in which PH10 = pregnant heifers in the period t = 0. |
(1) |
in which LCt = lactating cows in the period t; DCBt = dry cow before birth in the period t; and PHPt = pregnant heifer before birth in the period t. |
(2) |
in which LC1t = lactating cows available for first AI in the period t; LCt = lactating cow in the period t; ϵ = % mortality rate in adult animals; and ωt = % culling rate in cows per year, equal to zero for t < 50 (ωt = 0 FOR t = [1,2,3,4…49]). |
(3) |
in which LC2t = lactating cows available for second AI in the period t; VLD1t−1 = lactating cows available for first AI in the period t−1; ι = % oestrus detection rate in cows in the first AI; Λ = % conception rate in cows in the first AI; β = % pregnancy loss in cows <90 days; and Π = % mortality rate in lactating cows. |
(4) |
in which LC3t = lactating cows available for third AI in the period t; LC2t−1 = lactating cows available for second AI in the period t−1; ι = % oestrus detection rate in cows in the second AI; K = % conception rate in cows in the second AI; β = % pregnancy loss in cows <90 days; and Π = % mortality rate in lactating cows. |
(5) |
in which LC4t = lactating cows available for fourth AI in the period t; LC3t−1 = lactating cows available for third AI in the period t−1; λ = % oestrus detection rate in cows in the third AI; μ = % conception rate in cows in the third AI; β = % pregnancy loss in cows <90 days; and Π = % mortality rate in lactating cows. |
(6) |
in which LC5t = lactating cows available for fifth AI in the period t; LC4t−1 = lactating cows available for fourth AI in the period t−1; E = % oestrus detection rate in cows in the fourth AI; Z = % conception rate in cows in the fourth AI; β = % pregnancy loss in cows <90 days; and Π = % mortality rate in lactating cows. |
(7) |
in which LC6t = lactating cows available for sixth AI in the period t; LC5t−1 = lactating cows available for fifth AI in the period t−1; Ψ = % oestrus detection rate in cows in the fifth AI; Ω = % conception rate in cows in the fifth AI; β = % pregnancy loss in cows <90 days; and Π = % mortality rate in lactating cows. |
(8) |
in which LC7t = lactating cows available for seventh AI in the period t; LC6t−1 = lactating cows available for sixth AI in the period t−1; T = % oestrus detection rate in cows in the sixth AI; O = % conception rate in cows in the sixth AI; β = % pregnancy loss in cows <90 days; and Π = % mortality rate in lactating cows. |
(9) |
in which PLC1t = pregnant lactating cow after first AI in the period t; LC1t = lactating cows available for first AI in the period t; θ = % oestrus detection rate in cows in the first AI; Λ = % conception rate in cows in the first AI; β = % pregnancy loss in cows <90 days; and Π = % mortality rate in lactating cows. |
(10) |
in which PLC2t = pregnant lactating cow after second AI in the period t; LC2t = lactating cows available for second AI in the period t; ι = % oestrus detection rate in cows in the second AI; K = % conception rate in cows in the second AI; β = % pregnancy loss in cows <90 days; and Π = % mortality rate in lactating cows. |
(11) |
in which PLC3t = pregnant lactating cow after third AI in the period t; LC3t = lactating cows available for third AI in the period t; λ = % oestrus detection rate in cows in the third AI; π = % conception rate in cows in the third AI; β = % pregnancy loss in cows <90 days; and Π = % mortality rate in lactating cows. |
(12) |
in which PLC4t = pregnant lactating cow after fourth AI in the period t; LC4t = lactating cows available for fourth AI in the period t; E = % oestrus detection rate in cows in the fourth AI; Z = % conception rate in cows in the fourth AI; β = % pregnancy loss in cows <90 days; and Π = % mortality rate in lactating cows. |
(13) |
in which PLC5t = pregnant lactating cow after fifth AI in the period t; LC5t = lactating cows available for fifth AI in the period t; Ψ = % oestrus detection rate in cows in the fifth AI; Ω = % conception rate in cows in the fifth AI; β = % pregnancy loss in cows <90 days; and Π = % mortality rate in lactating cows. |
(14) |
in which PLC6t = pregnant lactating cow after sixth AI in the period t; LC6t = lactating cows available for sixth AI in the period t; T = % oestrus detection rate in cows in the sixth AI; O = % conception rate in cows in the sixth AI; β = % pregnancy loss in cows <90 days; and Π = % mortality rate in lactating cows. |
(15) |
in which PLC7t = pregnant lactating cow after seventh AI in the period t; LC7t = lactating cows available for seventh AI in the period t; H = % oestrus detection rate in cows in the seventh AI; I = % conception rate in cows in the seventh AI; β = % pregnancy loss in cows <90 days; and Π = % mortality rate in lactating cows. |
(16) |
in which DC = dry cow in the period t; PLC1t = pregnant lactating cow after first AI in the period t−11; PLC2t = pregnant lactating cow after second AI in the period t−11; PLC3t = pregnant lactating cow after third AI in the period t−11; PLC4t = pregnant lactating cow after fourth AI in the period t−11; PLC5t = pregnant lactating cow after fifth AI in the period t−11; PLC6t = pregnant lactating cow after sixth AI in the period t−11; PLC7t = pregnant lactating cow after seventh AI in the period t−11; Π = % mortality rate in lactating cows; ϵ = % mortality rate in adult animals; and β = % pregnancy loss in cows <90 days. |
(17) |
in which DCBt = dry cow before birth in the period t; DC = dry cow in the period t; and ϵ = % mortality rate in adult animals. |
(18) |
in which YFt = young female (3-12 months); FCt−3 = cow-calf (< 3 months) birth in the period t−3; and δ = % mortality rate in cow-calf (<1 year). |
(19) |
in which Ht = heifer in the period t; FCt−17 = cow-calf (< 3 months) birth in the period t−17; and δ = % mortality rate in cow-calf (<1 year). |
(20) |
in which PPHt = purchased pregnant heifers, equal to zero for t < 15 (Tat = 0 for t = [1, 2, 3… 14]). |
(21) |
in which H1t = heifers available for first AI in the period t; Ht = heifer in the period t; and ϵ = % mortality rate in adult animals. |
(22) |
in which H2t = heifers available for second AI in the period t; H1t–1 = heifers available for first AI in the period t−1; κ = % oestrus detection rate in heifers in the first AI; ρ = % conception rate in heifers in the first AI; ϵ = % mortality rate in adult animals; and ρ = % pregnancy loss in heifers <90 days. |
(23) |
in which H3t = heifers available for third AI in the period t; H2t−1 = heifers available for second AI in the period t−1; ϱ = % oestrus detection rate in heifers in the second AI; σ = % conception rate in heifers in the second AI; ϵ = % mortality rate in adult animals; and ρ = % pregnancy loss in heifers <90 days. |
(24) |
in which H4t = heifers available for fourth AI in the period t; H3t−1 = heifers available for third AI in the period t−1; ς = % oestrus detection rate in heifers in the third AI; τ = % conception rate in heifers in the third AI; ϵ = % mortality rate in adult animals; and ρ = % pregnancy loss in heifers <90 days. |
(25) |
in which H5t = heifers available for fifth AI in the period t; H4t−1 = heifers available for fourth AI in the period t−1; Γ = % oestrus detection rate in heifers in the fourth AI; Θ = % conception rate in heifers in the fourth AI; ϵ = % mortality rate in adult animals; and ρ = % pregnancy loss in heifers <90 days. |
(26) |
in which PH1t = pregnant heifers after first AI in the period t; H1t = heifers available for first AI in the period t; κ = % oestrus detection rate in heifers in the first AI; ρ = % conception rate in heifers in the first AI; ϵ = % mortality rate in adult animals; ρ = % pregnancy loss in heifers <90 days; and Δt = % pregnant heifers for sale, equal to zero for t < 35 (Δt = 0 for t = [1, 2, 3… 34]). PPH1t = purchased pregnant heifers, equal to zero for t < 15 (Δ_t = 0 for t = [1, 2, 3… 14]). |
(27) |
in which PH2t = pregnant heifers after second AI in the period t; H2t = heifers available for second AI in the period t; ϱ = % oestrus detection rate in heifers in the second AI; σ = % conception rate in heifers in the second AI; ϵ = % mortality rate in adult animals; ρ = % pregnancy loss in heifers <90 days; and Δt = % pregnant heifers for sale, equal to zero for t < 35 (Δt = 0 for t = [1, 2, 3… 34]). |
(28) |
in which PH3t = pregnant heifers after third AI in the period t; H3t = heifers available for third AI in the period t; ς = % oestrus detection rate in heifers in the third AI; τ = % conception rate in heifers in the third AI; ϵ = % mortality rate in adult animals; ρ = % pregnancy loss in heifers <90 days; and Δt = % pregnant heifers for sale, equal to zero for t < 35 (Δt = 0 for t = [1, 2, 3… 34]). |
(29) |
in which PH4t = pregnant heifers after fourth AI in the period t; H4t = heifers available for fourth AI in the period t; Γ = % oestrus detection rate in heifers in the fourth AI; Θ = % conception rate in heifers in the fourth AI; ϵ = % mortality rate in adult animals; ρ = % pregnancy loss in heifers <90 days; and Δt = % pregnant heifers for sale, equal to zero for t < 35 (Δt = 0 for t = [1, 2, 3… 34]). |
(30) |
in which PH5t = pregnant heifers after fifth AI in the period t; H5t = heifers available for fifth AI in the period t; X = % oestrus detection rate in heifers in the fifth AI; Φ = % conception rate in heifers in the fifth AI; ϵ = % mortality rate in adult animals; ρ = % pregnancy loss in heifers <90 days; and Δt = % pregnant heifers for sale, equal to zero for t < 35 (Δt = 0 for t = [1, 2, 3… 34]). |
(31) |
in which PHBt = pregnant heifer before birth in the period t; PH1t−14 = pregnant heifers after first AI in the period t−14; PH2t−14 = pregnant heifers after second AI in the period t−14; PH3t−14 = pregnant heifers after third AI in the period t−14; PH4t−14 = pregnant heifers after fourth AI in the period t−14; PH5t−14 = pregnant heifers after fifth AI in the period t−14; ϵ = % mortality rate in adult animals; and A = % pregnancy loss in heifers >90 days. |
(32) |
in which CM1 = calves born in year t = 1; γ = % gestations with bull-calf/cow-calf product by natural service; and LC1 = lactating cow in the period t = 1. |
(33) |
in which BCt = bull-calf - number of calves born after the reproductive program of the farm, taking into account the semen technology used in the period t>1; ξ = % gestations with bull-calf product in the first AI; o = % gestations with bull-calf product in the second AI; π = % gestations with bull-calf product in the third AI; ϒ = % gestations with bull-calf product in the fourth AI; φ = % gestations with bull-calf product in the fifth AI; χ = % gestations with bull-calf product in the sixth AI; P = % gestations with bull-calf product in the seventh AI; PLC1t−14 = pregnant lactating cow after first AI in the period t−14; PLC2t−14 = pregnant lactating cow after second AI in the period t−14; PLC3t−14 = pregnant lactating cow after third AI in the period t−14; PLC4t−14 = pregnant lactating cow after fourth AI the period t−14; PLC5t−14 = pregnant lactating cow after fifth AI in the period t−14; PLC6t−14 = pregnant lactating cow after sixth AI in the period t−14; PLC7t−14 = pregnant lactating cow after seventh AI in the period t−14; PH1t−14 = pregnant heifers after first AI in the period t−14; PH2t−14 = pregnant heifers after second AI in the period t−14; PH3t−14 = pregnant heifers after third AI in the period t−14; PH4t−14 = pregnant heifers after fourth AI in the period t−14; PH5t−14 = pregnant heifers after fifth AI in the period t−14; Π= % mortality rate in lactating cows; Β = % pregnancy loss in cows > 90 days; A = % pregnancy loss in heifers >90 days; and ϵ = % mortality rate in adult animals. |
(34) |
in which BCSt = bull-calf for sale in the period t; BCt = bull-calf in the period t; ψ = % mortality rate in bull-calf; and Ξ = % bull-calfs for sale. |
(35) |
in which FC1 = cow-calf (<3 months) in the period t = 1; γ = % gestations with bull-calf/cow-calf product by natural service; and LC1 = lactating cow in the period t = 1. |
(36) |
in which CFt = cow-calf - number of calves born after the reproductive program of the farm, taking into account the semen technology used in the period t>1; 1 – ξ = % gestations with cow-calf product in the first AI; 1 – o = % gestations with cow-calf product in the second AI; 1 – π = % gestations with cow-calf product in the third AI; 1 – ϒ = % gestations with bull-calf product in the fourth AI; 1 – φ = % gestations with bull-calf product in the fifth AI; 1 – χ = % gestations with bull-calf product in the sixth AI; 1 – P = % gestations with bull-calf product in the seventh AI; PLC1t−14 = pregnant lactating cow after first AI in the period t−14; PLC2t−14 = pregnant lactating cow after second AI in the period t−14; PLC3t–14 = pregnant lactating cow after third AI in the period t−14; PLC4t−14 = pregnant lactating cow after fourth AI the period t−14; PLC5t−14 = pregnant lactating cow after fifth AI in the period t−14; PLC6t−14 = pregnant lactating cow after sixth AI in the period t−14; PLC7t−14 = pregnant lactating cow after seventh AI in the period t−14; PH1t−14 = pregnant heifers after first AI in the period t−14; PH2t−14 = pregnant heifers after second AI in the period t−14; PH3t−14 = pregnant heifers after third AI in the period t−14; PH4t−14 = pregnant heifers after fourth AI in the period t−14; PH5t−14 = pregnant heifers after fifth AI in the period t−14; Π= % mortality rate in lactating cows; Β = % pregnancy loss in cows >90 days; A = % pregnancy loss in heifers > 90 days; and ϵ = % mortality rate in adult animals. |
(37) |
in which FF = female fattening in the period t; LC7t = lactating cows available for seventh in the period t; PLC7t = pregnant lactating cow after seventh AI in the period t; PLC1t−14 = pregnant lactating cow after first AI in the period t−14; PLC2t−14 = pregnant lactating cow after second AI in the period t−14; PLC3t−14 = pregnant lactating cow after third AI in the period t−14; PLC4t−14 = pregnant lactating cow after fourth AI in the period t−14; PLC5t−14 = pregnant lactating cow after fifth AI in the period t−14; PLC6t−14 = pregnant lactating cow after sixth AI in the period t−14; PLC7t−14 = pregnant lactating cow after seventh AI in the period t−14; H5t = heifers available for fifth AI in the period t; PH5t−14 = pregnant heifers after fifth AI in the period t−14; PH5t = pregnant heifers after fifth AI in the period t; PH1t−14 = pregnant heifers after first AI in the period t−14; PH2t−14 = pregnant heifers after second AI in the period t−14; PH3t−14 = pregnant heifers after third AI in the period t−14; PH4t−14 = pregnant heifers after fourth AI in the period t−14; PH5t−14 = pregnant heifers after fifth AI in the period t−14; H = % oestrus detection rate in cows in the seventh AI; I = % conception rate in cows in the seventh AI; Π = % mortality rate in lactating cows; β = % pregnancy loss in cows <90 days; Β = % pregnancy loss in cows >90 days; ϵ = % mortality rate in adult animals; X = % oestrus detection rate in heifers in the fifth AI; Φ = % conception rate in heifers in the fifth AI; A = % pregnancy loss in heifers >90 days; and ρ = % pregnancy loss in heifers <90 days. |
(38) |