The maximum entropy formalism and the idiosyncratic theory of biodiversity

Why does the neutral theory, which is based on unrealistic assumptions, predict diversity patterns so accurately? Answering questions like this requires a radical change in the way we tackle them. The large number of degrees of freedom of ecosystems pose a fundamental obstacle to mechanistic modelling. However, there are tools of statistical physics, such as the maximum entropy formalism (MaxEnt), that allow transcending particular models to simultaneously work with immense families of models with different rules and parameters, sharing only well-established features. We applied MaxEnt allowing species to be ecologically idiosyncratic, instead of constraining them to be equivalent as the neutral theory does. The answer we found is that neutral models are just a subset of the majority of plausible models that lead to the same patterns. Small variations in these patterns naturally lead to the main classical species abundance distributions, which are thus unified in a single framework.

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

[2]  Robert John,et al.  Nonrandom Processes Maintain Diversity in Tropical Forests , 2006, Science.

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

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

[5]  David Tilman,et al.  Niche tradeoffs, neutrality, and community structure: a stochastic theory of resource competition, invasion, and community assembly. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[6]  Ricard V. Solé,et al.  Habitat fragmentation and biodiversity collapse in neutral communities , 2004 .

[7]  G. A. Watterson,et al.  Models for the logarithmic species abundance distributions. , 1974, Theoretical population biology.

[8]  Steinar Engen,et al.  Analyzing Spatial Structure of Communities Using the Two‐Dimensional Poisson Lognormal Species Abundance Model , 2002, The American Naturalist.

[9]  Ricard V. Solé,et al.  Energy Flow-Networks and the Maximum Entropy Formalism , 1991 .

[10]  Sang Joon Kim,et al.  A Mathematical Theory of Communication , 2006 .

[11]  Rampal S. Etienne,et al.  Neutral Community Theory: How Stochasticity and Dispersal-Limitation Can Explain Species Coexistence , 2007 .

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

[13]  A. P. Levich,et al.  Variational modelling theorems and algocoenoses functioning principles , 2000 .

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

[15]  Stephen P. Hubbell,et al.  Local neighborhood effects on long-term survival of individual trees in a neotropical forest , 2001, Ecological Research.

[16]  Brian J. McGill,et al.  A Renaissance in the Study of Abundance , 2006, Science.

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

[18]  Hal Caswell,et al.  Community Structure: A Neutral Model Analysis , 1976 .

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

[20]  Steinar Engen,et al.  POPULATION DYNAMIC MODELS GENERATING SPECIES ABUNDANCE DISTRIBUTIONS OF THE GAMMA TYPE , 1996 .

[21]  Rodney W. Johnson,et al.  Axiomatic derivation of the principle of maximum entropy and the principle of minimum cross-entropy , 1980, IEEE Trans. Inf. Theory.

[22]  A K Dewdney,et al.  A general theory of the sampling process with applications to the "veil line". , 1998, Theoretical population biology.

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

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

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

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

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

[29]  Eric Garnier,et al.  From Plant Traits to Plant Communities: A Statistical Mechanistic Approach to Biodiversity , 2006, Science.

[30]  R. Lande,et al.  Population dynamic models generating the lognormal species abundance distribution. , 1996, Mathematical biosciences.

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

[32]  E. Jaynes.  Information Theory and Statistical Mechanics , 1957 .

[33]  J Wagensberg,et al.  On biomass diversity in ecology. , 1983, Bulletin of mathematical biology.

[34]  Daniel R. Lynch,et al.  Nonrandom Processes Maintain Diversity in Tropical Forests , 2006 .

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

[36]  Robert P. Anderson,et al.  Maximum entropy modeling of species geographic distributions , 2006 .

[37]  Salvador Pueyo,et al.  Self-similarity in species-area relationship and in species abundance distribution , 2006 .

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

[39]  Rampal S Etienne,et al.  Confronting different models of community structure to species-abundance data: a Bayesian model comparison. , 2005, Ecology letters.

[40]  Stephen P. Hubbell,et al.  Soil nutrients influence spatial distributions of tropical tree species , 2007, Proceedings of the National Academy of Sciences.

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

[42]  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.

[43]  D. Doak,et al.  The Statistical Inevitability of Stability‐Diversity Relationships in Community Ecology , 1998, The American Naturalist.

[44]  A. P. Levich,et al.  A search for maximum species abundances in ecological communities under conditional diversity optimization , 1997 .

[45]  R. Pearson,et al.  Predicting species distributions from small numbers of occurrence records: A test case using cryptic geckos in Madagascar , 2006 .

[46]  E. Charnov,et al.  Population fluctuations, power laws and mixtures of lognormal distributions , 2001 .

[47]  Kevin J. Gaston,et al.  The lognormal distribution is not an appropriate null hypothesis for the species–abundance distribution , 2005 .

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

[49]  P. Hernandez,et al.  The effect of sample size and species characteristics on performance of different species distribution modeling methods , 2006 .

[50]  Ramón Margalef,et al.  Información y diversidad específica en las comunidades de organismos , 1956 .

[51]  E. Jaynes.  The well-posed problem , 1973 .

[52]  James H Brown,et al.  The wealth of species: ecological communities, complex systems and the legacy of Frank Preston. , 2007, Ecology letters.

[53]  E. Leigh,et al.  Tropical forest diversity and dynamism : findings from a large-scale plot network , 2004 .

[54]  K. J. Willis,et al.  The ability of climate envelope models to predict the effect of climate change on species distributions , 2007 .

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

[56]  Meike J. Wittmann,et al.  Mathematical Ecology , 2006 .

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

[58]  Richard Condit,et al.  The impact of neutrality, niche differentiation and species input on diversity and abundance distributions , 2007 .

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

[60]  Mutsunori Tokeshi,et al.  NICHE APPORTIONMENT OR RANDOM ASSORTMENT: SPECIES ABUNDANCE PATTERNS REVISITED , 1990 .

[61]  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 .

[62]  R. Margalef,et al.  Through the looking glass: how marine phytoplankton appears through the microscope when graded by size and taxonomically sorted , 1994 .