Shortcut predictions for fitness properties at the mutation-selection-drift balance and for its buildup after size reduction under different management strategies

For populations at the mutation-selection-drift (MSD) balance, I develop approximate analytical expressions giving expectations for the number of deleterious alleles per gamete, the number of loci at which any individual is homozygous for deleterious alleles, the inbreeding depression rate, and the additive and dominant components of fitness variance. These predictions are compared to diffusion ones, showing good agreement under a wide range of situations. I also give approximated analytical predictions for the changes in mean and additive variance for fitness when a population approaches a new equilibrium after its effective size is reduced to a stable value. Results are derived for populations maintained with equal family contribution or with no management after size reduction, when selection acts through viability or fertility differences. Predictions are compared to previously published results obtained from transition matrices or stochastic simulations, a good qualitative fit being obtained. Predictions are also obtained for populations of various sizes under different sets of plausible mutational parameters. They are compared to available empirical results for Drosophila, and conservation implications are discussed.