Feasibility and coexistence of large ecological communities

The role of species interactions in controlling the interplay between the stability of ecosystems and their biodiversity is still not well understood. The ability of ecological communities to recover after small perturbations of the species abundances (local asymptotic stability) has been well studied, whereas the likelihood of a community to persist when the conditions change (structural stability) has received much less attention. Our goal is to understand the effects of diversity, interaction strengths and ecological network structure on the volume of parameter space leading to feasible equilibria. We develop a geometrical framework to study the range of conditions necessary for feasible coexistence. We show that feasibility is determined by few quantities describing the interactions, yielding a nontrivial complexity–feasibility relationship. Analysing more than 100 empirical networks, we show that the range of coexistence conditions in mutualistic systems can be analytically predicted. Finally, we characterize the geometric shape of the feasibility domain, thereby identifying the direction of perturbations that are more likely to cause extinctions.

[1]  J. Pitchford,et al.  Disentangling nestedness from models of ecological complexity , 2012, Nature.

[2]  Rudolf P. Rohr,et al.  On the structural stability of mutualistic systems , 2014, Science.

[3]  ALAN ROBERTS,et al.  The stability of a feasible random ecosystem , 1974, Nature.

[4]  Terence Tao,et al.  Random matrices: Universality of ESDs and the circular law , 2008, 0807.4898.

[5]  Thilo Gross,et al.  How to predict community responses to perturbations in the face of imperfect knowledge and network complexity , 2013, Proceedings of the Royal Society B: Biological Sciences.

[6]  James H. Brown,et al.  Effects of Size and Temperature on Metabolic Rate , 2001, Science.

[7]  R. Tyrrell Rockafellar,et al.  Convex Analysis , 1970, Princeton Landmarks in Mathematics and Physics.

[8]  Si Tang,et al.  Reactivity and stability of large ecosystems , 2014, Front. Ecol. Evol..

[9]  T. Tao,et al.  Random matrices: Universality of local eigenvalue statistics , 2009, 0906.0510.

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

[11]  Stefano Allesina,et al.  Food web models: a plea for groups. , 2009, Ecology letters.

[12]  Mark Kac,et al.  The Spherical Model of a Ferromagnet , 1952 .

[13]  Kim Sneppen,et al.  Food Web Assembly Rules for Generalized Lotka-Volterra Equations , 2016, PLoS Comput. Biol..

[14]  R. Redheffer.  Volterra Multipliers II , 1985 .

[15]  Mats Gyllenberg,et al.  Competitive exclusion and limiting similarity: a unified theory. , 2006, Theoretical population biology.

[16]  Alberto Seeger,et al.  Deterministic and stochastic methods for computing volumetric moduli of convex cones , 2010 .

[17]  Rudolf P. Rohr,et al.  Nested species interactions promote feasibility over stability during the assembly of a pollinator community , 2016, Ecology and evolution.

[18]  E. Kaszkurewicz,et al.  Matrix diagonal stability in systems and computation , 1999 .

[19]  Edward B. Baskerville,et al.  Spatial Guilds in the Serengeti Food Web Revealed by a Bayesian Group Model , 2010, PLoS Comput. Biol..

[20]  Robert Poulin,et al.  Food web including metazoan parasites for a brackish shallow water ecosystem in Germany and Denmark , 2011 .

[21]  Dmitriĭ Olegovich Logofet,et al.  Stability of Biological Communities , 1983 .

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

[23]  R. May,et al.  Nonlinear Aspects of Competition Between Three Species , 1975 .

[24]  Karsten Reise,et al.  Food web including metazoan parasites for a tidal basin in Germany and Denmark , 2011 .

[25]  Annette Ostling,et al.  Sensitivity analysis of coexistence in ecological communities: theory and application. , 2014, Ecology letters.

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

[27]  Mats Gyllenberg,et al.  Continuous coexistence or discrete species? A new review of an old question , 2012 .

[28]  Colin Fontaine,et al.  Stability of Ecological Communities and the Architecture of Mutualistic and Trophic Networks , 2010, Science.

[29]  Stefano Allesina,et al.  Predicting global community properties from uncertain estimates of interaction strengths , 2015, Journal of The Royal Society Interface.

[30]  Daniel C Reuman,et al.  Food webs are more than the sum of their tritrophic parts , 2009, Proceedings of the National Academy of Sciences.

[31]  D. O. Logofet.  Stronger-than-Lyapunov notions of matrix stability, or how "flowers" help solve problems in mathematical ecology , 2005 .

[32]  P. Yodzis.  The Indeterminacy of Ecological Interactions as Perceived Through Perturbation Experiments , 1988 .

[33]  Jordi Bascompte,et al.  Asymmetric Coevolutionary Networks Facilitate Biodiversity Maintenance , 2006, Science.

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

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

[36]  T. Tao,et al.  Random Matrices: Universality of Local Eigenvalue Statistics up to the Edge , 2009, 0908.1982.

[37]  Amos Maritan,et al.  Disentangling the effect of hybrid interactions and of the constant effort hypothesis on ecological community stability , 2014 .

[38]  Robert Poulin,et al.  Food web including metazoan parasites for an intertidal ecosystem in New Zealand , 2011 .

[39]  R. Bhatia.  Positive Definite Matrices , 2007 .

[40]  Joel E. Cohen,et al.  Community Food Webs: Data and Theory , 1990 .

[41]  M. Gilpin,et al.  Stability of feasible predator-prey systems , 1975, Nature.

[42]  Anders Nielsen,et al.  Conservation of species interaction networks , 2010 .

[43]  R. McGehee,et al.  Coexistence of species competing for shared resources. , 1976, Theoretical population biology.

[44]  A. Maritan,et al.  Effect of localization on the stability of mutualistic ecological networks , 2015, Nature Communications.

[45]  M. Scheffer,et al.  The sudden collapse of pollinator communities. , 2014, Ecology letters.

[46]  Owen L. Petchey,et al.  Provided for Non-commercial Research and Educational Use Only. Not for Reproduction, Distribution or Commercial Use. the Role of Body Size in Complex Food Webs: a Cold Case Author's Personal Copy , 2022 .

[47]  Stefano Allesina,et al.  The ghost of nestedness in ecological networks , 2013, Nature Communications.

[48]  Abraham Berman,et al.  Matrix Diagonal Stability and Its Implications , 1983 .

[49]  S. Opitz,et al.  Trophic interactions in Caribbean coral reefs , 1996 .

[50]  O. Hoegh‐Guldberg,et al.  Ecological responses to recent climate change , 2002, Nature.

[51]  R. Macarthur.  Fluctuations of Animal Populations and a Measure of Community Stability , 1955 .

[52]  Neo D. Martinez,et al.  Simple rules yield complex food webs , 2000, Nature.

[53]  U. Jacob.  Trophic Dynamics of Antarctic Shelf Ecosystems - Food Webs and Energy Flow Budgets , 2005 .

[54]  Robert R. Christian,et al.  Organizing and understanding a winter's seagrass foodweb network through effective trophic levels , 1999 .

[55]  Jason M. Ribando,et al.  Measuring Solid Angles Beyond Dimension Three , 2006, Discret. Comput. Geom..

[56]  R. G. Casten,et al.  Global Stability and Multiple Domains of Attraction in Ecological Systems , 1979, The American Naturalist.

[57]  G. Parisi,et al.  Statistical Field Theory , 1988 .

[58]  Jens O. Riede,et al.  Stepping in Elton's footprints: a general scaling model for body masses and trophic levels across ecosystems. , 2011, Ecology letters.

[59]  Stefano Allesina,et al.  The stability–complexity relationship at age 40: a random matrix perspective , 2015, Population Ecology.

[60]  B. Goh.  Global Stability in Many-Species Systems , 1977, The American Naturalist.

[61]  Carlos J. Melián,et al.  The nested assembly of plant–animal mutualistic networks , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[62]  Anthony R. Ives,et al.  Species Response to Environmental Change: Impacts of Food Web Interactions and Evolution , 2009, Science.

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

[64]  J. Bascompte,et al.  Global change and species interactions in terrestrial ecosystems. , 2008, Ecology letters.

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

[66]  Review: Vito Volterra, Leçons sur la Théorie Mathématique de la Lutte pour la Vie , 1936 .

[67]  B. S. Goh,et al.  Feasibility and stability in randomly assembled Lotka-Volterra models , 1977 .

[68]  Jeffrey M. Dambacher,et al.  RELEVANCE OF COMMUNITY STRUCTURE IN ASSESSING INDETERMINACY OF ECOLOGICAL PREDICTIONS , 2002 .