How to predict community responses to perturbations in the face of imperfect knowledge and network complexity

Recent attempts to predict the response of large food webs to perturbations have revealed that in larger systems increasingly precise information on the elements of the system is required. Thus, the effort needed for good predictions grows quickly with the system's complexity. Here, we show that not all elements need to be measured equally well, suggesting that a more efficient allocation of effort is possible. We develop an iterative technique for determining an efficient measurement strategy. In model food webs, we find that it is most important to precisely measure the mortality and predation rates of long-lived, generalist, top predators. Prioritizing the study of such species will make it easier to understand the response of complex food webs to perturbations.

[1]  Thilo Gross,et al.  Local dynamical equivalence of certain food webs , 2009, 0906.0381.

[2]  Maxi San Miguel,et al.  A measure of individual role in collective dynamics , 2010, Scientific Reports.

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

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

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

[6]  Thilo Gross,et al.  Generalized modeling of ecological population dynamics , 2010, Theoretical Ecology.

[7]  E. García‐Berthou,et al.  Invasive species are a leading cause of animal extinctions. , 2005, Trends in ecology & evolution.

[8]  G. Hardin.  The competitive exclusion principle. , 1960, Science.

[9]  Thilo Gross,et al.  Structural kinetic modeling of metabolic networks , 2006, Proceedings of the National Academy of Sciences.

[10]  B. Drossel,et al.  Boolean versus continuous dynamics on simple two-gene modules. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  H. Mooney,et al.  The evolutionary impact of invasive species , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[12]  R. May.  Qualitative Stability in Model Ecosystems , 1973 .

[13]  Thilo Gross,et al.  Enrichment and foodchain stability: the impact of different forms of predator-prey interaction. , 2004, Journal of theoretical biology.

[14]  Thilo Gross,et al.  Dynamical analysis of evolution equations in generalized models , 2010, 1012.4340.

[15]  Ricard V Solé,et al.  Press perturbations and indirect effects in real food webs. , 2009, Ecology.

[16]  P. Kareiva,et al.  Impact: Toward a Framework for Understanding the Ecological Effects of Invaders , 1999, Biological Invasions.

[17]  D. Pauly,et al.  A method for identifying keystone species in food web models , 2006 .

[18]  M. Mack,et al.  Impacts of biological invasions on disturbance regimes. , 1998, Trends in ecology & evolution.

[19]  D. Fell.  Metabolic control analysis: a survey of its theoretical and experimental development. , 1992, The Biochemical journal.

[20]  R. May.  Food webs. , 1983, Science.

[21]  K. McCann.  The diversity–stability debate , 2000, Nature.

[22]  Ferenc Jordán,et al.  Topological keystone species : measures of positional importance in food webs , 2006 .

[23]  M. Pascual,et al.  Ecological networks : Linking structure to dynamics in food webs , 2006 .

[24]  B. Menge,et al.  Indirect Effects in Marine Rocky Intertidal Interaction Webs: Patterns and Importance , 1995 .

[25]  J. Bascompte,et al.  Compartmentalization increases food-web persistence , 2011, Proceedings of the National Academy of Sciences.

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

[27]  Thilo Gross,et al.  Generalized Models Reveal Stabilizing Factors in Food Webs , 2009, Science.

[28]  P. Abrams.  Evolution and the Consequences of Species Introductions and Deletions , 1996 .

[29]  Mark Emmerson,et al.  Predicting community responses to perturbations in the face of imperfect knowledge and network complexity. , 2011, Ecology.

[30]  P. Cochat,et al.  Et al , 2008, Archives de pediatrie : organe officiel de la Societe francaise de pediatrie.

[31]  R. Paine,et al.  Species Introduction in a Tropical Lake , 1973, Science.

[32]  F. Jordán.  Keystone species and food webs , 2009, Philosophical Transactions of the Royal Society B: Biological Sciences.

[33]  H. Houthakker,et al.  Income and Price Elasticities in World Trade , 1969 .

[34]  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 .

[35]  Samuel S. M. Wong.  Computational Methods In Physics And Engineering , 1993 .

[36]  Ferenc Jordán,et al.  Identifying important species: Linking structure and function in ecological networks , 2008 .

[37]  Thilo Gross,et al.  Generalized models as a universal approach to the analysis of nonlinear dynamical systems. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[38]  Thilo Gross,et al.  General analysis of mathematical models for bone remodeling. , 2010, Bone.

[39]  P. Olver.  Nonlinear Systems , 2013 .

[40]  Neo D. Martinez,et al.  Simple prediction of interaction strengths in complex food webs , 2009, Proceedings of the National Academy of Sciences.

[41]  P ? ? ? ? ? ? ? % ? ? ? ? , 1991 .

[42]  J. A. Kuznecov.  Elements of applied bifurcation theory , 1998 .

[43]  B. Ebenman,et al.  Using sensitivity analysis to identify keystone species and keystone links in size-based food webs , 2011 .

[44]  P. Moyle,et al.  Fish Invasions in California: Do Abiotic Factors Determine Success? , 1996 .

[45]  Thilo Gross,et al.  Early Warning Signals for Critical Transitions: A Generalized Modeling Approach , 2011, PLoS Comput. Biol..

[46]  M. S. Hoddle,et al.  Population biology of invasive species. , 2001 .

[47]  Stefano Allesina,et al.  Who dominates whom in the ecosystem? Energy flow bottlenecks and cascading extinctions. , 2004, Journal of theoretical biology.

[48]  J. E. Cohen,et al.  Global stability, local stability and permanence in model food webs. , 2001, Journal of theoretical biology.

[49]  A. M. Edwards,et al.  The invisible niche: weakly density-dependent mortality and the coexistence of species. , 2009, Journal of theoretical biology.

[50]  Neo D. Martinez,et al.  Network structure and biodiversity loss in food webs: robustness increases with connectance , 2002, Ecology Letters.

[51]  Samuel S. M. Wong.  Computational methods in physics and engineering (2nd ed.) , 1997 .