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Calculating Heritability & Environmentability in Behavioral Genetics - Prof. Gregory Carey, Assignments of Genetics

University of Colorado Boulder (CU Boulder)Genetics
Prof. Gregory Carey

Problem sets related to behavioral genetics, specifically focusing on calculating heritability and environmentability using given correlation coefficients between different types of relatives. The equations and examples include correlations for siblings raised apart and together, biological parents and adopted-away offspring, and half-siblings. Additionally, the document covers a finnish study on alcohol use among male twins and their correlations for density and amount of alcohol consumption.

Typology: Assignments

Pre 2010

Uploaded on 02/13/2009

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Psychology 3102: Introduction to Behavioral Genetics (Carey)
Problem Set: Heritability and Environmentability
Two basic equations are required to calculate heritability and environmentability. The first equation is
h2 + e2 = 1
where h2 is the heritability and e2 is the environmentability. This equation simply states that the total
variance is composed of two sources, the genes and the environment. The proportion of variance due to
the genes is h2 and the proportion of variance due to the environment is e2. The second equation is
corr(relative 1, relative 2) =γh2 + ηe2 = 1
This equation states that the correlation between two types of relatives (e.g., MZ twins, or mothers and
offspring, or siblings) equals the genetic correlation between these two types of relatives (γ) times the
heritability (h2) plus the environmental correlation between the two types of relatives (η) times the
environmentability (e2). One requires two different correlation coefficients to solve for the unknowns in
these equations. For example, one can solve for them with the correlation coefficients for MZ twins and
DZ twins. One could also solve for them with the correlation coefficient between biological mothers and
their adopted-away offspring and the correlation coefficient between biological mothers and the offspring
that they raise.
1. Solve for h2 , e2 and η when the correlation for siblings raised apart is .23 and the correlation for
siblings raised together is .28.
2. Solve for h2 , e2 and η when the correlation for biological parents and adopted-away offspring .18 and
the correlation between adoptive mothers and their adoptive offspring is .15.
3. Solve for h2 , e2 and η when the correlation for half-siblings raised in the same household is .22 and the
correlation for half siblings raised in different households is .12.
4. In a Finnish study of alcohol use among male twins, the researchers studied two phenotypes. One was
"density", or a measure of the frequency and regularity with which one drinks alcohol. The second was
"amount" or a measure of the amount of alcohol that an individual would drink whenever he was
drinking. The researchers reported the following correlations for MZ and DZ twins on the two
phenotypes:
Phenotype MZ Correlation DZ Correlation
Density .61 .32
Amount .38 .11
For each of the two phenotypes, calculate the heritability, the enviroronmentability, and the correlation
between the environments of twins.
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Psychology 3102: Introduction to Behavioral Genetics (Carey)

Problem Set: Heritability and Environmentability

Two basic equations are required to calculate heritability and environmentability. The first equation is

h^2 + e^2 = 1

where h^2 is the heritability and e^2 is the environmentability. This equation simply states that the total variance is composed of two sources, the genes and the environment. The proportion of variance due to the genes is h^2 and the proportion of variance due to the environment is e^2. The second equation is

corr(relative 1, relative 2) =γ h^2 + η e^2 = 1

This equation states that the correlation between two types of relatives (e.g., MZ twins, or mothers and offspring, or siblings) equals the genetic correlation between these two types of relatives (γ) times the

heritability ( h^2 ) plus the environmental correlation between the two types of relatives (η) times the environmentability ( e^2 ). One requires two different correlation coefficients to solve for the unknowns in these equations. For example, one can solve for them with the correlation coefficients for MZ twins and DZ twins. One could also solve for them with the correlation coefficient between biological mothers and their adopted-away offspring and the correlation coefficient between biological mothers and the offspring that they raise.

  1. Solve for h^2 , e^2 and η when the correlation for siblings raised apart is .23 and the correlation for siblings raised together is .28.
  2. Solve for h^2 , e^2 and η when the correlation for biological parents and adopted-away offspring .18 and the correlation between adoptive mothers and their adoptive offspring is .15.
  3. Solve for h^2 , e^2 and η when the correlation for half-siblings raised in the same household is .22 and the correlation for half siblings raised in different households is .12.
  4. In a Finnish study of alcohol use among male twins, the researchers studied two phenotypes. One was "density", or a measure of the frequency and regularity with which one drinks alcohol. The second was "amount" or a measure of the amount of alcohol that an individual would drink whenever he was drinking. The researchers reported the following correlations for MZ and DZ twins on the two phenotypes:

Phenotype MZ Correlation DZ Correlation Density .61. Amount .38.

For each of the two phenotypes, calculate the heritability, the enviroronmentability, and the correlation between the environments of twins.

  1. In the same study, the researchers reported the following correlations for a vocabulary test and an arithmetic test.

Phenotype MZ Correlation DZ Correlation Vocabulary .75. Arithmetic .73.

For each of the two phenotypes, calculate the heritability, the enviroronmentability, and the correlation between the environments of twins.

  1. In what ways are the two cognitive phenotypes similar and in what ways are they different from the two alcohol-related phenotypes in terms of heritability and environmentability?
  2. Suppose the correlation between an adoptive mother and her adopted child is .02 and suppose the observed correlation between biological mother and own child reared together is .20. What is the heritability and environmentability of the trait? What is the effect of the parental environment on the trait? What would you predict the correlation between the birth mother and her adopted away offspring to be?
  3. The correlation between genetically unrelated adoptive siblings raised in the same household is. [that is, the parents adopt 2 genetically unrelated children]. The correlation between identical twins raised apart since birth is .45. What would you predict the correlation to be for the following types of relatives:
    • 8.a) biological siblings raised apart from birth
    • 8.b) biological siblings raised together in the same household?
    • 8.c) identical twins reared together?
    • 8.d) biological parent and adopted away offspring
  4. One large twin study was the National Merit twin study. One personality measure in this study was social dominance. People high on this trait like to assume positions of leadership and be the center of attention. People low on the trait prefer to remain in the background. The researchers obtained the following correlations for male and female twins:

MZ Males .57 MZ Females. DZ Males .12 DZ Females.