Statistical mechanics of relative species abundance

Abstract Statistical mechanics of relative species abundance (RSA) patterns in biological networks is presented. The theory is based on multispecies replicator dynamics equivalent to the Lotka–Volterra equation, with diverse interspecies interactions. Various RSA patterns observed in nature are derived from a single parameter related to productivity or maturity of a community. The abundance distribution is formed like a widely observed left-skewed lognormal distribution. It is also found that the “canonical hypothesis” is supported in some parameter region where the typical RSA patterns are observed. As the model has a general form, the result can be applied to similar patterns in other complex biological networks, e.g. gene expression.

[1]  Alessandro Vespignani,et al.  Epidemic dynamics and endemic states in complex networks. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  K. Tokita,et al.  Mass extinction in a dynamical system of evolution with variable dimension. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[3]  Robert M. May,et al.  Lifting the veil on abundance patterns , 1991, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[4]  Han Olff,et al.  A novel genealogical approach to neutral biodiversity theory , 2004 .

[5]  Opper,et al.  Replicators with random interactions: A solvable model. , 1989, Physical review. A, General physics.

[6]  R. May.  Patterns of species abundance and diversity , 1975 .

[7]  M. Willig,et al.  The Relationship Between Productivity and Species Richness , 1999 .

[8]  J. Fontanari,et al.  Complementarity and diversity in a soluble model ecosystem. , 2002, Physical review letters.

[9]  A. Barabasi,et al.  Lethality and centrality in protein networks , 2001, Nature.

[10]  Neo D. Martinez.  Artifacts or Attributes? Effects of Resolution on the Little Rock Lake Food Web , 1991 .

[11]  Alessandro Flammini,et al.  Stochastic model for the species abundance problem in an ecological community. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  M. Mézard,et al.  Spin Glass Theory and Beyond , 1987 .

[13]  Fontanari,et al.  Random replicators with high-order interactions , 2000, Physical review letters.

[14]  Jérôme Chave,et al.  Neutral theory and community ecology , 2004 .

[15]  R. Fisher,et al.  The Relation Between the Number of Species and the Number of Individuals in a Random Sample of an Animal Population , 1943 .

[16]  K. Tokita.  Species abundance patterns in complex evolutionary dynamics. , 2004, Physical review letters.

[17]  J. Fontanari,et al.  Extinctions in the random replicator model. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  P. Biscari.  Replica Symmetry Breaking in the Random Replicant Model , 1995 .

[19]  G. Sugihara.  Minimal Community Structure: An Explanation of Species Abundance Patterns , 1980, The American Naturalist.

[20]  Kunihiko Kaneko,et al.  Recursiveness, switching, and fluctuations in a replicating catalytic network. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  Henrik Jeldtoft Jensen,et al.  Time-dependent extinction rate and species abundance in a tangled-nature model of biological evolution. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  Yoichiro Ito,et al.  On the relation between fluctuation and response in biological systems , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[23]  Mads Kærn,et al.  Noise in eukaryotic gene expression , 2003, Nature.

[24]  Josef Hofbauer,et al.  Evolutionary Games and Population Dynamics , 1998 .

[25]  K. Tokita,et al.  Emergence of a complex and stable network in a model ecosystem with extinction and mutation. , 2002, Theoretical population biology.

[26]  MARK R. GARDNER,et al.  Connectance of Large Dynamic (Cybernetic) Systems: Critical Values for Stability , 1970, Nature.

[27]  I. Hiscock.  Communities and Ecosystems , 1970, The Yale Journal of Biology and Medicine.

[28]  B. McGill.  A test of the unified neutral theory of biodiversity , 2003, Nature.

[29]  R. Macarthur.  ON THE RELATIVE ABUNDANCE OF BIRD SPECIES. , 1957, Proceedings of the National Academy of Sciences of the United States of America.

[30]  R. Macarthur,et al.  On the Relative Abundance of Species , 1960, The American Naturalist.

[31]  John A. Wiens,et al.  Species diversity in ecological communities: edited by Robert E. Ricklefs and Dolph Schluter University of Chicago Press, 1993. $105.00 hbk, $35.00 pbk (414 pages) ISBN 0 226 71822 0/0 226 71823 9 , 1994 .

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

[33]  Annette Ostling,et al.  A THEORY OF SPATIAL STRUCTURE IN ECOLOGICAL COMMUNITIES AT MULTIPLE SPATIAL SCALES , 2005 .

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

[35]  F. A. Bazzaz,et al.  Plant Species Diversity in Old‐Field Successional Ecosystems in Southern Illinois , 1975 .

[36]  F. W. Preston.  The Canonical Distribution of Commonness and Rarity: Part I , 1962 .

[37]  ROBERT M. MAY,et al.  Will a Large Complex System be Stable? , 1972, Nature.

[38]  西森 秀稔.  Statistical physics of spin glasses and information processing : an introduction , 2001 .

[39]  R. May.  Unanswered questions in ecology. , 1999, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[40]  S. Hubbell,et al.  Neutral theory and relative species abundance in ecology , 2003, Nature.