The traits that are influenced by multiple genes are called polygenic. Usually, these traits are also influenced by environmental factors and thus, in such cases, called multifactorial. Many quantitative traits, such as blood pressure, weight and height, are multifactorial. As these traits are caused by additive effects of many factors, these traits tend to follow a normal distribution in a big enough population.

The qualitative traits are expressed qualitatively, i.e., a qualitative trait falls into distinct two or three categories, or is either present or not present. A qualitative trait is typically influenced by a single gene and hardly influenced by environmental factors. Some traits only falls into a few classes but has a polygenetic inheritance, which are called threshold traits.

Quantitative traits show continuous variation and are measured on a numerical scale. A quantitative trait is influenced by many different genes and usually with environment factors. The phenotypical value of a quantitative trait typically follows normal distribution in a population. Most persons have intermediate phenotypes and only a small subset of persons show extreme phenotype.

When two individuals with extreme phenotypes got married, all of their children show intermediate phenotypes with a variance, which is influenced by the recombination of the genes and environmental factors.

When two individuals with intermediate phenotypes got married, most of their children show intermediate phenotypes with a higher variance, and sometimes extreme phenotype may appear, which is a result of the separation and recombination of many genes and interaction of environmental factors.

In a random mating population, most of the individuals are intermediate.

Some common congenital malformations (such as cleft lip, cleft palate, spina bifida, and anencephalus) and complex diseases (such as coronary artery disease, hypertension, diabetes mellitus, asthma and schizophrenia) may be multifactorial. The incidence of these diseases may be higher than 1/1000. Pedigree analysis of these diseases shows that they have familial trend and suggests that there are genetic bases underlying them.

The multifactorial model, also known as polygene theory, asserts that the quantitative and threshold traits are determined by a number of genes and environmental factors that have small effects and work additively to produce the trait. The loci being associated with the quantitative trait are termed quantitative trait loci (QTL), which individually follow Mendelian inheritance. Taking the human height as an example, more than 200 QTLs have been identified.

The threshold traits neither follow normal distribution as quantitative traits nor follow the single-gene inheritance patterns. The threshold of liability model is commonly used to explain these disease. The liability underlying the trait is multifactorial. The threshold of liability must be crossed for a disease to be expressed. The threshold for males and females may be different. For example, pyloric stenosis (narrowing or obstruction of the area between the stomach and intestine) is more common in males than in females. Liability is also referred as vulnerability, susceptibility, or the predisposition for a disorder. Some may susceptibility specifically for the genetic partial of liability.

In a population, the liability follows normal distribution and a majority of the individuals have a liability close to the mean value. In a certain condition, the threshold of liability stands for the minimal pathogenic genes necessary for an individual to be affected. The closer the threshold is to the mean liability, the higher is the disease incidence in the population.

The multifactorial diseases are influenced by both genetic and environmental factors. The proportion of variation in trait in a population that is due to genetic variation is termed heritability. Heritability is shown in percentage.

Some diseases, such as asthma and manic depression, may have a heritability as high as 70% to 80%. These disease often show familial aggregation.

Some disease, such as peptic ulcer and congenital heart defect, may have a heritability lower than 30% to 40%. These disease barely show familial aggregation.

The multifactorial disease is common in some population, the incidence could be higher than 1/1000. The siblings of the affected individuals have chance of 1% to 10% of being affected, which is much lower than 1/2 or 1/4 seen in single-gene disorders. Consanguineous marriage increases the recurrence risk of multifactorial diseases at a lower level than that of single-gene disorders. The recurrence risk decreases rapidly as the coefficient of relationship decreases. The incidence of multifactorial disease varies obviously among populations.

The recurrence risk estimation is much more complex for multifactorial diseases. For most multifactorial diseases, empirical risks specific for each multifactorial disease are derived from direct observation of large collections of families.

When the heritability is 70% to 80% and the prevalence is 0.1% to 1%, the sibling recurrence risk can be estimated with Edward formula. The incidence (f) of first level relative is close to the square root of the prevalence (P), i.e., f ≈ P^1/2. For example, the cleft lip has a prevalence of 0.17% in China and its heritability is 76%, the recurrence of the siblings of an affected individual could be estimated as (0.0017)^1/2 = 4.12%.

When the heritability is higher than 80% or the prevalence is higher than 1%, f > P^1/2. When the heritability is higher lower than 70% or the prevalence is lower than 0.1%, f < P^1/2.

The recurrence risk is higher when more family member is affected. For example, the sibling recurrence risk for cleft lip is about 4% if one sibling is affected but increases to about 10% if two siblings are affected. In contrast, the recurrence risk for single-gene disorders does not change with the number of affected siblings.

The recurrence risk is higher when the condition of affected family member is more severe, as a more-severe condition indicates a more extreme liability or more pathogenic genes persisted. For example, the sibling recurrence risk is about 2.46% for unilateral cleft lip, 4.21% for unilateral cleft lip combined with cleft palate, 5.74% for bilateral cleft lip combined with cleft palate. In contrast, the recurrence risk for single-gene disorders does not change with the condition severity of affected siblings.

For the disease show sex difference, the recurrence risk is higher if affected individual is of the less commonly affected sex. The less common sex has a higher threshold and need a higher liability to be affected and thus higher liability could be transmitted.

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