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Loop Analysis: Evaluating Life History Pathways in Population Projection Matrices

Jan van Groenendael, Hans de Kroon, Susan Kalisz and Shripad Tuljapurkar
Ecology
Vol. 75, No. 8 (Dec., 1994), pp. 2410-2415
Published by: Wiley
DOI: 10.2307/1940894
Stable URL: http://www.jstor.org/stable/1940894
Page Count: 6
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Loop Analysis: Evaluating Life History Pathways in Population Projection Matrices
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Abstract

A new way of analyzing life histories is presented, based on the use of elasticities as derived from the limit properties of population projection matrices. In general there is not a simple relation between life history traits and matrix elements and their corresponding elasticity values. By recognizing the fact that a life history trait always is part of a life history pathway that can be contrasted to other pathways, this problem can be overcome. The various life history pathways form loops within the life cycle graph, the graphical representation of the projection matrix. It is shown that one can calculate the elasticities of such loops from the single elasticity values in the matrix in an unequivocal way. This presents a new and meaningful decomposition of total elasticity in population projection matrices and provides a potentially powerful tool to evaluate the importance of alternative life history options in demographic studies. This point is demonstrated using two previously published sets of data.

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