Animal Molecular Breeding 2024, Vol.14, No.4, 252-261 http://animalscipublisher.com/index.php/amb 253 continuous variability and are typically distributed normally due to the additive effects of numerous genes. The action of additive genes results in a phenotypic distribution that is intermediate between the parental populations, while multiplicative gene actions can create geometric series in trait expression (Núñez-Torres and Almeida-Secaira, 2022). Understanding these principles is crucial for developing effective breeding strategies that enhance economically important traits in livestock. 2.2 Polygenic inheritance and complex trait analysis Polygenic inheritance refers to the genetic architecture where multiple genes contribute to the expression of a single trait. In livestock, most economically significant traits are complex and influenced by numerous genetic and environmental factors. Genome-wide association studies (GWAS) have become a pivotal tool in identifying quantitative trait loci (QTL) that contribute to genetic variance in these traits. The use of dense SNP panels allows for the mapping of genes and mutations that affect these complex traits, providing insights into their genetic underpinnings and facilitating more precise selection in breeding programs (Schmid and Bennewitz, 2017; Singh et al., 2019; Bijma, 2021). 2.3 Concepts of heritability and genetic variance Heritability is a key concept in quantitative genetics, representing the proportion of phenotypic variance that can be attributed to genetic variance within a population. It is a critical factor in determining the potential for genetic improvement through selection. Genetic variance encompasses both additive and non-additive genetic effects, with additive variance being particularly important for selection as it directly contributes to the response to selection. Understanding the genetic variance and heritability of traits allows breeders to predict the outcomes of selection and optimize breeding strategies to enhance desirable traits in livestock populations (Figure 1) (Viana et al., 2016; Núñez-Torres and Almeida-Secaira, 2022; Kandel et al., 2023). In summary, the theoretical foundations of quantitative genetics in livestock breeding involve understanding Mendelian principles, polygenic inheritance, and the concepts of heritability and genetic variance. These principles guide the development of breeding strategies aimed at improving economically important traits through informed selection and genetic analysis. Figure 1 Schematic presentation of multiple ovulation embryo transfer in buffalo (Adopted from Kandel et al., 2023) 3 Tools and Methods in Quantitative Genetics 3.1 Quantitative trait loci (QTL) mapping Quantitative Trait Loci (QTL) mapping is a fundamental tool in quantitative genetics, used to identify genomic regions associated with the expression of quantitative traits. These loci may contain one or more genes that contribute to the trait's variance. QTL mapping typically involves analyzing biparental populations to detect associations between marker genotypes and trait phenotypes. Various methods, such as regression analysis,
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