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How Species InteractAltering the Standard View on Trophic Ecology$
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Roger Arditi and Lev Ginzburg

Print publication date: 2012

Print ISBN-13: 9780199913831

Published to Oxford Scholarship Online: May 2015

DOI: 10.1093/acprof:osobl/9780199913831.001.0001

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It Must Be Beautiful

It Must Be Beautiful

(p.129) Chapter 6 It Must Be Beautiful
How Species Interact

Roger Arditi

Lev R. Ginzburg

Oxford University Press

This chapter explains the role of ratio-dependence as an invariance in ecology. It analyzes the importance of using scaling invariance in mathematics and proposes that all models of interacting species must be fundamentally invariant to a proportional change in the system. It uses Newton's law of inertia as a metaphor for the Malthusian law of population growth and extends this to include interacting species. It looks into Andrey Kolmogorov's insight on the possibility of ratio-dependent interaction, and examines H. Reşit Akçakaya's famous field experiment of the Canadian lynx and hare cycles. It compares Reşit's number of unsupported parameters with other research to measure overfitting. It also discusses idealizations or limit myths of theories and applies this to the ratio-independence model.

Keywords:   ratio-dependence model, scaling invariance, interacting species, Andrey Kolmogorov, H. Reşit Akçakaya, overfitting, limit myth

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