Chapter

Constraints on Negative Relationships: Mathematical Causes and Ecological Consequences

James H. Brown, Edward J. Bedrick, S. K. Morgan Ernest, Jean-Luc E. Cartron and Jeffrey F. Kelly

in The Nature of Scientific Evidence

Published by University of Chicago Press

Published in print October 2004 | ISBN: 9780226789552
Published online February 2013 | e-ISBN: 9780226789583 | DOI: http://dx.doi.org/10.7208/chicago/9780226789583.003.0010
Constraints on Negative Relationships: Mathematical Causes and Ecological Consequences

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One problem in inferring process from pattern is that offsetting and indirect effects, nonlinearities, and other difficulties in complex systems may prevent a clear pattern from being generated even though the hypothesized process is operating. One such complication is the constraint on the magnitudes of correlations and covariances when some of the relationships are negative. The positive semidefinite (PSD) condition requires that each of the eigenvalues and each of the principal minors of a correlation matrix be nonnegative, thereby placing limits on the possible values of the correlation coefficient. Using simple ecological examples, this chapter illustrates how processes that can generate strongly negative correlations in a simple two-variable system can be constrained from generating such clear patterns when there are multiple variables. The PSD condition is more than a statistical curiosity; it reflects real constraints on the magnitudes and patterns of interactions in ecological networks and other complex systems.

Keywords: PSD condition; constraints; strongly negative correlations; patterns; ecological networks; complex systems; variables

Chapter.  10007 words.  Illustrated.

Subjects: Animal Pathology and Diseases

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