A Unified Model for Inclusive Inheritance in Livestock Species

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.

Inclusive inheritance for residual feed intake in pigs and rabbits

“…Thus, in that case, the transmissibility model is the animal model usually applied in genetic studies. For the sake of simplicity, reference to the “animal model” in the following article corresponds to the constrained transmissibility model with ; (b) they can be both lower than 0.5 in agreement with the vertical transmission of epigenetic marks (Tal, Kisdi, & Jablonka, 2010; Varona et al., 2015); (c) one coefficient can be higher than 0.5 in agreement with single parent inheritance [microbiota (Bright & Bulgheresi, 2010), culture (Feldman & Cavalli‐Sforza, 1975), see David and Ricard (2019) for details], which is of particular interest for the dam side. Since a trait maybe transmitted from one generation to the next by different sources of inheritance, the path coefficients of transmission estimated in the transmissibility model combine these different modes of transmission.…”

“…Non‐genetic inheritance is assumed when at least one of the two path coefficients of transmission (sire or dam) estimated by the transmissibility model differs from 0.5. It has been shown that, conversely to a model that aims at dissociating genetic from non‐genetic inherited effects, the parameters of the transmissibility model are practically identifiable in most situations, which is its main advantage (David & Ricard, 2019). Of course, therefore, this model does not aim at quantifying the proportion of variance explained by different sources of non‐genetic inherited effects.…”

“…Considering that for an animal i born from sire s and dam d : , , the M matrix is a symmetric matrix with 1s on the diagonal and r ij as off‐diagonal elements. In the case of two animals i , j with n common ancestors ( l ) , with , , where , are the number of sire and dam transmissions between ancestor l and animal i , respectively; and are the unknown sire and dam path coefficients of transmission, respectively, subject to the following constraints: , , (David & Ricard, 2019). Thus, in this model, the two path coefficients of transmission can take a large range of values that can model the different sources of inheritance: (aa) they can be both equal to 0.5 to model a purely genetic transmission.…”

“…However, the impact of these non‐genetic sources of inheritance on the phenotypic variability of traits of economic importance in livestock species has rarely been investigated. This is mainly due to the difficulty of disentangling the different sources of inheritance with only pedigree and phenotype data, and the lack of appropriate data structure (large variety of different categories of relatives with phenotype) (David & Ricard, 2019). To overcome this problem and still take into account the different sources of inheritance when estimating the transmissible potential of individual, David and Ricard (2019) proposed the transmissibility model.…”

“…This is mainly due to the difficulty of disentangling the different sources of inheritance with only pedigree and phenotype data, and the lack of appropriate data structure (large variety of different categories of relatives with phenotype) (David & Ricard, 2019). To overcome this problem and still take into account the different sources of inheritance when estimating the transmissible potential of individual, David and Ricard (2019) proposed the transmissibility model. Similarly to the animal model, the transmissibility model uses pedigree and phenotypic information to estimate variance components and predict a transmissible potential for an individual that combines all sources of inheritance.…”