Selection on plasticity of seasonal life-history traits using random regression mixed model analysis

Abstract

Theory considers the covariation of seasonal life-history traits as an optimal reaction norm, implying that deviating from this reaction norm reduces fitness. However, the estimation of reaction-norm properties (i.e., elevation, linear slope, and higher order slope terms) and the selection on these is statistically challenging. We here advocate the use of random regression mixed models to estimate reaction-norm properties and the use of bivariate random regression to estimate selection on these properties within a single model. We illustrate the approach by random regression mixed models on 1115 observations of clutch sizes and laying dates of 361 female Ural owl Strix uralensis collected over 31 years to show that (1) there is variation across individuals in the slope of their clutch size-laying date relationship, and that (2) there is selection on the slope of the reaction norm between these two traits. Hence, natural selection potentially drives the negative covariance in clutch size and laying date in this species. The random-regression approach is hampered by inability to estimate nonlinear selection, but avoids a number of disadvantages (stats-on-stats, connecting reaction-norm properties to fitness). The approach is of value in describing and studying selection on behavioral reaction norms (behavioral syndromes) or life-history reaction norms. The approach can also be extended to consider the genetic underpinning of reaction-norm properties.

Keywords: Bird; clutch size; natural selection; phenotypic plasticity; reaction norm.

Figure 1

Illustration of the main theoretical background of the reaction-norm concept in terms of two seasonal life-history traits. As the season advances (Time), environmental conditions and thus the potential clutch size C increase (Equation [1]; dotted line), but individuals experience different trajectories characterized by the initial condition C₀. Because the reproductive value of offspring V declines seasonally (Equation [2]), there is an optimal switching curve (solid line) that describes when an individual should stop increasing in condition and reproduce (filled dots). This switching curve is the optimal reaction norm maximizing V(t)C(t), showing a seasonal decrease in reproduction (Equation [3]). Timing reproduction earlier has fitness costs, because reproductive output decreases (gray squares), more so than offspring reproduction increases. Delaying reproduction increases reproductive output (gray dots), but has fitness costs because late-produced offspring are of lower value.

Figure 2

Yearly mean in clutch size and laying date for all Ural owl females included in the analysis. Laying date was expressed in days relative to its long-term median (31 March). Data consist of 1114 observations collected over 31 years. Line displays the linear regression (coefficients and test reported in the text).

Figure 3

(A) Plot of the variance in clutch size (solid line) and its approximate 95% confidence interval (dashed line) as a function of laying date. Values based on statistics of model 5 in Table 1 and applying the results of Fisher et al. (2004). (B) Plot of the reaction norms based on the fixed effects of elevation and slope and the Best Linear Unbiased Predictor (BLUP) values of model 5 for the individual females’ reaction norms (Table 1).