Genetics Quantitative

Dorian J. Garrick

Department of Animal Sciences, Colorado State University, Fort Collins, Colorado, U.S.A.


Genetics is the study of transmission of hereditary factors, such as deoxyribonucleic acid (DNA), or, more specifically, genes, from parents to offspring. These factors can be studied at a number of different levels including those having molecular, genomic, population, or statistical viewpoints. Quantitative genetics makes use of statistical procedures to study the variation that results in particular individuals exhibiting superior or inferior performance.

performance can be calculated, with about two-thirds of the animals performing at a level within one S.D. of the average. Other traits tend to be categorical in nature, and such traits may or may not be ordered. Consider equine coat color. Some common colors are bay, chestnut, black, buckskin, and palomino. These colors represent distinct categories and they cannot be precisely ordered. In contrast, many categorical traits such as calving ease or litter size can be ordered. A ewe having twins has a litter size that is intermediate between a single and triplets. Such an ordered categorical trait is often referred to as a threshold trait.


Quantitative genetics relates variation in measured or observed performance to inheritance by providing various models to explain observed variations in terms of hereditary factors. These alternative models attempt to describe possible explanations for observed behavior. The true model is never known, but statistical analyses can be undertaken to determine if observed variation is consistent with that predicted by the model. The simplest two models to describe genetic merit or genotype range from the single gene (monogenic) model to the infinitesimal or polygenic model.[1,2] With both extremes, the genetic factors are assumed to result from diploid DNA sequences, one half (a haploid) having been inherited from the sire and the other haploid from the dam. The inheritance of these genes is said to be Mendelian, even though the characteristic or trait that they influence may not be of a simple Mendelian nature. In the monogenic model, a single locus is responsible for observed variation. In the infinitesimal model, the genotype is assumed to be collectively determined by an infinite number of individual genes, each having a small almost non-significant influence. Intermediate models are also possible, including oligogenic models representing the effects of a few genes, or mixed inheritance models including one or more major genes in addition to residual polygenic effects.

A comprehensive range of traits is important to animal scientists and producers. Many traits such as weaning weight, which are continuous in nature, allows the observed performance of animals to be ordered or ranked. The average and the standard deviation of


The amount of variation observed in a quantitative or continuous trait can be quantified by calculating the phenotypic variance. Since animals in different herds or years typically exhibit different average levels of performance, the phenotypic variance, or its square root, the phenotypic standard deviation, is not simply calculated from observed performance of all animals, but is pooled from estimates of the variation among contemporaneous animals that is, animals in the same herd in the same year, adjusted for systematic influences on performance such as their age or calving date.

A few traits or characteristics such as coat color provide direct indication of the likely genotype or genetic make up of the individual. Most traits, particularly production traits such as bodyweight, milk production, fleece weight, litter size, or calving difficulty are strongly influenced by environmental effects in addition to the influence of genes. Accordingly, the phenotype or observed performance is usually considered to result from the combined effects of the genotype and the environment. The environment is rather a loose term and actually refers to at least two different kinds of influences. The first of these might be referred to as systematic effects. These include all the influences of the physical environment (such as the climate, management, and level of nutrition) that is common to a cohort or group of individuals. Additional systematic environmental effects include the influence of sex, age of the individual, age of the dam, birth, and rearing ranks. The second kind of environmental influence is probably more correctly referred to as non-genetic or residual effects. These influences contribute to the superiority or inferiority of the performance of an individual in comparison to its contemporaries of the same sex and age in the same herd, but are not passed on. Such influences are sometimes partitioned into so-called permanent environmental influences that repeatedly affect performance over the lifetime of an animal, and temporary environmental influences that are unique to a particular measurement.

The measure of relative importance of genetic and environmental influences in explaining variation observed within groups of contemporary animals is known as heritability. Heritability can be formally calculated as the proportion of observed or phenotypic variation that can be attributed to differences in genotypes. It is a measure of the strength of the relationship between genotype and phenotype. Heritability is an important determinant of response to selection as it influences the accuracy with which the underlying genotypes of animals can be predicted from observations of their phenotypic performance in relation to contemporaries.

Concepts such as phenotypic variation and herita-bility apply at the level of the population, rather than to individuals. These concepts exist regardless of whether the trait is influenced by one, a few, or many different genes. Heritability can be estimated from a statistical viewpoint by relating the superiority or inferiority of the performance of parents to the superiority or inferiority of the performance of offspring. If a quantitative characteristic was entirely due to genetic merit with no residual or temporary environmental influences, then the regression of offspring performance on performance of a parent would be one-half, reflecting the fact that each parent contributes half the genes to its offspring. This would correspond to a heritability of one. A lowly heritable trait would exhibit a much weaker relationship between parent and offspring performance. Many production traits have heritabilities of 0.2 0.3 whereas reproductive and survival traits typically have even lower heritabilities, often near 0.1.

Some loci that influence one trait may have so-called pleiotropic effects and influence other traits. These effects may be complementary if an allele is favorable for both traits or it may be that an allele is favorable for one trait and unfavorable for another trait. Both of these instances commonly occur, particularly for genes that influence variation in fundamental pathways that contribute to productive traits. The effect of such genes is to create a correlation between the genotypes for the traits. These genetic correlations may be positive or negative and will influence the response in performance of one trait when the other trait is subject to selection. Such correlations will also influence the rate at which both traits may respond to simultaneous selection, such as from use of an index.


Statistical procedures can be used to quantify the genetic merit of individuals from a population viewpoint, based on their own performance and also on performances of their relatives. Suppose a sire has hundreds of daughters that produce, on average, 1000 kg milk more than their contemporaries. Individual superior performance may come about from the effects of genes or from non-genetic or environmental reasons. However, such effects should average out when many offspring are considered and so the conclusion would be that the sire in question was passing on one or more favorable genetic factors that were contributing to the superiority of his daughters. This cumulative influence on offspring performance is known as a progeny difference or a transmitting ability in the beef and dairy industries, respectively, in the United States. Such sire effects are estimated from performance data and therefore may be subject to estimation errors. These errors could result in the assessment of the merit of an animal changing over time. To remind users of these assessments that they are predictions, the acronyms EPD (expected progeny difference) and PTA (predicted transmitting ability) are used. The value of the genes of the parents would be predicted as twice the value observed in the offspring, reflecting the fact that offspring inherit a random sample of half of their parents' genes. This estimate of the parental value is known as the estimated breeding value. From a Mendelian or molecular viewpoint, a breeding value (BV) would be described as the sum of average effects of particular alleles or DNA sequences. It is interesting that the same endpoint can be reached using a statistical basis and taking account of the fraction of the genome that relatives share in common to assess these values solely from pedigree and performance records.


Quantitative genetics bridges the gap among molecular, Mendelian, and population genetics. It encompasses both so-called traditional selection and marker-assisted selection that can be used to exploit quantitative trait loci (QTL). The introduction of DNA-based genetic markers has led to the use of statistical approaches to partition the genetic influence or BV into a polygenic component resulting from an unknown number of genes with unknown gene action at unknown locations and a QTL effect representing the influence of DNA sequences that are physically located at or near a particular genetic marker. These new developments show that the nature of quantitative genetics is expanding over time and that quantitative genetics might more appropriately be referred to as computational biology.


Genetics: Population. Published online only. Quantitative Trait Loci, p. 760 762.

Selection: Marker Assisted, p. 781 783. Selection: Traditional Methods, p. 784 786.


1. Bourdon, R.M. Understanding Animal Breeding; Prentice Hall: Englewood Cliffs, NJ, 1997.

2. Falconer, D.S.; Mackay, T.F.C. Introduction to Quantitative Genetics, 4th Ed.; Prentice Hall: Englewood Cliffs, NJ, 1996.

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