Multilocus epistasis, linkage, and genetic variance in breeding populations with few parents

In a previous study of maize (Zea mays L.) populations formed from few parents, we found that estimates of genetic variances were inconsistent with a simple additive genetic model. Our objective in the current study was to determine how multilocus epistasis and linkage affect the loss of genetic variance in populations created from a small number of parents (N). In simulation experiments, F-2 individuals from the same single cross were intermated to form progeny populations from N = 1, 2, 4, and 8 parents. Additive gene effects and metabolic flux epistasis due to L = 10, 50, and 100 loci were modeled. For additive, additive-with-linkage, epistatic, and epistasis-with-linkage models, we estimated the ratio between total genetic variance in the progeny population (V-N) and base population (V-B) as well as the 95th (Delta(95%)) and 75th (Delta(75%)) percentile differences between the estimated V-N /V (B) and the V-N /V (B) expected for the additive model. The mean V (N) /V (B) ratio was lower under epistasis than under additivity, indicating that metabolic flux epistasis hastens the decline in genetic variance due to small N. In contrast, Delta(95%) was higher with epistasis than with additivity across the different levels of N and L. Linkage had little effect on the mean V-N /V-B , whereas it increased Delta(95%) and Delta(75%) under both additivity and epistasis. Smaller N and L led to higher V-N /V-B particularly when epistasis was present. Overall, the results indicated that while metabolic flux epistasis led to a faster average decline in genetic variance, it also led to greater variability in this decline to the point that V-N /V-B was larger than expected in many populations.