Heritability - II

At the end of the exercises in Heritability - I, it was pointed out how individuals with the same genotypic value can have a range of phenotypic values. This Applet demonstrates the variability in phenotypic values for a given genotypic value. The mathematical model begins with three variables–P (the phenotypic value), G (the genotypic value), and E (the environmental value). There are two constants in the model–h (the square root of heritability) and e (the square root of environmentability). There are two equations to the model. The first equation gives the phenotypic value (P) as a function of the genotypic value (G) and the environmental value (E):

.

The second equation says that the heritability and environmentability add up to the total phenotypic variance (which is set to 1.0 in this example):

In this exercise, you begin with the distribution of phenotypes in the population (a black normal curve). You provide the heritability and a genotypic value (G), and the Applet plots the distribution of phenotypic values for the genotypic value that you specified (a red normal curve). It is assumed that the phenotypic, genotypic, and environmental values have a standard normal distribution (i.e., a normal distribution with a mean of 0.0 and a standard deviation of 1.0).

Exercises:

1. Set the genotypic value to 0.0 and the heritability to .50. The red curve gives the distribution of phenotypic values for all individuals with a genotypic value of 0.0. Notice how the red curve is less "spread out" than the black curve. This means that there is less phenotypic variability among individuals with a genotypic value of 0.0 than there is among all individuals (i.e., those with any genotypic value).
2. Set the genotypic value to 0.0 and the heritability to 0.0. The black curve will seem to disappear. It is really there, but it is hidden by the red curve because the two curves are identical. In this case, individuals with a genotypic value of 0.0 have the same variability as the general population.
3. Set the genotypic value to 1.0 and the heritability to 0.0. You get the same results as you did in Exercise 2!
4. Keep the heritability at 0.0 and pick several reasonable genotypic values. You keep getting the same results as you did in Exercise 2. Can you figure out why?
5. Redo exercise 1–genotypic value of 0.0 and heritability of .50–and compare the red and black curves. Let us assume that the phenotype is the personality trait of extraversion-introversion so that people scoring above the population mean are on the outgoing side people scoring below the mean are on the introverted, shy and retiring side. The red curve says something of the following–if we took a very large number of people who all had the same average genotype for extraversion, how would they eventually turn out? The red curve suggests a noticeable amount of variability in the phenotypes of these people–they definitely will not all have "average" phenotypes.
6. Keep the heritability at .50 but change the genotypic value to 1.0. This models a large number of people with genotypes predisposing them to be on the extraverted side. Notice how their mean phenotypic value is greater than the population mean. This implies that on average these people will be extraverted. But again notice the variability around the mean–not every individual will be more extraverted than average. The area under the red curve from its lowest point to the population mean (the vertical black line at a phenotypic value of 0.0) gives the proportion of these people who will be on the introverted side of the dimension.
7. Again, remember that the heritability of most behavioral traits is in the moderate range (.30 to .60). Use heritabilities of this range, plug in different genotypic values, and examine the distributions. To interpret the results, it is helpful to pick a single trait (e.g., generosity, impulsivity, verbal acuity) and imagine what the phenotypes of the individuals with that single genotypic value would be.
8. As a final exercise, try to predict what the distribution would look like if the heritability were 1.0 and then see if your prediction is correct. Heritability is above .90 for many physical traits like height and hair and eye color, but there are no well documented behavioral traits with a heritability this high.