Behavioural Genetic Interactive Modules

Families

Overview

Tutorial

The panel to the right represents the percentage of total variance that each of these four components accounts for. We assume that the variation in the trait (including measurement error) is completely accounted for by these four latent variables and so these four percentages will always sum to 100%. Moving the sliders results in a corresponding change in these figures.

The panel at the bottom of the window contains a graphical and numerical display of the correlations that we would expect to observe for the trait, if the trait had the relative balance of genetic and environmental effects specified in the top panel (i.e. 100% heritable). The leftmost column is labelled Proband, the "correlation" between individuals and themselves. Of course, this correlation will always be a complete positive correlation of 1.0 (the maximum possible correlation). In the second column, the height of the green bar and the number below represents the correlation we would expect to observe between MZ twins. Likewise, the next three columns represent the correlations we would expect to see between DZ twins, full siblings and parent-offspring. The next two columns represent the expected correlations for MZ and DZ twins reared apart (i.e. no shared environment, but still shared genes). The correlation for half-siblings (half siblings raised in the same family) is next; finally, the expected correlation between the proband and any unrelated individual chosen at random is shown.

The only controls in this module are the four sliders in the top left panel. Moving the A slider up increases the relative proportion of trait variance attributable to additive genetic variation. Because all the other parameters are set to zero, this will suddenly jump to 100%. That is, the value for Heritability given in the top right panel will read 100%, indicating that the trait is completely determined by the additive effects of genes.

Looking at the expected correlations under this somewhat unrealistic scenario, we see that they represent the expected proportion of allele sharing for the different types of relatives. Because MZ twins share all their genes, then if the trait is completely determined by additive genetic effects, MZ twins will correlate completely for the trait. DZ twins, full siblings and parent-offspring pairs, all of whom share only half their alleles, are only expected to show a correlation of 0.50. Because this simple model states no environmental effects, twins reared apart are expected to be just as similar to each other as those reared together.

We would be very unlikely to ever see this pattern of correlations in families for any complex behavioral trait. For certain Mendelian traits with complete penetrance, we might observe a pattern of familial correlations close to this. Given that measurement error is incorporated into the nonshared environmental component of variance, it is extremely unlikely that this will ever be zero.

So try sliding the nonshared environment E control upwards. Note what happens: in the top right window we can see that the magnitude of the nonshared environmental component increases and all of the expected correlations between family members drop.

Note that the familial correlations remain in proportion with each other, however, when varying the E component. That is, the DZ twin correlation always remains half the expected MZ correlation, for example. Although the nonshared environmental is now contributing to the variance of the trait, it does not (by definition) contribute to the similarity between family members. Under this scenario, what makes related individuals similar is still completely the additive effect of genes, so we would still expect similarity to reflect exactly the expected proportion of allele sharing between relative pairs.

Now try increasing the C slider. Note how some correlations rise and some fall, all at different rates. It is the nature of this relationship, between the aetiological components of variance and the expected familial correlations that is the key to many quantitative genetic methods. Incorporating dominance (the D slider) further influences the pattern of expected correlations.

The expected correlations for each type of relative pair are entirely determined by the four population parameters. The Behavioral Genetics Appendix gives an account of how familial correlations can be expressed in terms of the sharing we would expect for variance components, which can be derived from basic biology (for the genetic components) or by definition (for the environmental components).

Questions

1. The correlation bars only range between 0 and 1 but correlations can be negative. Why would we never expect to observe a negative correlation between family members if we assume this simple model is an accurate reflection of the trait aetiology? (Note: In certain special circumstances we might actually expect to observe negative correlations between relatives (e.g. sibling interaction))

2. The correlation between unrelated individuals is always fixed at 0. Why is this?

3. Is there any configuration of variance components that makes every different type of relative pair have a unique expected correlation? If not, why not?

4. The expected correlation for full siblings is calculated as half the additive genetic variance (heritability) plus a quarter of the dominance genetic variance plus shared environmental variance.

   Set the population parameters to 20%, 12%, 20% and 48% for the heritability, dominance, shared environmental and nonshared environmental variance respectively (note: this can be a bit tricky, as moving one slider may cause one component to increase but all the others also fall! This is because they represent proportions and so must always sum to 1, i.e. 100%).

   See that the expected correlation between siblings is now 0.33. Check that this corresponds to the value we would calculate using the information given above. At these population parameter values, the expected correlation between parent and offspring is 0.30. By moving the sliders and observing the changes in these values, try to determine the rule that gives the expected correlation between parent and offspring. Also, what is it for half siblings?

5. This module makes several assumptions that we would not necessarily want to make in a proper analysis. One, for example, involves the equal environment assumption. Typically we assume that MZ and DZ twins share equally similar environments; this modules extends this assumption to parents and half-siblings however. That is, there is only one shared environmental parameter for all the different types of relatives in this module. Can you give an example of when this assumption might not be valid?

Answers

1. Under our model, the trait is composed of four independent components: additive and dominance genetic effects, shared and nonshared environmental effects. None of these could, theoretically, induce a negative correlation between family members (remember that nonshared effects do not tend to make pairs of individuals dissimilar, rather they are effects which make tend to make pairs of individuals neither similar nor dissimilar). If a trait were entirely due to nonshared environmental effects, then we would expect family members to be just as similar (and alternatively, just as dissimilar) as pairs of unrelated individuals.

   Note that it might be possible to observe a negative familial correlation in a sample if the nonshared environmental variance is very high and the sample size is low. In this case, the expected correlation would be positive but near zero, but the small sample size would imply a large degree of sampling error in the estimation of the correlation.

2. This correlation is by definition 0, which means that, on average, we would expect to see no relationship between unrelated individuals. Imagine that we chose 1000 pairs of unrelated individuals at random and measured them for a particular trait. If we found a negative correlation this would imply that we had somehow managed to pair low scoring individuals with high scoring individuals. If we found a positive correlation this would imply that we had tended to pair high-scoring individuals with high-scoring individuals, low-scoring with low-scoring. If we do not expect either of these processes to occur (there is no reason they should do if the sampling is random) then we must expect a zero correlation. Note that this says nothing about the level of variation in the population of unrelated individuals for the trait. That is, whether or not the trait had a very large or a very small variance, we would still expected unrelated individuals picked at random from any population to display a zero correlation.

3. DZ twins and full siblings will always have the same expected correlation under this model. In the eyes of this model, DZ twins are just like normal full siblings. Genetically speaking there is also no difference between DZ twins and full siblings: DZ twins are siblings that just happen to have been conceived at the same time. As question 5 indicates however, there may be other reasons which suggest that equating DZ twins and full siblings might not be sensible.

4. Parents and offspring also share half their additive genetic variance but they do not share dominance genetic variance. Half siblings share a quarter of the additive genetic variance. Both types of relative pair share all shared environmental variance (by definition) (although, typically, we would not expect the magnitude of this to be the same for all different types of relative pair - see question and answer 5).

5. One example would be if we were to study young MZ and DZ twins and their parents for a trait such as bladder control. The types of environment that tend to induce a correlation between young twins for this trait would probably be quite different from any environment that induced a correlation between parent and offspring for this trait. Imagine that exposure to potty training influences bladder control (and acts as a shared environmental source of trait variance), for example.

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   Site created by S.Purcell, last updated 6.11.2000