Managing Populations with Unimodal Dynamics

Richard Levins, Tamara Awerbuch, Hyung Park

Department of Biostatistics, Harvard University, Boston, USA.
Department of Global Health and Population, Harvard University, Boston, USA.

DOI: 10.4236/am.2013.410A2009                

Abstract

In this work, we analyzed the impact of interventions on populations which exhibit unimodal dynamics. The six landmarks that characterize the “shape” of the unimodal reproduction curve f ( x ) of the difference equation, X _n+1 = f ( X _n ) , are defined and used in order to examine and determine the behavior of dynamics of populations. By using the Li-Yorke criterion for determination of chaos we propose a qualitative intervention rule that can be applied without any explicit population equation. This proposed strategy for intervention brings out many interesting behaviors in population dynamics. A qualitative decision rule can be applied with a straight edge without any population equation and therefore offers a robust strategy for the management of populations.

Keywords

Qualitative Analysis; Difference Equations; Unimodal Dynamics; Intervention Strategies; Chaos; Li-Yorke Criterion; Pest Management; Species Enrichment; Pre-Image Sets

Conflicts of Interest

The authors declare no conflicts of interest.

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