Behavioural Genetic Interactive Modules

Variance Components : ACE

This module aims to illustrate the way in which variation in a quantitative trait can be attributed to different sources. Namely, we consider variation due to additive genetic effects and variation due to environmental effects, which may or may not be shared between two members of the same family.

Tutorial

This module is split in two halves: the first considers variation in a sample of individuals, the second considers variation in identical (MZ) and non-identical (DZ) twin pairs. Clicking on the appropriate tab takes you between these two parts (the two parts are otherwise independent from each other).

We shall begin by looking only at individuals. The module presents a panel, shown above: clicking the Individual button causes the module to add a new individual to the sample. The slider on this panel represents the relative balance of additive genetic and environmental effects for the trait of interest. Moving the slider to the left would indicate that genes have a stronger influence on the trait.

When we say that genes are more important for a trait, we mean that having a very high score or very low score is more likely to be due to an individual's genetic makeup rather than any environmental factors. On average, however, the influence of genes (or environments) would neither tend to make individuals higher nor lower.

When a new individual is generated, the trait value is entered into the sheet, as shown to the left. However, the trait value is broken down into the part due to additive effects of genes and the part due to the environment. Remember the basic biometric model:

 
       P = G + E

That is, a phenotype (P) is considered to result from independent effects of genes and environment.

The two boxes shown at the bottom represent the mean value of genetic and environmental effects. As you add more individuals you will see that these both tend towards zero: this would be the phenotypic population mean of the trait also.

Changing the slider to control the relative balance will not change the mean effect of genes or environment in this module. Rather, if the relative balance is heavily loaded on the genetic side, you will see that the absolute values of the scores is, on average, larger. That is, the effect of genes is more likely to be very high or very low than the effect of the environment. This is what it means to say that 'genes are more important' for the trait. Certain constellations of genes might cause very high scores, certain constellations might cause very low scores. In contrast, the effects of the environment will have very little impact on the trait, in either direction.

Just as we calculated the variance of a trait in the first module, we can calculate the variance of these two components in an identical manner. As shown in the panel to the right, we simply take the deviations from the mean (i.e. the first row, for G, is -0.514 - 0.061 = -0.57 after rounding), square them and then take the average.

The variances for these components of the trait are calculated and shown in the panel below. The module is set such that the trait is always simulated with a mean of zero and a variance of 1 (i.e. a standardised trait). The proportions of variance will always be close to the absolute variances, therefore, but these are also shown in the panel. (Note: the sample variance will not always be exactly 1, due to the fluctuations inherent in random sampling).

In this instance we see that the variance due to the genetic component is approximately equal to the variance of the environmental component, as specified in the top panel. In this case, the relative magnitude of these components of variance reflect how much impact each source of variance has on the trait and should be reflected in the pattern of scores for the individuals in the sample.

Try changing the position of the slider to see how this is reflected in the pattern of scores and variances. Note that you must press the Reset button after changing the slider, or else the sample will represent a mixture of different populations. The module only allows 199 individuals to be simulated.

But...

This point is very important: in reality we would never get the chance to observe the two components in this way. That is, we can only measure P. We have no direct way of knowing G or E - all we know is that they will sum to P in any one individual. We therefore have no way of directly calculating the variance of these components. This module is not meant to represent how research proceeds: this is more or less what happens in reality though.

If we had measured some specific gene or some specific aspect of the environment for each individual, then we would be able to calculate the variance in the trait of interest attributable to these specific sources of variation. In this case, however, we have not measured anything else apart from the trait itself. We could not be able to say anything more about the trait over and above a simple description of the distribution of the trait in the sample.

As we shall see in the second half of this module, and fundamentally, in the next module, the ability to estimate the components of variance depends crucially on basic biological theory and the measurement of the trait in related individuals. Biology predicts how similar we would expect related individuals to be because we know the expected sharing of different components of variance between different types of individuals.

Twins : Shared and nonshared environments

Clicking on the Twins tab at the top of the module will bring up this slightly different panel:

Instead of generating individuals we are now generating pairs of twins: these twin pairs may either be monozygotic (MZ) twins or dizygotic (DZ) twins.

The relative balance of genes and environment is still determined in the same way by the top slider. There is now an extra slider below, however, which represents how much of the environmental effects are shared between twins. Environmental effects that are shared impact equally on both members of the twin pair. Also, this sharing is the same for both MZ and DZ twin pairs.

In the case above, we see that the influence of genes is just as great as the influence of the environment. The environmental influence is then further subdivided into a component which is shared between both members of a twin pair and a component which is not. This latter component we call the nonshared environment. Therefore, the relative balance of additive genes, shared environment and nonshared environment is 50 : 25 : 25 in this case.

Clicking on one of the twin pair buttons causes the module to simulate values for a twin pair, but broken up into these three distinct components. Again, each individual's trait score would represent the sum of these three components. Note that there is also a box below representing the components for the second twin, labelled Twin B.

If an MZ twin pair is generated, note how their scores for the additive genetic component (A) and the shared environmental component (C) will always be identical. The nonshared environmental effects (E) will be different for each twin however.

For DZ twin pairs, only the shared environmental components will be identical. The additive genetic effects will tend to be similar, but not identical. That is, if Twin A has a very large, positive additive genetic effect, then it is likely that Twin B will also have an additive genetic effect that is above the mean (i.e. greater than zero). This will not be the case for the nonshared effects however, they will be unrelated between the two twins (this will also hold for MZ twins).

Proceeding as before, we can calculate the variance of each of these three components. We do this separately for Twin A and Twin B however. If we did not, we could underestimate that variation due to the effects of A and C that we would expect to observe in the natural population. This is because these components tend to be more similar (i.e. less variable) between twins.

As before, we can now calculate the variance of these three components in a straightforward manner (separately for Twin A and Twin B). In this case, they reflect the 50 : 25 : 25 ratio we specified, as expected.

Remember, however, that as before, we would not be able to directly observe these component in any one individual or pair of twins. The next module will illustrate how we can use the covariance between twin pairs to estimate the components of variance.

Exploring the module

Try changing the relative balance of effects in both parts of the module to get a sense for the way in which the simulated components vary. Also note that the estimates of variance are identical whether or not all MZ twins are simulated or all DZ twins are simulated. From the point of view of this module, there is indeed no difference between the two types of twin. This is actually a necessary assumption in the analysis of twin data: one implication of this is often called the equal-environment assumption: effectively that the relative balance of shared to nonshared environmental effects is the same for MZ and DZ twins. As the next module will illustrate, MZ and DZ twins only differ in the expected covariance of trait scores between the twins.

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Site created by S.Purcell, last updated 6.11.2000