A Unified Model for Inclusive Inheritance in Livestock Species

doi:10.1534/genetics.119.302375

. 2019 Aug;212(4):1075-1099.

doi: 10.1534/genetics.119.302375. Epub 2019 Jun 17.

A Unified Model for Inclusive Inheritance in Livestock Species

Ingrid David¹, Anne Ricard^{2

3}

Affiliations

¹ GenPhySE, INRA, Université de Toulouse, INPT, ENVT, 31326 Castanet Tolosan, France Ingrid.david@inra.fr.
² GABI, INRA, AgroParisTech, Université Paris Saclay, Département Sciences du Vivant, UMR 1313, 78352 Jouy-en-Josas, France.
³ Institut Français du Cheval et de l'Equitation, Département Recherche et Innovation, 61310 Exmes, France.

PMID: 31209104
PMCID: PMC6707455
DOI: 10.1534/genetics.119.302375

A Unified Model for Inclusive Inheritance in Livestock Species

Ingrid David et al. Genetics. 2019 Aug.

. 2019 Aug;212(4):1075-1099.

doi: 10.1534/genetics.119.302375. Epub 2019 Jun 17.

Authors

Ingrid David¹, Anne Ricard^{2

3}

Affiliations

¹ GenPhySE, INRA, Université de Toulouse, INPT, ENVT, 31326 Castanet Tolosan, France Ingrid.david@inra.fr.
² GABI, INRA, AgroParisTech, Université Paris Saclay, Département Sciences du Vivant, UMR 1313, 78352 Jouy-en-Josas, France.
³ Institut Français du Cheval et de l'Equitation, Département Recherche et Innovation, 61310 Exmes, France.

PMID: 31209104
PMCID: PMC6707455
DOI: 10.1534/genetics.119.302375

Abstract

For years, animal selection in livestock species has been performed by selecting animals based on genetic inheritance. However, evolutionary studies have reported that nongenetic information that drives natural selection can also be inherited across generations (epigenetic, microbiota, environmental inheritance). In response to this finding, the concept of inclusive heritability, which combines all sources of information inherited across generations, was developed. To better predict the transmissible potential of each animal by taking into account these diverse sources of inheritance and improve selection in livestock species, we propose the "transmissibility model." Similarly to the animal model, this model uses pedigree and phenotypic information to estimate variance components and predict the transmissible potential of an individual, but differs by estimating the path coefficients of inherited information from parent to offspring instead of using a set value of 0.5 for both the sire and the dam (additive genetic relationship matrix). We demonstrated the structural identifiability of the transmissibility model, and performed a practical identifiability and power study of the model. We also performed simulations to compare the performances of the animal and transmissibility models for estimating the covariances between relatives and predicting the transmissible potential under different combinations of sources of inheritance. The transmissibility model provided similar results to the animal model when inheritance was of genetic origin only, but outperformed the animal model for estimating the covariances between relatives and predicting the transmissible potential when the proportion of inheritance of nongenetic origin was high or when the sire and dam path coefficients were very different.

Keywords: inclusive inheritance; livestock; model.

PubMed Disclaimer

Figures

**Figure 1**
Path coefficient diagram describing the transmission of the different inherited factors in livestock species. a, genetic effects; epi, epigenetic effect; mic, microbiota effect; cult, cultural effect; y, phenotype; e, residual. Indices s, d, o and i refer to sire, dam, offspring, and comate i, respectively.

**Figure 2**
Profile likelihood *vs.* parameters to estimate in a model designed to disentangle genetic and epigenetic effects and in the transmissibility model. The true model is $y_{i} = a_{i} + e p i_{i} + e_{i}$ . The values of the true model are $H^{2} = \frac{σ_{a}^{2} + σ_{e p i}^{2}}{σ_{a}^{2} + σ_{e p i}^{2} + σ_{e}^{2}} = 0.4$ , r = $\frac{σ_{a}^{2}}{σ_{a}^{2} + σ_{e p i}^{2}} = 0.5$ , and six different combinations for the epigenetic path coefficient of transmission are considered. The two models of estimation are $y_{i} = a_{i} + e p i_{i} + e_{i}$ (mod1) and the transmissibility model $y_{i} = t_{i} + e_{i}$ . First four left panels: profile likelihoods for the parameters $H_{0}^{2}$ , $r_{0}, λ_{s 0},$ and $λ_{d 0}$ for mod1. Three last panels: profile likelihoods for $τ_{0}^{2}, ω_{s 0},$ and $ω_{d 0}$ . Top to bottom: small, medium, and large pedigree sizes; colors of lines: different values of the combination $λ_{s},$ $λ_{d}$ . Dotted horizontal line: the $χ^{2}$ threshold value.

**Figure 3**
Power to detect nongenetic inheritance with a transmissibility model considering equal path coefficients of transmission for the sire and the dam. The true model is $y_{i} = x_{i} β + a_{i} + e p i_{i} + e_{i},$ considering same sire and dam epigenetic path coefficients of transmission $(λ = λ_{s} = λ_{d})$ . Values of the true model are $H^{2} = \frac{σ_{a}^{2} + σ_{e p i}^{2}}{σ_{a}^{2} + σ_{e p i}^{2} + σ_{e}^{2}} = 0.2, 0.4$ or 0.6, r = $\frac{σ_{a}^{2}}{σ_{a}^{2} + σ_{e p i}^{2}} = 0.3, 0.5,$ or 0.7 and varying values for the path coefficient of transmission $λ \in [0.05, 0.5]$ . The model of estimation is the transmissibility model $y_{i} = x_{i} β + t_{i} + e_{i},$ which considers the same path coefficients of transmission for the sire and the dam $(ω_{d} = ω_{s} = ω)$ . The null hypothesis H0 is $ω = 0.5$ , the alternative hypothesis is H1 $ω \neq 0.5$ .

**Figure 4**
Power to detect nongenetic inheritance with the transmissibility model considering different path coefficients of transmission for the sire and the dam. The true model is $y_{i} = x_{i} β + a_{i} + e p i_{i} + e_{i}$ . Values of the true model are $H^{2} = \frac{σ_{a}^{2} + σ_{e p i}^{2}}{σ_{a}^{2} + σ_{e p i}^{2} + σ_{e}^{2}} = 0.2, 0.4,$ or 0.6, r = $\frac{σ_{a}^{2}}{σ_{a}^{2} + σ_{e p i}^{2}} = 0.3, 0.5,$ or 0.7 and varying values for the sire and dam epigenetic path coefficient of transmission $λ_{s} \in [0.05, 0.5] and λ_{d} \in [0.05, 0.5] .$ The model of estimation is the transmissibility model $y_{i} = x_{i} β + t_{i} + e_{i}$ . The null hypothesis H0 is $ω_{d} = ω_{s} = 0.5$ , the alternative hypothesis is H1 $ω_{d} \neq 0.5$ or $ω_{s} \neq 0.5$

**Figure 5**
Sire and dam transmissibilities estimated using the animal and transmissibility models for the different datasets. Dotted lines show the simulated values.

**Figure 6**
Ratio of regression coefficient between relatives to simulated regression coefficient estimated by the animal and transmissibility models for the different datasets. The types of relatives are: 1, paternal grand dam-offspring; 2, maternal grand dam-offspring; 3, paternal half-sib of the sire (paternal uncle 1)-offspring; 4, maternal half-sib of the sire (paternal uncle 2); offspring; 5, paternal half-sib of the dam (maternal uncle 1)-offspring; 6, maternal half-sib of the dam (maternal uncle 2)-offspring; 7, paternal half-sibs; 8, full-sibs.

See this image and copyright information in PMC

Cited by

The potential of microbiota information to better predict efficiency traits in growing pigs fed a conventional and a high-fiber diet.
Déru V, Tiezzi F, Carillier-Jacquin C, Blanchet B, Cauquil L, Zemb O, Bouquet A, Maltecca C, Gilbert H. Déru V, et al. Genet Sel Evol. 2024 Jan 19;56(1):8. doi: 10.1186/s12711-023-00865-4. Genet Sel Evol. 2024. PMID: 38243193 Free PMC article.
An improved transmissibility model to detect transgenerational transmitted environmental effects.
David I, Ricard A. David I, et al. Genet Sel Evol. 2023 Sep 21;55(1):66. doi: 10.1186/s12711-023-00833-y. Genet Sel Evol. 2023. PMID: 37735633 Free PMC article.
Gut microbiota and host genetics contribute to the phenotypic variation of digestive and feed efficiency traits in growing pigs fed a conventional and a high fiber diet.
Déru V, Tiezzi F, Carillier-Jacquin C, Blanchet B, Cauquil L, Zemb O, Bouquet A, Maltecca C, Gilbert H. Déru V, et al. Genet Sel Evol. 2022 Jul 27;54(1):55. doi: 10.1186/s12711-022-00742-6. Genet Sel Evol. 2022. PMID: 35896976 Free PMC article.
Mapping the past, present and future research landscape of paternal effects.
Rutkowska J, Lagisz M, Bonduriansky R, Nakagawa S. Rutkowska J, et al. BMC Biol. 2020 Nov 27;18(1):183. doi: 10.1186/s12915-020-00892-3. BMC Biol. 2020. PMID: 33246472 Free PMC article.
Inclusive inheritance for residual feed intake in pigs and rabbits.
David I, Aliakbari A, Déru V, Garreau H, Gilbert H, Ricard A. David I, et al. J Anim Breed Genet. 2020 Nov;137(6):535-544. doi: 10.1111/jbg.12494. Epub 2020 Jul 22. J Anim Breed Genet. 2020. PMID: 32697021 Free PMC article.

See all "Cited by" articles

References

1. Abecia L., Fondevila M., Balcells J., McEwan N., 2007. The effect of lactating rabbit does on the development of the caecal microbial community in the pups they nurture. J. Appl. Microbiol. 103: 557–564. 10.1111/j.1365-2672.2007.03277.x - DOI - PubMed
1. Aguilera O., Fernández A. F., Muñoz A., Fraga M. F., 2010. Epigenetics and environment: a complex relationship. J. Appl. Phys. 109: 243–251. 10.1152/japplphysiol.00068.2010 - DOI - PubMed
1. Bonduriansky R., Crean A. J., Day T., 2012. The implications of nongenetic inheritance for evolution in changing environments. Evol. Appl. 5: 192–201. 10.1111/j.1752-4571.2011.00213.x - DOI - PMC - PubMed
1. Braunschweig M., Jagannathan V., Gutzwiller A., Bee G., 2012. Investigations on transgenerational epigenetic response down the male line in F2 pigs. PLoS One 7: e30583 10.1371/journal.pone.0030583 - DOI - PMC - PubMed
1. Bright M., Bulgheresi S., 2010. A complex journey: transmission of microbial symbionts. Nat. Rev. Microbiol. 8: 218–230. 10.1038/nrmicro2262 - DOI - PMC - PubMed

MeSH terms

Actions
Actions
Actions
Actions
Actions

LinkOut - more resources

Full Text Sources

[1] Abecia L., Fondevila M., Balcells J., McEwan N., 2007. The effect of lactating rabbit does on the development of the caecal microbial community in the pups they nurture. J. Appl. Microbiol. 103: 557–564. 10.1111/j.1365-2672.2007.03277.x - DOI - PubMed

[2] Abecia L., Fondevila M., Balcells J., McEwan N., 2007. The effect of lactating rabbit does on the development of the caecal microbial community in the pups they nurture. J. Appl. Microbiol. 103: 557–564. 10.1111/j.1365-2672.2007.03277.x - DOI - PubMed

[3] Aguilera O., Fernández A. F., Muñoz A., Fraga M. F., 2010. Epigenetics and environment: a complex relationship. J. Appl. Phys. 109: 243–251. 10.1152/japplphysiol.00068.2010 - DOI - PubMed

[4] Aguilera O., Fernández A. F., Muñoz A., Fraga M. F., 2010. Epigenetics and environment: a complex relationship. J. Appl. Phys. 109: 243–251. 10.1152/japplphysiol.00068.2010 - DOI - PubMed

[5] Bonduriansky R., Crean A. J., Day T., 2012. The implications of nongenetic inheritance for evolution in changing environments. Evol. Appl. 5: 192–201. 10.1111/j.1752-4571.2011.00213.x - DOI - PMC - PubMed

[6] Bonduriansky R., Crean A. J., Day T., 2012. The implications of nongenetic inheritance for evolution in changing environments. Evol. Appl. 5: 192–201. 10.1111/j.1752-4571.2011.00213.x - DOI - PMC - PubMed

[7] Braunschweig M., Jagannathan V., Gutzwiller A., Bee G., 2012. Investigations on transgenerational epigenetic response down the male line in F2 pigs. PLoS One 7: e30583 10.1371/journal.pone.0030583 - DOI - PMC - PubMed

[8] Braunschweig M., Jagannathan V., Gutzwiller A., Bee G., 2012. Investigations on transgenerational epigenetic response down the male line in F2 pigs. PLoS One 7: e30583 10.1371/journal.pone.0030583 - DOI - PMC - PubMed

[9] Bright M., Bulgheresi S., 2010. A complex journey: transmission of microbial symbionts. Nat. Rev. Microbiol. 8: 218–230. 10.1038/nrmicro2262 - DOI - PMC - PubMed

[10] Bright M., Bulgheresi S., 2010. A complex journey: transmission of microbial symbionts. Nat. Rev. Microbiol. 8: 218–230. 10.1038/nrmicro2262 - DOI - PMC - PubMed

Save citation to file

Email citation

Add to Collections

Add to My Bibliography

Your saved search

Create a file for external citation management software

Your RSS Feed

A Unified Model for Inclusive Inheritance in Livestock Species

Affiliations

A Unified Model for Inclusive Inheritance in Livestock Species

Authors

Affiliations

Abstract

Figures

Similar articles

Cited by

References

MeSH terms

LinkOut - more resources

Full Text Sources