The ‘algebra of evolution’: The Robertson–Price identity and viability selection for body mass in a wild bird population

G. K. Hajduk, C. A. Walling, A. Cockburn, L. E. B. Kruuk

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

By the Robertson–Price identity, the change in a quantitative trait owing to selection, is equal to the trait's covariance with relative fitness. In this study, we applied the identity to long-term data on superb fairy-wrens Malurus cyaneus, to estimate phenotypic and genetic change owing to juvenile viability selection. Mortality in the four-week period between fledging and independence was 40%, and heavier nestlings were more likely to survive, but why? There was additive genetic variance for both nestling mass and survival, and a positive phenotypic covariance between the traits, but no evidence of additive genetic covariance. Comparing standardized gradients, the phenotypic selection gradient was positive, βP = 0.108 (0.036, 0.187 95% CI), whereas the genetic gradient was not different from zero, βA = −0.025 (−0.19, 0.107 95% CI). This suggests that factors other than nestling mass were the cause of variation in survival. In particular, there were temporal correlations between mass and survival both within and between years. We suggest that use of the Price equation to describe cross-generational change in the wild may be challenging, but a more modest aim of estimating its first term, the Robertson–Price identity, to assess within-generation change can provide valuable insights into the processes shaping phenotypic diversity in natural populations.

This article is part of the theme issue ‘Fifty years of the Price equation’.
Original languageEnglish
Number of pages10
JournalPhilosophical Transactions of the Royal Society B: Biological Sciences
Issue number1797
Early online date9 Mar 2020
Publication statusPublished - 27 Apr 2020

Keywords / Materials (for Non-textual outputs)

  • natural selection
  • quantitative genetics
  • price equation
  • selection gradient
  • Malurus


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