Estimating additive genetic variation and heritability of phenotypic traits


Erin Rentz



Components of Phenotypic Variation


Breeding Designs

Important Terms






        For any trait of interest, observed differences among individuals may be due to differences in the genes coding for this trait or may be the result of variation in environmental condition. In many cases it is a combination of the two.


Understanding the amount that genes, passed from parent to offspring, influence a trait may be useful in a variety of situations. In the field of medicine, it can be useful in determining an individual's risk of developing a specific disease. This information has also been critical in crop breeding programs where growers seek to maximize desirable traits such as quantity, sweetness, and shelf-life.


In the field of ecology, one may be interested in the extent to which phenotypic differences among populations of a given species, such as size or color, are influenced by differences in environmental conditions. Estimating the genetic components of phenotypic variation and heritability may help the researcher to address such questions.



It is important to keep in mind, however, that the components of phenotypic variation are a function of the conditions in the population at the time the assessment is made. Changes in the environment or in the gene frequencies will change the relative contributions of genetic and environmental components.


When examining variation in phenotypic traits you are:

á       Looking at a specific trait or several traits where the phenotype can be quantified in a population

á       Looking at how phenotype is affected by environment and genetics in that specific environment. This is:

o      Dependent on the frequencies of a given gene in a population

o      Dependent on environmental conditions

¤        One way to think of it is that if you have a species that grows in oak woodlands as well as high on alpine slopes, environmental conditions may have a greater influence on the plant in the alpine environment than genetic considerations while in the grassland, the genotype may be more important in determining phenotype.


Therefore generalizations should not be made concerning the heritability of a trait without considering the environment or genetic makeup of the population.


Components of Phenotypic Variation


When working with a quantifiable phenotypic trait, the measurement taken for a specific individual will be its phenotypic value (P). This value can be broken down into two main components: that portion that is a result of the individuals genotype (G) and the amount portion that is due to environmental conditions (E).


Text Box:  
phenotypicvalue	genotypicvalue	environmental deviation




These two main components can be subdivided further.


Components of Genotypic Value

There are three main components that contribute to the genotypic value:

Text Box:  
breedingvalue	dominancedeviation	Interaction or epistasis







Breeding Value


The breeding value, (A), is a measure of how much an individualÕs genetic make up contributes to the phenotypic value of the next generation. The breeding value is a calculation determined by the gene frequencies in a population for a given locus, and a measure called the average effect.


When considering an allele, we would like to know how much that single allele, if found in an offspring, will change the trait measure of that individual away from the population mean. This is called the average effect.


When looking at a single locus trait with two possible alleles for a population in Hardy-Weinberg Equilibrium, the average effect is determined by looking at the range of the value for a specific trait between the two homozygotes for the different alleles and where the heterozygote trait characteristic falls between these two. It is also based on the frequencies of the two alleles in the population.


A more detailed explanation of average effect and breeding value can be found in Chapter 7 of Falconer and MacKay (1996).


Dominance Deviation and Multilocus Interactions


Because all genes do not always act additively, but may interact, it is important to include in the genetic value a measure of the amount of interaction. When looking at a single locus, interaction between alleles that results in phenotypic expression that is not purely additive is referred to as the Dominance deviation, (D).

Interactions between genes at different loci that act on the same characteristic are referred to as Interaction or epistasis (I).


Parts of Environmental Value


Environmental effects include a variety of different factors including climatic factors such as temperature and rainfall patterns, nutritional factors such as soil nutrients or availability of food resources, and various other factors that cannot always be identified by the researcher. Also included in the environmental value is maternal effects or how the health of the maternal organism affects that of the offspring.


Phenotypic Variation

When analyzing the phenotypic values of a trait within a population, comparisons are made using variance and, as above, the phenotypic variance is divided between various components.

  Text Box:  
Phenotypic Variance	Additive Genetic Variance	Non-Additive Genetic Variance	Environmental Variance


In addition, because the components of phenotypic variance are not always independent, there are additional terms of covariance to take into consideration. For example, interactions between the environmental variance and additive genetic variance could be accounted for using a term of covariance.



As mentioned above, researchers are often specifically interested in estimating how much the characteristics of the offspring are dependent on the parent. This is referred to as heritability. Heritability is the ratio of the genetic variance over the phenotypic variance. Broad sense heritability includes all components of genetic variance.



Narrow sense heritability includes only the additive genetic variance and it is this form of heritability that usually of interest.



It is also referred to as resemblance between relatives.


Because individual components of variance are not directly measurable, it is necessary to use comparative measurements of phenotype to determine the contribution of individual variance components.


For example:

o      By measuring a specific trait such as height in individual organisms from several populations, one could determine the range of height measurements for that species.

o      Individuals from different populations could then be grown in a common garden and measured at the same point of maturity as the original organisms. The common garden would eliminate the environmental variance experienced between the different populations.

o      Therefore, the difference between the phenotype variance of the wild populations and that of the common garden would give an estimate of the total genetic variance.




Breeding Designs


The genetic similarity between related organisms can be used to further distinguish individual components of variance. Breeding designs involve using  a series of  crosses in which relatedness among offspring or between parents and offspring is known, and from these crosses partition phenotypic variation into  the variance components described above. In general, breeding designs are used under the following assumptions:



1.   Working with diploid organisms

2.   No linkage

3.   No environment x genetic correlation

4.   Same amount of inbreeding in parental lines

5.   No apparent inbreeding depression

6.   No selection, mutation; random mating

7.   No competition

From Mazer and Lebuhn, 1999)


There are several different categories of breeding designs:

Parent - Offspring designs compare phenotypic variance between parents and offspring.


Parent-offspring regression is one of the most commonly used methods. A specific phenotypic trait is measured for both the parent and the offspring at the same age and compared using regression. The slope of regression of offspring on parents will tell you about resemblance between relatives, h2.



One parent - offspring formula



A one parent-offspring is a comparison between either the mother or father and the offspring and gives an estimate of half of the narrow sense heritability:

The slope of the father-offspring regression may differ from the slope of the mother-offspring regression due to maternal effects, a component of the environmental variance and could therefore be used to determine the effect of the maternal environment on a specific trait.



formula for mid-parent offspring regression


A mid-parent-offspring averages the two parents and gives an estimate of the total narrow sense heritability. For examples of research using parent-offspring regression, please see Keller et al. (2001), Oosterhout and Brakefield (1999), and Ward (2000).


Full-sib designs compare phenotypes of siblings that share mother and father with other sibling groups

Half-sib designs compare phenotypes of siblings that share one parent with other sibling groups.

Nested designs use a combination of full-sib and half-sib offspring to distinguish variance components.



Text Box:  
From Lynch and Walsh,1998












For example, a in a nested full-sib, half-sib mating design males are crossed with a series of different females. Offspring with the same fathers and mothers (z111, z112, z113) represent full-sibs while offspring with different mothers (z111, z121, z131) represent half-sibs. An ANOVA is used to determine different components of genetic variance.


For a summary of the different design types, see Mazer and LeBuhn, (1999). For more information on crossing designs and their analysis, see Lynch and Walsh, (1998).



Important Terms


Phenotype -the observable properties of a trait in an individual


Genotype -genetic make-up of a trait in an individual


Hardy-Weinberg Equilibrium - One loci, two alleles at the frequency of p and q, will maintain those frequencies over in an infinitely large random mating population with no mutation, selection or gene flow.


If p is the frequency of A alleles in the population, and q is the frequency of A' alleles (p + q = 1), then the frequency of individuals in the next will be as follows:


p2                   AA individuals

q2                A'A' individuals

2pq             AA' individuals  - where p2+2pq + q2=1



Additive Gene Interaction vs. Dominance -


Additive Gene Interaction - all genes contribute equally to the final phenotype.



Dominance - one gene contributes more or less to the final phenotype.







Example Journal Articles


Keller, L.F., Grant, P.R., Grant, B.R., Petren, K. 2001. Heritability of Morphological Traits in DarwinÕs Finches: Misidentified Paternity and Maternal Effects. Heredity 87-3:325-336.


Lavi,U. et al. 1998 Components of genetic variance and genetic correlations between traits in Mango. Scientia Horticulturae 75.


Oosterhout, C.V. and Brakefield, P.M., 1999. Quantitative Genetic Variation in Bicyclus Anynana Metapopulations Netherlands Journal of Zoology49-2:67-80.


Pante, Ma. Josefa R., Gjerde, B., McMillan, I. And Misztal, I. 2002. Estimation of additive and dominance genetic variances for body weight at harvest in rainbow trout, Onconrhychus mykiss. Aquaculture 204  383-392.


Ward, S.M. 2001. Response to selection for reduced grain saponin content in quinoa (Chenopodium quinoa Willd.) Field Crops Research 68-2:157-163.



Falconer,D.S. and Mackay, T. 1996. Introduction to Quantitative Genetics. Longman, Essex, England.


Lynch, M. and Walsh, B. 1998. Genetics and Analysis of Quantitative Traits. Sinauer, Sunderland, MA.


Mazer,S. and LeBuhn, G. 1999. Genetic Variation in Life History Traits In: Vuorisalo,T.O and Mutikainen,P.K. Life History Evolution in Plants. Kluwer, Boston, MA


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Page Last Updated: May 30, 2002