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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 Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691134178.001.0001

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Excitable and Nonexcitable Population Dynamics

Excitable and Nonexcitable Population Dynamics

(p.53) Chapter Four Excitable and Nonexcitable Population Dynamics
Food Webs (MPB-50)

Kevin S. McCann

Princeton University Press

This chapter examines the dynamics of basic population models, with a particular focus on the general biological conditions under which population dynamics are stabilized, or destabilized, by increased population growth rates. Three classes of population models are discussed in relation to excitable and nonexcitable interactions: continuous logistic growth models, discrete equations, and continuous models with stage-structured lags. The chapter shows how increasing per capita growth rates tend to stabilize population models as a result of excitable interactions; that is, when dynamic trajectories monotonically approach an equilibrium after a localized perturbation. However, lags in population models tend to give rise to dynamics with oscillatory decays to equilibrium or sustained oscillations around the carrying capacity. Such oscillatory decays or sustained oscillations are only further destabilized by increased growth or production rates. The chapter concludes with a review of empirical evidence for excitable dynamics.

Keywords:   population models, population dynamics, population growth, nonexcitable interactions, continuous logistic growth models, discrete equations, stage-structured lags, excitable interactions, oscillatory decay, oscillation

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