Quantitative genetics seeks to understand the inheritance of complex traits—traits that are influenced by a mix of genetic and environmental factors and do not segregate in simple Mendelian ratios. Complex traits can be categorical traits, threshold traits, counting (meristic) traits, or continuously variable traits. Any trait for which we cannot directly infer genotype from phenotype is a target for quantitative genetic analysis.

The genetic architecture of a trait is the full description of the number of genes affecting the trait, their relative contributions to the phenotype, the contribution of environmental factors to the phenotype, and an understanding of how the genes interact with one another and with environmental factors. To decipher the genetic architecture of complex traits, quantitative geneticists have developed a simple mathematical model that decomposes the phenotypes of individuals into differences that are due to genetic factors (g) and those that are due to environmental factors (e).

The differences in trait values among members of a population can be summarized by a statistical measure called the variance. The variance measures the extent to which individuals deviate from the population mean. The variance for a trait can be partitioned into a part that is due to genetic factors (the genetic variance) and a part that is due to environmental factors (the environmental variance). A key assumption behind partitioning the trait variance into genetic and environmental components is that genetic and environmental factors are uncorrelated or independent.

The degree to which variation for a trait in a population is explained by genetic factors is measured by the broad-sense heritability (H²) of the trait. H² is the ratio of the genetic variance to the phenotypic variance. Broad-sense heritability expresses the degree to which the differences in the phenotypes among the individuals in a population are determined by differences in their genotypes. The measurement of H² in humans has revealed that many traits have genetic influences, including physical attributes, mental functions, personality features, psychiatric disorders, and even political attitudes.

Parents transmit genes but not genotypes to their offspring. At each generation, new dominance interactions between the alleles at a locus are created. To incorporate this phenomenon into the mathematical model for quantitative variation, the genetic deviation (g) is decomposed into the additive (a) and dominance (d) deviations. Only the additive deviation is transmitted from parents to offspring. The additive deviation represents the heritable part of the phenotype in the narrow sense. The additive part of the variance in a population is the heritable part of the variance. Narrow-sense heritability (h²) is the ratio of the additive variance to the phenotypic variance. Narrow-sense heritability provides a measure of the degree to which the phenotypes of individuals are determined by the genes they inherit from their parents.

A knowledge of the narrow-sense heritability of a trait is fundamental to understanding how a trait will respond to selective breeding or the force of natural selection. Plant and animal breeders use their knowledge of narrow-sense heritability for traits of interest to guide plant and animal improvement programs. Narrow-sense heritability is used to predict the phenotypes of offspring and estimate the breeding value of individual members of the breeding population.

The genetic loci underlying variation in complex traits are known as quantitative trait loci, or QTL for short. There are two experimental methods for characterizing QTL and determining their locations in the genome. First, QTL mapping looks for statistical correlations between the genotypes at marker loci and trait values in populations with known pedigrees such as a BC₁ population. QTL mapping provides estimates of the number of genes controlling a trait, whether the alleles at the QTL exhibit additivity or dominance, and whether each QTL has a small or large effect on the trait. Second, association mapping looks for statistical correlations between the genotypes at marker loci and trait values in random-mating populations. Association mapping can allow researchers to identify the genes that underlie the QTL. Genome-wide association (GWA) studies use markers blanketing the entire genome.

Most traits of importance in medicine, agriculture, and evolutionary biology show complex inheritance. Examples include disease risk in humans, yield in soybeans, milk production in dairy cows, and the full spectrum of phenotypes that differentiate all the species of plants, animals, and microbes on earth. Quantitative genetic analyses are at the forefront of understanding the genetic basis of these critical traits.