Selection Index and its Precision

Introduction

The concept of employing a selection index or total score in breeding programs has its roots in the work of Birth and Harel. This approach involves assigning index values to individuals, aiming to achieve the closest correlation possible with the composite breeding values of each individual. The utilization of an index is crucial for the efficient selection of multiple traits.

Importance of Selection Index

• Economic Importance: Not all traits considered in selection hold equal economic significance. Differential weighting is necessary, aligning with the economic return expected from improving each trait. This tailored approach ensures optimization in overall economic value.
• Variability in Heritability: Traits exhibit varying heritability levels, implying that the same intensity of selection may not yield proportional improvements for all traits.
• Interrelationships among Traits: Phenotypic and genetic interrelationships among traits necessitate consideration. Emphasizing one trait may impact others, requiring a comprehensive approach to selection.

Information Required for Developing a Selection Index

• Relative Economic Importance: Knowledge about the relative economic importance of each trait guides the definition of selection goals. The aim is to improve the overall enterprise, with traits weighted according to their economic significance.
• Heritability and Variance: Information on the heritability and genetic variance for each trait, as well as the phenotypic variance, is crucial for understanding the potential for genetic improvement.
• Covariances: Understanding the phenotypic and genetic covariances among traits, often expressed through correlations, is essential for accurate selection decisions.

Optimal Selection Procedure

• The most effective selection procedure involves utilizing all available information to estimate each individual's breeding value, creating an index of merit. This comprehensive approach ensures a holistic evaluation of multiple traits, aligning with the overall breeding goals of the enterprise.
• In the realm of animal and plant breeding, effective selection strategies demand a wealth of information sourced from various relatives, encompassing not only individuals but also parents, full siblings, half-siblings, and more. When traits are sex-limited, data on unmeasurable individuals must be derived from different types of relatives. The ultimate goal is to amalgamate this diverse information into a unified index, forming the basis for intelligent selection decisions.

Multiple Trait Selection

• Selection for the enhancement of economic value in animals or plants is a complex task that involves considering several traits simultaneously, rather than focusing on a single trait. This approach, known as multiple trait selection, recognizes that economic value hinges on the interplay of various characteristics. 
• For instance, the profitability of a pig herd is intricately tied to factors such as fertility, mothering ability, growth rate, food utilization efficiency, and carcass qualities.

Optimizing Economic Value

• To achieve the swiftest enhancement of economic value, the most effective method involves applying selection concurrently to all relevant traits. Each trait receives appropriate weighting, factoring in its relative economic importance, heritability, and the genetic and phenotypic correlations between traits.
• The integration of these component traits into a cohesive score or index facilitates selection as if it were a single character. This approach ensures the most expeditious improvement of economic value.

Precision or Efficiency of an Index

The degree of correlation between index values and breeding values serves as a metric for the efficiency of an index. Essentially, a higher correlation indicates a more effective index in predicting breeding values. The construction of the index is optimized to maximize its utility in leveraging available information. Comparisons among various indices, formed with different measurements, can be made by assessing their correlations. This analysis helps determine the inclusion or exclusion of specific traits in the index, enhancing its overall effectiveness. 

The efficiency (r_La) is computed as follows:
The index of the individual is I = b₁, P_{1 .} b₂ P₂ + b₃ P₃ +...
The equations for variances and covariances of the breeding value are

First, we need to know the variance of index values. Equation (1) can be seen as

where variances and covariances are written in the notation of equation (2) This expression can be put into a form that is easier to calculate Rearranging the terms gives

Substituting for the term in brackets from equation (2) leads to

Next, we need to know the covariance of index values with breeding values. This is  for the following risen. 

The efficiency of an index is gauged by the correlation between index values and breeding values, with a higher correlation indicating superior predictive capabilities. The scaling of an index ensures that one unit of the index corresponds to one unit of the predicted breeding value, maintaining a correlation of unity (r = 1). This correlation is essentially the multiple correlation, showcasing the proportion of additive variance accounted for by the measurements integrated into the index. Conversely, (1-r²) signifies the unaccounted fraction of additive variance, leaving room for further improvement by incorporating additional measurements.

Selection in Retrospect

Conducting selection experiments with livestock is a resource-intensive process, requiring several years for conclusive outcomes. However, recent evidence underscores the efficacy of selection in altering animal populations. Notable experiments with Drosophila and laboratory mammals, including rats, demonstrate the impact of selection on quantitative traits.

Selection in Plants:

• The landmark example of selection potential is the Illinois selection experiment for high and low corn oil content. 
• Starting with an initial oil content of 4.68 percent, the high line increased to 16.64 percent, while the low line decreased by less than one percent, showcasing the tangible outcomes of selection.

Selection of Laboratory Mammals:

• Castle's pioneering work on quantitative traits in rats, particularly selection for hooded patterns, exemplifies the outcomes of selection in laboratory mammals. 
• Long-term responses to selection for body size in mice have been extensively reported, demonstrating significant genetic changes attributed to selection.

Selection Plateaux

• Experiments involving selection for highly heritable quantitative traits in laboratory animals, such as mice, rats, Drosophila, and Tribolium castaneum, have shown rapid responses over 10 to 30 generations. 
• However, these populations often exhibit plateaus, indicating a point beyond which further improvement slows or ceases. 
• The concept of plateaus is explored in the context of farm animals, where the effectiveness of selection for economically important traits is still under investigation.