Journal of Mathematical Biology

, Volume 27, Issue 4, pp 429–450

A quantitative genetic model for growth, shape, reaction norms, and other infinite-dimensional characters

  • Mark Kirkpatrick
  • Nancy Heckman


Infinite-dimensional characters are those in which the phenotype of an individual is described by a function, rather than by a finite set of measurements. Examples include growth trajectories, morphological shapes, and norms of reaction. Methods are presented here that allow individual phenotypes, population means, and patterns of variance and covariance to be quantified for infinite-dimensional characters. A quantitative-genetic model is developed, and the recursion equation for the evolution of the population mean phenotype of an infinite-dimensional character is derived. The infinite-dimensional method offers three advantages over conventional finite-dimensional methods when applied to this kind of trait: (1) it describes the trait at all points rather than at a finite number of landmarks, (2) it eliminates errors in predicting the evolutionary response to selection made by conventional methods because they neglect the effects of selection on some parts of the trait, and (3) it estimates parameters of interest more efficiently.

Key words

Quantitative genetics Infinite-dimensional characters Growth Morphological shapes Reaction norms 


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Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Mark Kirkpatrick
    • 1
  • Nancy Heckman
    • 2
  1. 1.Department of ZoologyUniversity of TexasAustinUSA
  2. 2.Department of StatisticsUniversity of British ColumbiaVancouverCanada

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