Qualitative predictions in model ecosystems

We compare qualitative predictions of press perturbation response from community matrix models with those of a range of numerical simulations on the same models. A technique of weighting the proportion of countervailing feedback cycles in qualitative response predictions (weighted predictions) was tested against quantitative predictions from the inverse community matrix. Specifically, in nine each of 5- and 10- variable models (of varying complexity) we randomly assigned quantitative values of interaction strength and measured correspondence with qualitative predictions in terms of response strength and sign. Based on the techniques and analyses presented herein, we report an expanded scope of inference for qualitative models of any size and complexity and conclude that system structure is of overriding importance.

[1]  R. Bellman,et al.  A Survey of Matrix Theory and Matrix Inequalities , 1965 .

[2]  M. Marcus,et al.  A Survey of Matrix Theory and Matrix Inequalities , 1965 .

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

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

[5]  Lennart Persson,et al.  Size-Structured Populations , 1988, Springer Berlin Heidelberg.

[6]  C. Darwin On the Origin of Species by Means of Natural Selection: Or, The Preservation of Favoured Races in the Struggle for Life , 2019 .

[7]  Lawrence B. Slobodkin,et al.  A Critique for Ecology , 1991 .

[8]  Oswald J. Schmitz,et al.  PRESS PERTURBATIONS AND THE PREDICTABILITY OFECOLOGICAL INTERACTIONS IN A FOOD WEB , 1997 .

[9]  J. Timothy Wootton,et al.  THEORETICAL CONCEPTS AND EMPIRICAL APPROACHES TO MEASURING INTERACTION STRENGTH , 1998 .

[10]  W. J. Thron,et al.  Encyclopedia of Mathematics and its Applications. , 1982 .

[11]  Antonio Bodini,et al.  Reconstructing trophic interactions as a tool for understanding and managing ecosystems: application to a shallow eutrophic lake , 2000 .

[12]  J. Lawton,et al.  Number of trophic levels in ecological communities , 1977, Nature.

[13]  Andrew Sih,et al.  Predation: direct and indirect impacts on aquatic communities , 1988 .

[14]  Peter Kareiva,et al.  Special Feature: Higher Order Interactions as a Foil to Reductionist Ecology , 1994 .

[15]  Dmitriĭ Olegovich Logofet,et al.  Matrices and Graphs Stability Problems in Mathematical Ecology , 1993 .

[16]  H. Mooney,et al.  Human Domination of Earth’s Ecosystems , 1997, Renewable Energy.

[17]  James P. Quirk,et al.  Qualitative Economics and the Stability of Equilibrium , 1965 .

[18]  John Vandermeer,et al.  On the Covariance of the Community Matrix , 1972 .

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

[20]  R. Levins The strategy of model building in population biology , 1966 .

[21]  E. Berlow,et al.  QUANTIFYING VARIATION IN THE STRENGTHS OF SPECIES INTERACTIONS , 1999 .

[22]  R. Levins Evolution in Changing Environments: Some Theoretical Explorations. (MPB-2) , 1968 .

[23]  Hisao Nakajima,et al.  Sensitivity and stability of flow networks , 1992 .

[24]  L. Oksanen,et al.  Exploitation Ecosystems in Gradients of Primary Productivity , 1981, The American Naturalist.

[25]  R. Paine,et al.  Food-web analysis through field measurement of per capita interaction strength , 1992, Nature.

[26]  Howard Whitley Eves,et al.  Elementary Matrix Theory , 1980 .

[27]  R. Levins,et al.  On the variance of eigenvalues of the community matrix : Derivation and appraisal , 2000 .

[28]  Charles J. Puccia,et al.  Qualitative Modeling of Complex Systems: An Introduction to Loop Analysis and Time Averaging , 1986 .

[29]  P. Yodzis,et al.  The stability of real ecosystems , 1981, Nature.

[30]  R. Levins,et al.  The dynamics of aquatic systems. 2. The effects of nutrient enrichment on model plankton communities1,2 , 1977 .

[31]  S. Gleeson Density Dependence is Better Than Ratio Dependence , 1994 .

[32]  J. Diamond,et al.  Ecology and Evolution of Communities , 1976, Nature.

[33]  C. Puccia,et al.  Models and Field Data of New England Tide Pools1 , 1983 .

[34]  Jeffrey M. Dambacher,et al.  Parsimonious interpretation of the impact of vegetation, food, and predation on snowshoe hare , 1999 .

[35]  R. Arditi,et al.  Coupling in predator-prey dynamics: Ratio-Dependence , 1989 .

[36]  C. Rossi,et al.  Feedback analysis in reserve management: studying local myths using qualitative models , 2000 .

[37]  R. Levins Asymmetric Competition Among Distant Taxa , 1979 .

[38]  A. Bodini,et al.  A Multimethodological Approach for the Sustainable Management of Perifluvial Wetlands of the Po River (Italy) , 2000, Environmental management.

[39]  Michel Loreau,et al.  Functional diversity governs ecosystem response to nutrient enrichment , 2000, Nature.

[40]  A. D. Bazykin Analysis of ecological systems: State-of-the-art in ecological modelling: William K. Lauenroth, Gaylord V. Skogerboe and Marshall Flug (Editors). Developments in Environmental Modelling, 5. Elsevier, Amsterdam, 1983. 992 pp., Dfl. 320.00. ISBN 0-444-42179-3 , 1986 .

[41]  R. Yeaton,et al.  An Ecological Analysis of Chaparral and Pine Forest Bird Communities on Santa Cruz Island and Mainland California , 1974 .

[42]  Hiram W. Li,et al.  Ecological Analysis of Species Introductions into Aquatic Systems , 1981 .

[43]  L. Slobodkin,et al.  Community Structure, Population Control, and Competition , 1960, The American Naturalist.

[44]  L Stone,et al.  Phytoplankton-bacteria-protozoan interactions: a qualitative model portraying indirect effects , 1990 .

[45]  Antonio Bodini,et al.  Representing Ecosystem Structure through Signed Digraphs. Model Reconstruction, Qualitative Predictions and Management: The Case of a Freshwater Ecosystem , 1998 .

[46]  R. Ricklefs,et al.  Competition and the structure of bird communities. , 1975, Monographs in population biology.

[47]  M. Gilpin,et al.  Perturbation Experiments in Community Ecology: Theory and Practice , 1984 .

[48]  G. Mittelbach,et al.  Trophic Relations and Ontogenetic Niche Shifts in Aquatic Ecosystems , 1988 .

[49]  R Levins,et al.  DISCUSSION PAPER: THE QUALITATIVE ANALYSIS OF PARTIALLY SPECIFIED SYSTEMS , 1974, Annals of the New York Academy of Sciences.

[50]  J. Lawton,et al.  On feeding on more than one trophic level , 1978, Nature.

[51]  S. Roxburgh,et al.  Stability and coexistence in a lawn community: mathematical prediction of stability using a community matrix with parameters derived from competition experiments , 2000 .