Statistical mechanics of ecological systems: Neutral theory and beyond

It is of societal importance to advance the understanding of emerging patterns of biodiversity from biological and ecological systems. The neutral theory offers a statistical-mechanical framework that relates key biological properties at the individual scale with macroecological properties at the community scale. This article surveys the quantitative aspects of neutral theory and its extensions for physicists who are interested in what important problems remain unresolved for studying ecological systems.

[1]  J. Terborgh,et al.  Estimating the global conservation status of more than 15,000 Amazonian tree species , 2015, Science Advances.

[2]  Massimo Vergassola,et al.  The Impact of Environmental Fluctuations on Evolutionary Fitness Functions , 2015, Scientific Reports.

[3]  H. Watson Remarks On the Geographical Distribution of British Plants; Chiefly in Connection With Latitude, Elevation, and Climate , 2015 .

[4]  Stefano Allesina,et al.  Predicting the stability of large structured food webs , 2015, Nature Communications.

[5]  Steven W Kembel,et al.  Backbones of evolutionary history test biodiversity theory for microbes , 2015, Proceedings of the National Academy of Sciences.

[6]  R. Kadmon,et al.  A neutral theory with environmental stochasticity explains static and dynamic properties of ecological communities. , 2015, Ecology letters.

[7]  David Kenfack,et al.  An estimate of the number of tropical tree species , 2015, Proceedings of the National Academy of Sciences.

[8]  P. Bork,et al.  Tara Oceans studies plankton at planetary scale , 2015, Science.

[9]  S. Suweis,et al.  Neutral dynamics with environmental noise: Age-size statistics and species lifetimes. , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  Amaury Lambert,et al.  Phylogenies support out-of-equilibrium models of biodiversity. , 2015, Ecology letters.

[11]  L. Harmon,et al.  Unifying ecology and macroevolution with individual-based theory , 2015, Ecology letters.

[12]  Amos Maritan,et al.  Towards a unified descriptive theory for spatial ecology: predicting biodiversity patterns across spatial scales , 2015 .

[13]  J. C. de Almeida,et al.  Concluding Remarks , 2015, Clinical practice and epidemiology in mental health : CP & EMH.

[14]  D. Kessler,et al.  Generalized model of island biodiversity. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  C. Flather,et al.  Niche versus Neutrality: A Dynamical Analysis , 2014, The American Naturalist.

[16]  James P O'Dwyer,et al.  A mean field model for competition: from neutral ecology to the Red Queen. , 2014, Ecology letters.

[17]  A. Maritan,et al.  Spatial maximum entropy modeling from presence/absence tropical forest data , 2014, 1407.2425.

[18]  S. Hubbell,et al.  Temporal variability of forest communities: empirical estimates of population change in 4000 tree species. , 2014, Ecology letters.

[19]  Ryan A Chisholm,et al.  Species ages in neutral biodiversity models. , 2014, Theoretical population biology.

[20]  Enrico Bertuzzo,et al.  Metapopulation persistence and species spread in river networks. , 2014, Ecology letters.

[21]  Samir Suweis,et al.  Early Warning Signs in Social-Ecological Networks , 2014, bioRxiv.

[22]  J. Masoliver,et al.  Erratum: First-passage and escape problems in the Feller process [Phys. Rev. E 86, 041116 (2012)] , 2014 .

[23]  Andrea Rinaldo,et al.  Complex Interaction of Dendritic Connectivity and Hierarchical Patch Size on Biodiversity in River-Like Landscapes , 2013, The American Naturalist.

[24]  Annette Ostling,et al.  Emergent neutrality or hidden niches , 2013 .

[25]  M. Scheffer,et al.  Interpretation and predictions of the Emergent neutrality model: a reply to Barabás et al. , 2013 .

[26]  J. Terborgh,et al.  Hyperdominance in the Amazonian Tree Flora , 2013, Science.

[27]  A. Maritan,et al.  Emergence of structural and dynamical properties of ecological mutualistic networks , 2013, Nature.

[28]  Charles K. Fisher,et al.  The transition between the niche and neutral regimes in ecology , 2013, Proceedings of the National Academy of Sciences.

[29]  Charles K. Fisher,et al.  Niche and neutral theories correspond to distinct ecological phases , 2013 .

[30]  M. Scheffer,et al.  Repeated Parallel Evolution Reveals Limiting Similarity in Subterranean Diving Beetles , 2013, The American Naturalist.

[31]  M. A. Muñoz,et al.  The effect of quenched disorder in neutral theories , 2013, 1304.0965.

[32]  J. Masoliver,et al.  Publisher's Note: First-passage and escape problems in the Feller process [Phys. Rev. E86, 041116 (2012)] , 2012 .

[33]  A. Maritan,et al.  Absence of detailed balance in ecology , 2012, 1210.5819.

[34]  S. Carpenter,et al.  Anticipating Critical Transitions , 2012, Science.

[35]  Jayanth R Banavar,et al.  Spatial aggregation and the species-area relationship across scales. , 2012, Journal of theoretical biology.

[36]  J. Masoliver,et al.  First-passage and escape problems in the Feller process. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[37]  M. A. Muñoz,et al.  Spontaneously broken neutral symmetry in an ecological system. , 2012, Physical review letters.

[38]  Andrea Rinaldo,et al.  An exactly solvable coarse-grained model for species diversity , 2012, 1206.6590.

[39]  A. McKane,et al.  Stochastic formulation of ecological models and their applications. , 2012, Trends in ecology & evolution.

[40]  Nicholas Chia,et al.  Quantification of the relative roles of niche and neutral processes in structuring gastrointestinal microbiomes , 2012, Proceedings of the National Academy of Sciences.

[41]  M. A. Muñoz,et al.  What Ecological Factors Shape Species-Area Curves in Neutral Models? , 2012, PloS one.

[42]  S. Hubbell,et al.  The case for ecological neutral theory. , 2012, Trends in Ecology & Evolution.

[43]  A. Rinaldo,et al.  Dendritic connectivity controls biodiversity patterns in experimental metacommunities , 2012, Proceedings of the National Academy of Sciences.

[44]  A Maritan,et al.  On species persistence-time distributions. , 2012, Journal of theoretical biology.

[45]  R. Ricklefs,et al.  Global Correlations in Tropical Tree Species Richness and Abundance Reject Neutrality , 2012, Science.

[46]  Marten Scheffer,et al.  Emergent neutrality leads to multimodal species abundance distributions , 2012, Nature Communications.

[47]  A. Hastings,et al.  Multivariate Moran process with Lotka-Volterra phenomenology. , 2011, Physical review letters.

[48]  J. Harte Maximum Entropy and Ecology: A Theory of Abundance, Distribution, and Energetics , 2011 .

[49]  R. Chisholm Time-dependent solutions of the spatially implicit neutral model of biodiversity. , 2011, Theoretical population biology.

[50]  Carlos J. Melián,et al.  NEUTRAL BIODIVERSITY THEORY CAN EXPLAIN THE IMBALANCE OF PHYLOGENETIC TREES BUT NOT THE TEMPO OF THEIR DIVERSIFICATION , 2011, Evolution; international journal of organic evolution.

[51]  S. Hubbell,et al.  The unified neutral theory of biodiversity and biogeography at age ten. , 2011, Trends in ecology & evolution.

[52]  M. A. Muñoz,et al.  Quasi-Neutral Theory of Epidemic Outbreaks , 2011, PloS one.

[53]  Shurong Zhou,et al.  Negative density dependence can offset the effect of species competitive asymmetry: a niche-based mechanism for neutral-like patterns. , 2011, Journal of theoretical biology.

[54]  Si Tang,et al.  Stability criteria for complex ecosystems , 2011, Nature.

[55]  S. Hubbell,et al.  Species–area relationships always overestimate extinction rates from habitat loss , 2011, Nature.

[56]  R. Muneepeerakul,et al.  How restructuring river connectivity changes freshwater fish biodiversity and biogeography , 2011 .

[57]  Rampal S. Etienne,et al.  The Spatial Limitations of Current Neutral Models of Biodiversity , 2011, PloS one.

[58]  Enrico Bertuzzo,et al.  Spatial effects on species persistence and implications for biodiversity , 2011, Proceedings of the National Academy of Sciences.

[59]  W. Fagan,et al.  A niche remedy for the dynamical problems of neutral theory , 2011, Theoretical Ecology.

[60]  Y. Iwasa,et al.  Neutral theory as a predictor of avifaunal extinctions after habitat loss , 2011, Proceedings of the National Academy of Sciences.

[61]  Michel Loreau,et al.  A mathematical synthesis of niche and neutral theories in community ecology. , 2011, Journal of theoretical biology.

[62]  R. Muneepeerakul,et al.  Evolution of dispersal in explicitly spatial metacommunities. , 2011, Journal of theoretical biology.

[63]  N. Goldenfeld,et al.  Life is Physics: Evolution as a Collective Phenomenon Far From Equilibrium , 2010, 1011.4125.

[64]  Lindsay A. Turnbull,et al.  Different but equal: the implausible assumption at the heart of neutral theory , 2010, The Journal of animal ecology.

[65]  N. Temme,et al.  A sampling theory for asymmetric communities. , 2010, Journal of theoretical biology.

[66]  D. Storch,et al.  Predictions of Taylor's power law, density dependence and pink noise from a neutrally modeled time series. , 2010, Journal of theoretical biology.

[67]  Werner Ulrich,et al.  A meta-analysis of species-abundance distributions , 2010 .

[68]  Rampal S Etienne,et al.  Protracted speciation revitalizes the neutral theory of biodiversity. , 2010, Ecology letters.

[69]  B. Haegeman,et al.  Self-consistent approach for neutral community models with speciation. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[70]  A. Maritan,et al.  Applications of the principle of maximum entropy: from physics to ecology , 2010, Journal of physics. Condensed matter : an Institute of Physics journal.

[71]  R. Muneepeerakul,et al.  Inferring plant ecosystem organization from species occurrences. , 2010, Journal of theoretical biology.

[72]  R. May Ecological science and tomorrow's world , 2010, Philosophical Transactions of the Royal Society B: Biological Sciences.

[73]  James P O'Dwyer,et al.  Field theory for biogeography: a spatially explicit model for predicting patterns of biodiversity , 2010, Ecology letters.

[74]  Jayanth R Banavar,et al.  Inferring species interactions in tropical forests , 2009, Proceedings of the National Academy of Sciences.

[75]  Stephen J Cornell,et al.  Species-area curves, neutral models, and long-distance dispersal. , 2009, Ecology.

[76]  Thomas Butler,et al.  Robust ecological pattern formation induced by demographic noise. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[77]  Andrea Rinaldo,et al.  Predicting spatial similarity of freshwater fish biodiversity , 2009, Proceedings of the National Academy of Sciences.

[78]  Jordi Bascompte,et al.  The architecture of mutualistic networks minimizes competition and increases biodiversity , 2009, Nature.

[79]  Rampal S Etienne,et al.  Neutral Models with Generalised Speciation , 2009, Bulletin of mathematical biology.

[80]  M. Cencini,et al.  Speciation-rate dependence in species-area relationships. , 2009, Journal of theoretical biology.

[81]  P. Babak,et al.  A neutral model of edge effects. , 2009, Theoretical population biology.

[82]  C. Gardiner Stochastic Methods: A Handbook for the Natural and Social Sciences , 2009 .

[83]  A. Maritan,et al.  Incipient criticality in ecological communities , 2008, Proceedings of the National Academy of Sciences.

[84]  Jordi Bascompte,et al.  A neutral‐niche theory of nestedness in mutualistic networks , 2008 .

[85]  Richard Condit,et al.  Biodiversity in a Warmer World , 2008, Science.

[86]  J. Harte,et al.  Maximum entropy and the state-variable approach to macroecology. , 2008, Ecology.

[87]  David Kenfack,et al.  A general framework for the distance–decay of similarity in ecological communities , 2008, Ecology letters.

[88]  Yan Wong,et al.  A coalescence approach to spatial neutral ecology , 2008, Ecol. Informatics.

[89]  Rampal S Etienne,et al.  Relaxing the zero-sum assumption in neutral biodiversity theory. , 2008, Journal of theoretical biology.

[90]  R. Muneepeerakul,et al.  Neutral metacommunity models predict fish diversity patterns in Mississippi–Missouri basin , 2008, Nature.

[91]  C. M. Mutshinda,et al.  Species abundance dynamics under neutral assumptions: a Bayesian approach to the controversy , 2008 .

[92]  B. Haegeman,et al.  Dynamics of neutral biodiversity. , 2008, Mathematical biosciences.

[93]  Rampal S Etienne,et al.  The implicit assumption of symmetry and the species abundance distribution. , 2007, Ecology letters.

[94]  Amos Maritan,et al.  Patterns of relative species abundance in rainforests and coral reefs , 2007, Nature.

[95]  E. Leigh,et al.  Neutral theory: a historical perspective , 2007, Journal of evolutionary biology.

[96]  Rampal S Etienne,et al.  The zero-sum assumption in neutral biodiversity theory. , 2007, Journal of theoretical biology.

[97]  V. Savage,et al.  Setting the absolute tempo of biodiversity dynamics. , 2007, Ecology letters.

[98]  Stephen J Cornell,et al.  Species-area relationships from a spatially explicit neutral model in an infinite landscape. , 2007, Ecology letters.

[99]  Steven C Walker,et al.  When and why do non-neutral metacommunities appear neutral? , 2007, Theoretical population biology.

[100]  A. J. McKane,et al.  Stochastic models of evolution in genetics, ecology and linguistics , 2007, cond-mat/0703478.

[101]  Peter B Adler,et al.  A niche for neutrality. , 2007, Ecology letters.

[102]  Nigel Goldenfeld,et al.  Biology's next revolution , 2007, Nature.

[103]  Amos Maritan,et al.  Dynamical evolution of ecosystems , 2006, Nature.

[104]  Joseph A. Veech,et al.  A probability‐based analysis of temporal and spatial co‐occurrence in grassland birds , 2006 .

[105]  B. Houchmandzadeh,et al.  Species abundance distribution and population dynamics in a two-community model of neutral ecology. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[106]  N. U. Prabhu,et al.  Stochastic Processes and Their Applications , 1999 .

[107]  P. Babak Continuous probabilistic approach to species dynamics in Hubbell's zero-sum local community. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[108]  Rampal S Etienne,et al.  The merits of neutral theory. , 2006, Trends in ecology & evolution.

[109]  Nigel Goldenfeld,et al.  On the origin and robustness of power-law species–area relationships in ecology , 2006, Proceedings of the National Academy of Sciences.

[110]  Stephen P. Hubbell,et al.  Neutral theory in macroecology and population genetics , 2006 .

[111]  M. D. Weiser,et al.  Empirical evaluation of neutral theory. , 2006, Ecology.

[112]  Stephen P Hubbell,et al.  Neutral theory and the evolution of ecological equivalence. , 2006, Ecology.

[113]  R. Ricklefs The unified neutral theory of biodiversity: do the numbers add up? , 2006, Ecology.

[114]  J. Chave,et al.  Theoretical biology: Comparing models of species abundance , 2006, Nature.

[115]  Marten Scheffer,et al.  Self-organized similarity, the evolutionary emergence of groups of similar species. , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[116]  A. Maritan,et al.  A Novel Ensemble in Statistical Physics , 2006 .

[117]  Dominique Gravel,et al.  Reconciling niche and neutrality: the continuum hypothesis. , 2006, Ecology letters.

[118]  Salvador Pueyo,et al.  Diversity : between neutrality and structure , 2006 .

[119]  S. Hubbell,et al.  Density dependence explains tree species abundance and diversity in tropical forests , 2005, Nature.

[120]  Alessandro Flammini,et al.  Species lifetime distribution for simple models of ecologies. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[121]  Rampal S Etienne,et al.  A dispersal-limited sampling theory for species and alleles. , 2005, Ecology letters.

[122]  S. Pacala,et al.  Ecological drift in niche-structured communities: neutral pattern does not imply neutral process , 2005 .

[123]  Jayanth R Banavar,et al.  Spatial scaling in model plant communities. , 2005, Physical review letters.

[124]  David F. R. P. Burslem,et al.  Biotic interactions in the tropics: their role in the maintenance of species diversity. , 2005 .

[125]  Rampal S. Etienne,et al.  A new sampling formula for neutral biodiversity , 2005 .

[126]  Stephen P. Hubbell,et al.  Neutral theory in community ecology and the hypothesis of functional equivalence , 2005 .

[127]  S. Nee The neutral theory of biodiversity: do the numbers add up? , 2005 .

[128]  A. McKane,et al.  Sampling Hubbell's neutral theory of biodiversity , 2004 .

[129]  Michael B Bonsall,et al.  Life History Trade-Offs Assemble Ecological Guilds , 2004, Science.

[130]  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.

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

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

[133]  O. Phillips,et al.  Extinction risk from climate change , 2004, Nature.

[134]  H. Olff,et al.  How Dispersal Limitation Shapes Species–Body Size Distributions in Local Communities , 2004, The American Naturalist.

[135]  B. Houchmandzadeh,et al.  Analytical solution of a neutral model of biodiversity. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[136]  Michel Loreau,et al.  Community Patterns in Source‐Sink Metacommunities , 2003, The American Naturalist.

[137]  Brian J. McGill,et al.  Strong and weak tests of macroecological theory , 2003 .

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

[139]  John Harte,et al.  Ecology: Tail of death and resurrection , 2003, Nature.

[140]  Jonathan M. Chase,et al.  Ecological Niches: Linking Classical and Contemporary Approaches , 2003 .

[141]  R. Lande,et al.  Stochastic Population Dynamics in Ecology and Conservation , 2003 .

[142]  Alexander H. Hartmann,et al.  Introduction to Statistical Physics , 2003 .

[143]  Ricard V Solé,et al.  Analytic solution of Hubbell's model of local community dynamics. , 2003, Theoretical population biology.

[144]  M. Tribus,et al.  Probability theory: the logic of science , 2003 .

[145]  R. Kubo Statistical Physics II: Nonequilibrium Statistical Mechanics , 2003 .

[146]  J. Bouchaud An introduction to statistical finance , 2002 .

[147]  Jérôme Chave,et al.  A Spatially Explicit Neutral Model of β-Diversity in Tropical Forests , 2002 .

[148]  M. Meadows The Unified Theory of Biodiversity and Biogeography BY STEPHEN P. HUBBELL xiv + 375 pp., 21.5 × 14 × 2.2 cm, ISBN 0 691 02128 7 paperback, US$ 29.95/GB£ 19.95, Princeton, NJ, USA/Woodstock, UK: Princeton University Press, 2001 , 2002, Environmental Conservation.

[149]  S. Levin,et al.  Comparing Classical Community Models: Theoretical Consequences for Patterns of Diversity , 2002, The American Naturalist.

[150]  J. Plotkin,et al.  Species-area curves, spatial aggregation, and habitat specialization in tropical forests. , 2000, Journal of theoretical biology.

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

[152]  R. Solé,et al.  Mean-field stochastic theory for species-rich assembled communities. , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[153]  Graham Bell,et al.  The Distribution of Abundance in Neutral Communities , 2000, The American Naturalist.

[154]  Peter Kareiva,et al.  Spatial ecology : the role of space in population dynamics and interspecific interactions , 1998 .

[155]  H. Eugene Stanley,et al.  Dynamics of North American breeding bird populations , 1998, Nature.

[156]  Rick Durrett,et al.  Spatial Models for Species-Area Curves , 1996 .

[157]  J. L. Gittleman,et al.  The Future of Biodiversity , 1995, Science.

[158]  Siegfried H Lehnigk,et al.  The Generalized Feller Equation And Related Topics , 1993 .

[159]  H. Berg Cold Spring Harbor Symposia on Quantitative Biology.: Vol. LII. Evolution of Catalytic Functions. Cold Spring Harbor Laboratory, Cold Spring Harbor, NY, 1987, ISBN 0-87969-054-2, xix + 955 pp., US $150.00. , 1989 .

[160]  J. Diamond The present, past and future of human-caused extinctions. , 1989, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[161]  Robert M. May,et al.  Perspectives in Ecological Theory , 1989 .

[162]  M. Kimura,et al.  The neutral theory of molecular evolution. , 1983, Scientific American.

[163]  E. Lieb,et al.  The inverse problem in classical statistical mechanics , 1984 .

[164]  M. Willig,et al.  Randomness, Area, and Species Richness , 1982 .

[165]  T. E. Martin Species-Area Slopes and Coefficients: A Caution on Their Interpretation , 1981, The American Naturalist.

[166]  B. D. Coleman On random placement and species-area relations , 1981 .

[167]  P. Chesson,et al.  Environmental Variability Promotes Coexistence in Lottery Competitive Systems , 1981, The American Naturalist.

[168]  S. Gould An Allometric Interpretation of Species-Area Curves: The Meaning of the Coefficient , 1979, The American Naturalist.

[169]  Stephen P. Hubbell,et al.  Tree Dispersion, Abundance, and Diversity in a Tropical Dry Forest , 1979, Science.

[170]  R. Holley,et al.  Ergodic Theorems for Weakly Interacting Infinite Systems and the Voter Model , 1975 .

[171]  Thomas W. Schoener,et al.  STABILITY AND COMPLEXITY IN MODEL ECOSYSTEMS , 1974 .

[172]  R. May,et al.  Stability and Complexity in Model Ecosystems , 1976, IEEE Transactions on Systems, Man, and Cybernetics.

[173]  G. Varley,et al.  Dynamics of Populations , 1973 .

[174]  D. M. Power NUMBERS OF BIRD SPECIES ON THE CALIFORNIA ISLANDS , 1972, Evolution; international journal of organic evolution.

[175]  R M May,et al.  Niche overlap as a function of environmental variability. , 1972, Proceedings of the National Academy of Sciences of the United States of America.

[176]  W. Ewens The sampling theory of selectively neutral alleles. , 1972, Theoretical population biology.

[177]  P. W. Frank,et al.  Annual Review of Ecology and Systematics , 1971 .

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

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

[180]  R. Macarthur,et al.  The Theory of Island Biogeography , 1969 .

[181]  J. J. Levin A nonlinear Volterra equation not of convolution type , 1968 .

[182]  R. A. Silverman,et al.  Special functions and their applications , 1966 .

[183]  R. Paine Food Web Complexity and Species Diversity , 1966, The American Naturalist.

[184]  F. W. Preston Time and Space and the Variation of Species , 1960 .

[185]  G. E. Hutchinson,et al.  Homage to Santa Rosalia or Why Are There So Many Kinds of Animals? , 1959, The American Naturalist.

[186]  W. Feller TWO SINGULAR DIFFUSION PROBLEMS , 1951 .

[187]  F. W. Preston The Commonness, And Rarity, of Species , 1948 .

[188]  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 .

[189]  O. Arrhenius,et al.  Species and Area , 1921 .

[190]  G. D,et al.  American Naturalist , 1867, Nature.

[191]  G. Beemster,et al.  Functional Ecology , 2010 .

[192]  James S Clark,et al.  Beyond neutral science. , 2009, Trends in ecology & evolution.

[193]  R. Holt Emergent neutrality. , 2006, Trends in ecology & evolution.

[194]  B. McGill,et al.  A unified theory for macroecology based on spatial patterns of abundance , 2003 .

[195]  蒋志刚,et al.  Week 11: macroecology , 2021 .

[196]  R. Ricklefs,et al.  A comment on Hubbell's zero‐sum ecological drift model , 2003 .

[197]  Jérôme Chave,et al.  A spatially explicit neutral model of beta-diversity in tropical forests. , 2002, Theoretical population biology.

[198]  S. Ethier,et al.  Coupling and ergodic theorems for Fleming-Viot processes , 1998 .

[199]  W. Ebeling Stochastic Processes in Physics and Chemistry , 1995 .

[200]  D. Tilman Competition and Biodiversity in Spatially Structured Habitats , 1994 .

[201]  C. J-F,et al.  THE COALESCENT , 1980 .

[202]  ScienceDirect Bulletin of mathematical biology , 1973 .

[203]  J. Connell On the role of the natural enemies in preventing competitive exclusion in some marine animals and in rain forest trees , 1971 .

[204]  G. F. Gause The struggle for existence , 1971 .

[205]  J. Millis,et al.  THE UNIVERSITY OF , 2000 .

[206]  E. H. Simpson Measurement of Diversity , 1949, Nature.

[207]  S. Chandrasekhar Stochastic problems in Physics and Astronomy , 1943 .

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

[209]  A. Chakraborty,et al.  A simple model for how the risk of pandemics from different virus families depends on viral and human traits , 2021, Mathematical Biosciences.