The Statistical Scale Effect as a Source of Positive Genetic Correlation Between Mean and Variability: A Simulation Study

The selection objective for animal production is the highest income with the lowest production cost, whilst ensuring the highest animal welfare. A selection experiment for environmental variability of birth weight in mice showed a correlated response in the mean after 20 generations starting from a crossed panmictic population. The relationship between the birth weight and its environmental variability explained the correlated response. The scale effect represents a potential cause of this correlation. The relationship between the mean and the variability implies: the higher the mean, the higher the variability. The study was to quantify by simulation the genetic correlation between a trait and its environmental variability. This can be attributable to the scale effect in a range of coefficients of variation and heritabilities between 0.05 and 0.50. The resulting genetic correlation ranged from 0.1335 to 0.7021 being the highest for the highest heritability and the lowest CV. The scale effect for a trait with heritability between 0.25 and 0.35 and CV between 0.15 and 0.25 generated a genetic correlation between 0.43 and 0.57. The genetic coefficient of variation (GCV) affecting residual variability was modulated by the strength reducing the impact of the scale effect. GCV ranged from 0.0050 to 1.4984. The strength of the scale effect might be in the range between 0 and 1. The scale effect would explain many reported genetic correlation and the additive genetic variance for the variability. This is relevant when increasing the mean of a trait jointly with the reduction of its variability.