Quantitative system drift

We consider a biological system composed of multiple genetically variable components, the combined result of which is a quantitative trait under stabilizing selection for an optimal value. We show mathematically that, while the mean value of the system is ultimately constrained to remain near its optimum, the values of individual components are free to drift far from their initial values. Each components drift, though qualitatively similar to neutral drift, is slower by a factor that depends on the fraction of the systems genetic variance contributed by the component. Our results provide a population-genetic basis for system drift, the concept that individual components of a biological system can evolve despite selective constraint on their combined product. A special case is a single polygenic trait under stabilizing selection, where our results predict that the mean genetic contributions to the trait of different subregions of the genome, such as the chromosomes, can drift despite constraint on the genome-wide genetic value. We explore the implications of this latter result for selection against interspecific hybrids and selection against turnovers of sex-determining systems. We further apply our general results to a continuous public goods game played between two species, where they predict that individual species contributions to a costly public good can drift freely. Finally, we show that symmetric mutation between alleles that increase and decrease components contributions to the system provides a weak long-term brake on components drift.