Table 1.
Definition of the model parameters.
| Symbol | Definition |
|---|---|
| s | Sex |
| a | Age |
| c | Category (e.g., elite) |
| g | QTL Genotype |
| t | Generation number |
| Csacg | Class of individuals defined by s,a,c,g at t |
| qsacgt | Selection rate on Csacg |
| λsacgt | EBV threshold for Csacg EBV |
| θsacgt | QTL weight in Csacg EBV |
| gj | jth Individual QTL genotype |
| mj | jth Individual Polygenic value |
| fs,a,c,t,g | Frequency of the genotype g in the animals defined by (s,a,c) at time t |
| μs,a,c,t,g | Mean polygenic value of animals defined by (s,a,c) at time t |
| Ns | Number of sex s animals |
| τghk | Probability to carry the g genotype when parents genotypes are h,k |
| ηi | Selection indicator (0/1) for the ith individual |
| Fs,t,k | Frequency of genotype k in sex s at t |
| δsac | Proportion of age a in sex s at t |
| I(j,t) | Global EBV of the jth individual at t |
| c(t,g) | EBV Penalty term for the genotype g at t |
| π | Minimum proportion of obtained Genetic progress on the main trait |
| ΔG | Genetic progress on the main trait |
| Φ(β) | Normal distribution function |
| i(q) | Selection intensity |
| λ | Coefficient controlling the importance of the ΔG constraint on the objective function |