Heteroscedastic Reaction Norm Models Improve the Assessment of Genotype by Environment Interaction for Growth, Reproductive, and Visual Score Traits in Nellore Cattle
Abstract
:Simple Summary
Abstract
1. Introduction
2. Material and Methods
2.1. Dataset Description
2.2. Environment Descriptor
2.3. Reaction Norm Models (RNM)
2.4. Model Comparison
2.5. Environmental Sensitivity
3. Results
3.1. Reaction Norm Models
3.2. Heritability Estimates
3.3. Environmental Sensitivity
4. Discussion
4.1. Reaction Norm Models
4.2. Heritability Estimates
4.3. Environmental Sensitivity
5. Conclusions
Supplementary Materials
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Traits 1 | N | Female | Male | Min | Mean | Max | sd | CG |
---|---|---|---|---|---|---|---|---|
BWG | 553,381 | 276,994 | 276,387 | 70 | 157.2 | 278 | 32.95 | 11,657 |
WC | 553,381 | 276,994 | 276,387 | 1 | 3 a | 5 | - | 11,657 |
WP | 553,381 | 276,994 | 276,387 | 1 | 3 a | 5 | - | 11,657 |
WM | 553,381 | 276,994 | 276,387 | 1 | 3 a | 5 | - | 11,657 |
YW | 457,118 | 233,320 | 223,798 | 150 | 293 | 500 | 51.34 | 10,583 |
WYG | 442,086 | 223,468 | 218,618 | 30 | 104.3 | 250 | 37.29 | 10,306 |
YC | 529,673 | 270,252 | 259,421 | 1 | 3 a | 5 | - | 7246 |
YP | 529,673 | 270,252 | 259,421 | 1 | 3 a | 5 | - | 7246 |
YM | 529,673 | 270,252 | 259,421 | 1 | 3 a | 5 | - | 7246 |
SC | 444,675 | - | 444,675 | 15 | 26.7 | 45 | 3.83 | 10,099 |
AFC | 140,162 | 140,162 | - | 544 | 1012 | 1220 | 132 | 3897 |
Variable | Trait 1 | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
BWG | WC | WP | WM | YW | WYG | YC | YP | YM | SC | AFC | |
Birth year | X | X | X | X | X | X | X | X | X | X | X |
Birth season | X | X | X | X | X | X | X | X | X | X | X |
Sex | X | X | X | X | X | X | X | X | X | ||
Farm at birth | X | X | X | X | X | X | X | X | X | ||
Farm at weaning | X | X | X | X | X | X | X | X | |||
Weaning management group | X | X | X | X | X | X | X | X | |||
Yearling management group | X | X | X | X | X | X | X | ||||
Farm at yearling | X | X | X | X | X | X | X |
Trait 1 | Model 2 | Coefficient 3 | b0 | b1 | b2 | b3 | σ2m | σ2e 4 | Np 5 | AIC | AICw |
---|---|---|---|---|---|---|---|---|---|---|---|
BWG | RNM_homo | b0 (int) | 55.67 | −1.51 | 204.08 | 5 | 3,173,163.90 | 0.00 | |||
b1 (slp) | −0.29 | 0.47 | |||||||||
maternal | 113.94 | ||||||||||
RNM_hete | b0 (int) | 55.07 | −0.18 | 5.32 | 6 | 3,173,157.20 | 0.00 | ||||
b1 (slp) | −0.04 | 0.35 | −0.01 | ||||||||
maternal | 114.05 | ||||||||||
RNM_quad | b0 (int) | 55.88 | −0.94 | −0.83 | 5.31 | 10 | 3173156.30 | 0.00 | |||
b1 (slp) | −0.11 | 1.38 | 0.45 | −0.02 | |||||||
b2 (qdr) | −0.15 | 0.51 | 0.57 | 0.01 | |||||||
maternal | 114.06 | ||||||||||
RNM_l-l | b0 (int) | 56.98 | 0.84 | −3.75 | 5.30 | 10 | 3,173,160.00 | 0.00 | |||
b1 (slp1) | 0.09 | 1.61 | −1.58 | −0.04 | |||||||
b2 (slp2) | −0.21 | −0.53 | 5.54 | 0.04 | |||||||
maternal | 114.06 | ||||||||||
RNM_q-q | b0 (int) | 55.77 | −1.95 | −1.59 | 1.88 | 5.31 | 15 | 3,173,130.20 | 1.00 | ||
b1 (slp1) | −0.14 | 3.37 | 1.48 | −2.90 | −0.06 | ||||||
b2 (qdr1) | −0.19 | 0.73 | 1.23 | −1.69 | −0.02 | ||||||
b3 (qrd2) | 0.13 | −0.83 | −0.80 | 3.66 | 0.06 | ||||||
maternal | 114.00 | ||||||||||
WC | RNM_homo | b0 (int) | 0.1428 | 0.0044 | 0.7004 | 5 | 33,076.51 | 0.06 | |||
b1 (slp) | 0.62 | 0.0004 | |||||||||
maternal | 0.2300 | ||||||||||
RNM_hete | b0 (int) | 0.1426 | 0.0013 | −0.3559 | 6 | 33,070.84 | 0.94 | ||||
b1 (slp) | 0.30 | 0.0001 | 0.0107 | ||||||||
maternal | 0.2301 | ||||||||||
RNM_quad | b0 (int) | 0.1523 | 0.0031 | −0.0078 | −0.3649 | 10 | 33,257.81 | 0.00 | |||
b1 (slp) | 0.09 | 0.0077 | 0.0007 | 0.0055 | |||||||
b2 (qdr) | −0.38 | 0.15 | 0.0027 | −0.0018 | |||||||
maternal | 0.2304 | ||||||||||
RNM_l-l | b0 (int) | 0.1510 | 0.0121 | −0.0177 | −0.3657 | 10 | 33,159.66 | 0.00 | |||
b1 (slp1) | 0.33 | 0.0091 | −0.0123 | 0.0001 | |||||||
b2 (slp2) | −0.28 | −0.78 | 0.0273 | 0.0117 | |||||||
maternal | 0.2302 | ||||||||||
RNM_q-q | b0 (int) | 0.1470 | 0.0081 | −0.0011 | −0.0059 | −0.3640 | 15 | 33,210.89 | 0.00 | ||
b1 (slp1) | 0.13 | 0.0253 | 0.0108 | −0.0237 | 0.0029 | ||||||
b2 (qdr1) | −0.04 | 0.86 | 0.0062 | −0.0113 | −0.0007 | ||||||
b3 (qrd2) | −0.10 | −0.93 | −0.89 | 0.0259 | 0.0022 | ||||||
maternal | 0.2303 | ||||||||||
WP | RNM_homo | b0 (int) | 0.2349 | 0.0026 | 0.7900 | 5 | 104,255.53 | 0.55 | |||
b1 (slp) | 0.33 | 0.0003 | |||||||||
maternal | 0.2056 | ||||||||||
RNM_hete | b0 (int) | 0.2349 | 0.0014 | −0.2359 | 6 | 104,255.91 | 0.45 | ||||
b1 (slp) | 0.17 | 0.0003 | 0.0049 | ||||||||
maternal | 0.2056 | ||||||||||
RNM_quad | b0 (int) | 0.2426 | 0.0006 | −0.0076 | −0.2381 | 10 | 104,425.75 | 0.00 | |||
b1 (slp) | 0.01 | 0.0072 | 0.0009 | 0.0030 | |||||||
b2 (qdr) | −0.29 | 0.19 | 0.0029 | −0.0066 | |||||||
maternal | 0.2065 | ||||||||||
RNM_l-l | b0 (int) | 0.2431 | 0.0113 | −0.0199 | −0.2358 | 10 | 104,334.27 | 0.00 | |||
b1 (slp1) | 0.23 | 0.0097 | −0.0148 | 0.0072 | |||||||
b2 (slp2) | −0.22 | −0.82 | 0.0337 | −0.0118 | |||||||
maternal | 0.2061 | ||||||||||
RNM_q-q | b0 (int) | 0.2391 | −0.0006 | −0.0044 | 0.0018 | −0.2380 | 15 | 104,375.02 | 0.00 | ||
b1 (slp1) | −0.01 | 0.0199 | 0.0092 | −0.0192 | 0.0023 | ||||||
b2 (qdr1) | −0.12 | 0.84 | 0.0060 | −0.0102 | −0.0063 | ||||||
b3 (qrd2) | 0.02 | −0.92 | −0.89 | 0.0222 | 0.0037 | ||||||
maternal | 0.2059 | ||||||||||
WM | RNM_homo | b0 (int) | 0.2078 | 0.0017 | 0.8269 | 5 | 128,693.45 | 0.73 | |||
b1 (slp) | 0.12 | 0.0009 | |||||||||
maternal | 0.2506 | ||||||||||
RNM_hete | b0 (int) | 0.2078 | 0.0013 | -0.1902 | 6 | 128,695.39 | 0.27 | ||||
b1 (slp) | 0.10 | 0.0009 | 0.0011 | ||||||||
maternal | 0.2506 | ||||||||||
RNM_quad | b0 (int) | 0.2160 | −0.0002 | −0.0073 | −0.1937 | 10 | 128,882.36 | 0.00 | |||
b1 (slp) | −0.01 | 0.0074 | 0.0006 | 0.0023 | |||||||
b2 (qdr) | −0.29 | 0.13 | 0.0029 | −0.0051 | |||||||
maternal | 0.2512 | ||||||||||
RNM_l-l | b0 (int) | 0.2160 | 0.0096 | −0.0180 | −0.1945 | 10 | 128,781.97 | 0.00 | |||
b1 (slp1) | 0.20 | 0.0103 | −0.0150 | 0.0015 | |||||||
b2 (slp2) | −0.22 | −0.83 | 0.0320 | 0.0005 | |||||||
maternal | 0.2508 | ||||||||||
RNM_q-q | b0 (int) | 0.2119 | −0.0015 | −0.0054 | 0.0030 | −0.1935 | 15 | 128,842.18 | 0.00 | ||
b1 (slp1) | −0.02 | 0.0216 | 0.0099 | −0.0208 | 0.0103 | ||||||
b2 (qdr1) | −0.15 | 0.84 | 0.0065 | −0.0110 | 0.0035 | ||||||
b3 (qrd2) | 0.04 | −0.92 | −0.89 | 0.0238 | −0.0119 | ||||||
maternal | 0.2511 |
Traits 1 | Model 2 | Coefficient 3 | b0 | b1 | b2 | b3 | σ2e 4 | Np 5 | AIC | AICw |
---|---|---|---|---|---|---|---|---|---|---|
YW | RNM_homo | b0 (int) | 350.81 | 56.63 | 361.68 | 4 | 4,164,832 | 0.00 | ||
b1 (slp) | 0.69 | 19.29 | ||||||||
RNM_hete | b0 (int) | 336.55 | 23.99 | 5.92 | 5 | 4,164,587 | 0.00 | |||
b1 (slp) | 0.38 | 12.14 | 0.14 | |||||||
RNM_quad | b0 (int) | 336.43 | 22.33 | −1.68 | 5.94 | 9 | 4,164,537 | 0.00 | ||
b1 (slp) | 0.31 | 15.23 | 0.03 | 0.15 | ||||||
b2 (qdr) | −0.06 | 0.01 | 1.98 | −0.03 | ||||||
RNM_l-l | b0 (int) | 343.00 | 30.15 | −16.51 | 5.95 | 9 | 4,164,520 | 1.00 | ||
b1 (slp1) | 0.34 | 23.10 | −13.08 | 0.19 | ||||||
b2 (slp2) | −0.17 | −0.52 | 26.99 | −0.09 | ||||||
RNM_q-q | b0 (int) | 335.44 | 8.72 | −10.35 | 18.07 | 5.94 | 14 | 4,164,531 | 0.00 | |
b1 (slp1) | 0.12 | 17.05 | 4.76 | −6.06 | 0.23 | |||||
b2 (qdr1) | −0.25 | 0.52 | 4.97 | −7.02 | 0.04 | |||||
b3 (qrd2) | 0.27 | −0.41 | −0.87 | 13.10 | −0.13 | |||||
WYG | RNM_homo | b0 (int) | 113.46 | 35.97 | 261.28 | 4 | 3,780,797 | 0.00 | ||
b1 (slp) | 0.89 | 14.49 | ||||||||
RNM_hete | b0 (int) | 92.02 | 13.28 | 5.64 | 5 | 3,780,155 | 0.00 | |||
b1 (slp) | 0.59 | 5.49 | 0.15 | |||||||
RNM_quad | b0 (int) | 98.20 | 15.19 | −5.09 | 5.65 | 9 | 3,779,938 | 0.00 | ||
b1 (slp) | 0.47 | 10.41 | −1.80 | 0.17 | ||||||
b2 (qdr) | −0.40 | −0.44 | 1.63 | −0.03 | ||||||
RNM_l-l | b0 (int) | 103.55 | 26.12 | −20.92 | 5.66 | 9 | 3,779,976 | 0.00 | ||
b1 (slp1) | 0.56 | 20.68 | −15.95 | 0.20 | ||||||
b2 (slp2) | −0.46 | −0.78 | 20.06 | −0.09 | ||||||
RNM_q-q | b0 (int) | 97.78 | 8.25 | −7.79 | 6.07 | 5.64 | 14 | 3,779,882 | 1.00 | |
b1 (slp1) | 0.21 | 15.09 | 8.03 | −9.56 | 0.22 | |||||
b2 (qdr1) | −0.27 | 0.72 | 8.31 | −10.29 | 0.03 | |||||
b3 (qrd2) | 0.17 | −0.68 | −0.98 | 13.24 | −0.09 | |||||
AFC | RNM_homo | b0 (int) | 3391.50 | 1873.80 | 3668.90 | 4 | 1,597,302 | 0.00 | ||
b1 (slp) | 1.00 | 1045.10 | ||||||||
RNM_hete | b0 (int) | 828.06 | 309.89 | 8.65 | 5 | 1,593,825 | 0.00 | |||
b1 (slp) | 0.93 | 133.86 | 0.46 | |||||||
RNM_quad | b0 (int) | 651.88 | 150.00 | −107.08 | 8.84 | 9 | 1,592,165 | 0.00 | ||
b1 (slp) | 0.60 | 94.51 | −31.44 | 0.56 | ||||||
b2 (qdr) | −0.82 | −0.64 | 25.86 | −0.15 | ||||||
RNM_l-l | b0 (int) | 746.31 | 331.13 | −354.60 | 8.88 | 9 | 1,592,410 | 0.00 | ||
b1 (slp1) | 0.89 | 187.18 | −171.16 | 0.77 | ||||||
b2 (slp2) | −0.89 | −0.86 | 210.83 | −0.52 | ||||||
RNM_q-q | b0 (int) | 631.40 | 178.12 | −61.62 | −46.08 | 8.82 | 14 | 1,592,007 | 1.00 | |
b1 (slp1) | 0.62 | 131.68 | 26.11 | −59.51 | 0.54 | |||||
b2 (qdr1) | −0.30 | 0.28 | 67.02 | −64.41 | −0.17 | |||||
b3 (qrd2) | −0.20 | −0.56 | −0.85 | 86.62 | 0.02 | |||||
SC | RNM_homo | b0 (int) | 3.03 | 0.23 | 3.78 | 4 | 2,059,717.9 | 0.00 | ||
b1 (slp) | 0.53 | 0.06 | ||||||||
RNM_hete | b0 (int) | 3.02 | 0.17 | 1.33 | 5 | 2,059,691.4 | 0.00 | |||
b1 (slp) | 0.43 | 0.05 | 0.03 | |||||||
RNM_quad | b0 (int) | 3.06 | 0.15 | −0.04 | 1.34 | 9 | 2,059,612.4 | 0.00 | ||
b1 (slp) | 0.26 | 0.11 | 0.02 | 0.02 | ||||||
b2 (qdr) | −0.28 | 0.56 | 0.01 | −0.02 | ||||||
RNM_l-l | b0 (int) | 3.07 | 0.20 | −0.13 | 1.36 | 9 | 2,059,618.7 | 0.00 | ||
b1 (slp1) | 0.46 | 0.06 | −0.01 | 0.07 | ||||||
b2 (slp2) | −0.18 | −0.07 | 0.18 | −0.10 | ||||||
RNM_q-q | b0 (int) | 3.05 | 0.14 | −0.06 | 0.04 | 1.34 | 14 | 2,059,596.1 | 1.00 | |
b1 (slp1) | 0.18 | 0.20 | 0.06 | −0.08 | −0.02 | |||||
b2 (qdr1) | −0.20 | 0.72 | 0.03 | −0.04 | −0.04 | |||||
b3 (qrd2) | 0.09 | −0.78 | −0.90 | 0.06 | 0.05 |
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Carvalho Filho, I.; Silva, D.A.; Teixeira, C.S.; Silva, T.L.; Mota, L.F.M.; Albuquerque, L.G.; Carvalheiro, R. Heteroscedastic Reaction Norm Models Improve the Assessment of Genotype by Environment Interaction for Growth, Reproductive, and Visual Score Traits in Nellore Cattle. Animals 2022, 12, 2613. https://doi.org/10.3390/ani12192613
Carvalho Filho I, Silva DA, Teixeira CS, Silva TL, Mota LFM, Albuquerque LG, Carvalheiro R. Heteroscedastic Reaction Norm Models Improve the Assessment of Genotype by Environment Interaction for Growth, Reproductive, and Visual Score Traits in Nellore Cattle. Animals. 2022; 12(19):2613. https://doi.org/10.3390/ani12192613
Chicago/Turabian StyleCarvalho Filho, Ivan, Delvan A. Silva, Caio S. Teixeira, Thales L. Silva, Lucio F. M. Mota, Lucia G. Albuquerque, and Roberto Carvalheiro. 2022. "Heteroscedastic Reaction Norm Models Improve the Assessment of Genotype by Environment Interaction for Growth, Reproductive, and Visual Score Traits in Nellore Cattle" Animals 12, no. 19: 2613. https://doi.org/10.3390/ani12192613
APA StyleCarvalho Filho, I., Silva, D. A., Teixeira, C. S., Silva, T. L., Mota, L. F. M., Albuquerque, L. G., & Carvalheiro, R. (2022). Heteroscedastic Reaction Norm Models Improve the Assessment of Genotype by Environment Interaction for Growth, Reproductive, and Visual Score Traits in Nellore Cattle. Animals, 12(19), 2613. https://doi.org/10.3390/ani12192613