Mean fitness is maximized in small populations under stabilizing selection on highly polygenic traits

Stabilizing selection commonly acts on complex traits that affect individual fitness. Here, we relate mean fitness under stabilizing selection to population size and trait architecture, using a simple application of theoretical predictions for the distribution of phenotypic values in a single-trait Gaussian stabilizing selection model. We show that mean fitness is maximized by a finite (often small) population size when the total mutation rate $U$ across trait-affecting loci is reasonably large. Namely, this occurs when $U>V_M/8\left(V_S+V_E\right)$ , where $V_M$ is the variance of the distribution of effect sizes of new mutations, $V_S$ determines the strength of stabilizing selection, and $V_E$ is the environmental variance. We validate these predictions using individual-based simulations and briefly discuss their implications for interpreting genetic load and adaptability in small populations.