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Food Webs (MPB-50)$
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Kevin S. McCann

Print publication date: 2011

Print ISBN-13: 9780691134178

Published to University Press Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691134178.001.0001

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date: 13 December 2017

Classic Food Web Theory

Classic Food Web Theory

Chapter:
(p.170) Chapter Ten Classic Food Web Theory
Source:
Food Webs (MPB-50)
Author(s):

Kevin S. McCann

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691134178.003.0010

This chapter examines the basic assumptions of classic food web theory. It first considers the classic whole-community approach, which assumes that any specific matrix represents a sample from a “statistical universe” of interaction strengths for a given set of n species. It then describes some matrix approaches to see if context-dependent techniques can be applied to matrix theory, along with the simple graphical techniques of Gershgorin discs employed as an intuitive approach to eigenvalues. It argues that there are some rather intriguing “gravitational-like” properties of Gershgorin discs for some important biologically motivated matrices. The chapter proceeds by discussing some classic whole-matrix results that highlight the connections between the stability of lower-dimensional modules and whole food webs. Finally, it shows how the ideas derived from classic whole-system matrix approaches generally agree with the results of modular theory.

Keywords:   food web theory, whole-community approach, interaction strength, matrix theory, Gershgorin discs, eigenvalue, module, food webs, whole-system matrix, modular theory

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