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An Approach to the Perturbation Analysis of Optimal Life Histories
Author(s) -
Caswell Hal,
Real Leslie A.
Publication year - 1987
Publication title -
ecology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.144
H-Index - 294
eISSN - 1939-9170
pISSN - 0012-9658
DOI - 10.2307/1938376
Subject(s) - perturbation (astronomy) , indeterminacy (philosophy) , constraint (computer aided design) , mathematical optimization , indeterminate , mathematics , natural selection , simple (philosophy) , selection (genetic algorithm) , computer science , physics , artificial intelligence , quantum mechanics , philosophy , geometry , epistemology , pure mathematics
It has been suggested that, while natural selection may not produce optimal phenotypes, it should at least produce populations whose phenotypes differ in the directions of their optima. Optimization models are thus most readily tested in terms of the response of an optimal strategy to perturbations. This paper presents a method for calculating the perturbation response of a constrained optimum when the constraint function is at least approximately linear. We consider examples from life—history theory, but the method is widely applicable. Even for simple two—variable optimization problems subject to linear constraints, the response to perturbations is surprisingly indeterminate and sometimes counter—intuitive. This indeterminacy is resolved by the values of the second derivatives of fitness with respect to its components.