology.

[27]  R. Parmenter,et al.  Vegetation change following removal of keystone herbivores from desert grasslands in New Mexico , 2001 .

[28]  D. Doak,et al.  The Keystone-Species Concept in Ecology and ConservationManagement and policy must explicitly consider the complexity of interactions in natural systems , 1993 .

[29]  Oswald J. Schmitz,et al.  Top predator control of plant biodiversity and productivity in an old‐field ecosystem , 2003 .

[30]  K. Sigmund,et al.  On the stabilizing effect of predators and competitors on ecological communities , 1989, Journal of mathematical biology.

[31]  Peter A. Abrams,et al.  The theory of limiting similarity , 1983 .

[32]  Franz J. Weissing,et al.  BIOLOGICAL CONDITIONS FOR OSCILLATIONS AND CHAOS GENERATED BY MULTISPECIES COMPETITION , 2001 .

[33]  D. Janzen.  Herbivores and the Number of Tree Species in Tropical Forests , 1970, The American Naturalist.

[34]  G. Polis,et al.  Food webs: integration of patterns and dynamics , 1997 .

[35]  N. Pierce.  Origin of Species , 1914, Nature.

[36]  S B Saila,et al.  Interspecific competition, predation and species diversity. , 1970, Journal of theoretical biology.

[37]  S. J. Arnold.  Species Densities of Predators and Their Prey , 1972, The American Naturalist.

[38]  G. E. Hutchinson,et al.  CIRCULAR CAUSAL SYSTEMS IN ECOLOGY , 1948, Annals of the New York Academy of Sciences.

[39]  S. Schreiber.  On the stabilizing eect of specialist predators on founder-controlled communities , 2003 .

[40]  Franz J. Weissing,et al.  Fundamental Unpredictability in Multispecies Competition , 2001, The American Naturalist.

[41]  David Tilman,et al.  Limiting Similarity in Mechanistic and Spatial Models of Plant Competition in Heterogeneous Environments , 1994, The American Naturalist.

[42]  S Pacala,et al.  Limiting Similarity, Species Packing, and System Stability for Hierarchical Competition‐Colonization Models , 1999, The American Naturalist.

[43]  J. Connell.  Diversity in tropical rain forests and coral reefs. , 1978, Science.

[44]  J. Huisman,et al.  Biodiversity of plankton by species oscillations and chaos , 1999, Nature.

[45]  Marcus W. Feldman,et al.  Species Packing and Predation Pressure , 1975 .

[46]  P. Chesson.  Mechanisms of Maintenance of Species Diversity , 2000 .