Dr. Valérie Poupon

09 February 2024In plant and animal breeding it is important to carefully choose the statistical model to analyze our data, so that we can successfully predict and then select the best individuals, and maximize our genetic gain. There are several aspects to consider, one of which is whether we want to perform backward and/or forward selection. That is, whether we are interested in selecting parents and/or offspring. Depending on the answer, we can choose to use a **Parental Model** (for selecting parents) or an **Animal Model** (for selecting parents and/or offspring), also known as **Individual Model**. In this blog, we will discuss both types of model, and highlight for each their advantages and disadvantages.

**Parental Model**

This model type is used when you are interested in selecting parents, or specific crosses. In forestry, for example, this model type is widely used to select female parental trees for seed production. In some cases, it can be used when we only have access to the information at the family level, such as biomass production resulting from a specific cross.

One important advantage of using a Parental Model over an Animal Model is that it only calculates the parental effects, therefore reducing the necessary mathematical calculations and, in turn, increasing the speed and convergency of the model. Another advantage is that, in the cutting-edge field of genomic selection, using this model type substantially reduces the number of individuals required to be genotyped to train the model. Here, genotyping the offspring is not required, and therefore provides a more cost-effective strategy.

In the case of a Parental Model, the male and/or female additive effects are estimated as **general combining abilities** (GCAs), which correspond to 1/2 of their associated **breeding values** (BVs). Depending on the type of mating design used, Parental Models can provide varied levels of insight into the data. For example, with full-siblings and a well-connected mating design, we can reliably estimate additive effects and, albeit with lower precision, dominance effects. The latter effects are estimated as **specific combining abilities** (SCAs), which represent the interaction between alleles in the same locus from a given pair of parents. A simple example of this Parental Model with full-sibling families can be formulated as:

where is the vector of response values, is the overall mean, is the vector of random male effects (i.e., male GCAs), is the vector of random female effects (i.e., female GCAs), is the vector of random interaction of male by female effects (i.e., SCAs), and is the vector of random residual effects.

Note that with half-sibling family data, we can only estimate the additive effects of one of the parents (and of any grandparent included in the pedigree), as the other genetic components are confounded with the residual term. Similarly, in the case of non-connected crosses, i.e., each parent is crossed with only one other parent, additive and dominance genetic components are also confounded with each other; hence, the only possible model that can be fitted is:

Finally, note that it is possible to include the pedigree information of the parents in a Parental Model, via an additive relationship matrix.

**Animal Model**

In contrast to the previous model type, an Animal Model estimates both parental and offspring genetic effects, allowing for backward and forward selection. In some cases, forward selection is the focus; for example, when the parents are too old or deceased by the time we have access to the offspring's data (e.g., as is typically the case in aquaculture). Importantly, this model directly estimates the BVs, for all individuals, instead of GCAs as the parental model does.

One major consideration when fitting this model type is that it requires the full pedigree information included as an additive relationship matrix. It is through this process that it becomes possible to obtain a BV for all the individuals that are described in the pedigree file, including those that do not have a phenotypic measurement.

The main drawback of the Animal Model is that, given the much larger set of effects to predict (all individuals included in the pedigree), the size and computational complexity of the analysis can escalate considerably. Nevertheless, with the availability of modern computational tools (such as those incorporated in ASReml-R), it is possible to fit models associated with increasingly large pedigrees and with more complex model structures. Furthermore, it is also possible to fit a **Reduced Animal Model** where BVs are estimated only for individuals with phenotypic records. A simple version of the Animal Model can be expressed as:

where is the vector of response values, is the overall mean, is the vector of random additive effects (BVs), and is the vector of random residual effects. Note that, as with the Parental Model, it is also possible to obtain the dominance effects with full-sib data by extending the model to incorporate the effect as:

**Relationship Matrix**

As mentioned above, the pedigree information is added to the model via an additive genetic relationship matrix. For the Animal Model, this is done by reading a pedigree file that includes each of the individuals together with their parents, and then the parents of the parents, and so on. For the Parental Model, however, it is not required to have the pedigree information of the offspring as it will not be used. Most statistical software, including ASReml-R, will read this pedigree file and process it internally to generate the numerator relationship matrix which is later used to solve the **Henderson’s mixed model system of equations**. Importantly, the more connected an individual is through the pedigree, the more information is available to estimate its GCA or BV. In addition, stronger connectivity (and therefore relationships) will lead to more accurate estimates of the additive effects.

**Related blogs**

Single record animal model in ASReml

Unraveling breeding values: How one value depends on others

**About the author**

Dr. Valérie Poupon is a quantitative geneticist with a Ph.D. in Genetics and Tree Breeding from the Czech University of Life Sciences (CULS). She currently works as a Statistical Consultant at VSN International, UK. She has experience in quantitative genetics and field trial analysis, with multi-trial and multi-trait data.

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