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

Abstract

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, β_P = 0.108 (0.036, 0.187 95% CI), whereas the genetic gradient was not different from zero, β_A = -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'.

Keywords: Malurus; Price equation; natural selection; quantitative genetics; selection gradient.

Figure 1.

The relationship between nestling mass (binned into approximately 1 g categories) and survival from fledging to independence (12–41 days). The sample sizes of individuals in each group are given within the bars. (Online version in colour.)

Figure 2.

Posterior distributions of the estimates of components of covariance between nestling mass and juvenile survival in superb fairy-wrens (from model I, table 1). Red diagonal hashed lines indicate the additive genetic covariance, green diagonal lines indicate the environmental (non-genetic) covariance (defined as in §2) and blue horizontal lines indicate the phenotypic covariance. Survival was modelled as a threshold trait with a probit link function, so the parameter estimates are on the latent scale. Despite the positive phenotypic covariance and additive genetic variance for both traits (electronic supplementary material, figure S1), there was little support for positive additive genetic covariance.

Figure 3.

Posterior distributions of the estimates of the selection gradients for nestling mass. (a) Genetic and non-genetic gradients: red diagonal hashed lines indicate the additive genetic gradient β_A, green diagonal lines indicate the environmental (non-genetic) gradient β_E and blue horizontal lines indicate the phenotypic gradient β_P. (b) Tests of equivalence of gradients. Purple horizontal lines indicate the difference $({\beta }_{\mathrm{P}}-{\beta }_{\mathrm{A}})$ between the phenotypic and genetic gradients, and brown diagonal lines indicate the difference $({\beta }_{\mathrm{E}}-{\beta }_{\mathrm{A}})$ between environmental and genetic gradients. (Online version in colour.)

Figure 4.

A phenotypic trait in an individual may be determined by a range of factors, including the individual's genotype and environmental variation; these effects are depicted by single-headed arrows. The diagram represents a scenario whereby both the trait of interest (such as body size) and a component of fitness change in a correlated manner owing to temporal variation (both within or between years), generating a statistical correlation between trait and fitness depicted by the double-headed purple arrow. The net result is a phenotypic covariance between trait and fitness, and hence the appearance of selection, but no potential for any evolutionary response. After [14,15], but considering, in particular, the confounding effects of temporal variation. (Online version in colour.)