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


Hajduk, Gabrielle; Walling, Craig; Cockburn, Andrew; Kruuk, Loeske (2021), The ‘algebra of evolution’: the Robertson-Price identity and viability selection for body mass in a wild bird population, Dryad, Dataset,


By the Robertson-Price Identity, the change in a quantitative trait due to selection is equal to the trait’s covariance with relative fitness. We used a long-term study of superb fairy-wrens Malurus cyaneus to consider phenotypic and genetic change within a generation due 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 two traits, but no evidence of additive genetic covariance. Comparing standardised 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.

Usage Notes

Data files are in .RData format.
"ainv.SFW.MCMCglmm.RData" is the inverse relatedness matrix for the superb fairy-wren study population 1988-2013.

"SFWnestlings.RData"  contains the phenotypic data on nestling mass and survival, with the following columns:
'label' - nestling ID
'weight' - nestling mass
'alive41daysF' - if alive at 41 days (4 weeks after fledgling)
'helpersCat' - number of helpers at nest, in categories of 0, 1 or 2+
'chickAge' - age at weighing, in days
'genF' - pedigree inbreeding coefficient  
'pre1992' - two-level factor to correct for change in weighing protocol prior to 1992
'WPO' - two-level factor to indicate with nestling was within-pair or extra-pair offspring
'cohortFac' - cohort as a factor
'HatchDateFac' - hatchdate fortnight as factor
'animal' - nestling ID as factor level linked to ainv file

R code is provided in Hajduk_SFWcode_PhilTrans.pdf.

Further details of the different variables are provided in the paper. These data are part of the long-term
study of superb fairy-wrens in the Australian National Botanic Gardens, and the paper is part of Gabi Hajduk's
PhD project.