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Open Access Publications from the University of California

Reverse first principles: Weber's law and optimality in different senses

  • Author(s): Wilkes, Jason Taylor
  • Advisor(s): Cosmides, Leda
  • et al.

The relationship between optimality and evolvability is analyzed through a case study of Weber's law, a common property of many sensory systems across a wide array of species. After demonstrating a variety of senses in which Weber's law is mathematically optimal, we ask whether principled methods exist for evaluating such optimality analyses. We argue that at least one such method exists: examining the evolvability of a trait with respect to each of the different metrics that it happens to optimize. Through evolvability analyses of Weber's law, it is demonstrated that optimality-equivalent measures of phenotypic quality need not be selectively equivalent: a trait that is optimal by two measures may have very different behavior under selection for each. This non-equivalence allows different optimality analyses of the same phenomenon to be assessed by a standard other than intuition, and in a manner requiring fewer degrees of freedom than are needed to model selection from scratch. Two qualitatively different models of selection are explored: phenotypic selection, a basic form in which mutations directly affect the model phenotype, and embryological selection, a more exotic form in which mutations affect the algorithm by which the phenotype is built.

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