Threshold II:

Heritability and the Threshold Model

This exercise applies the principles of heritability to the threshold model. You should do the exercises on heritability before you do this exercise. To understand the Applet, let's begin with a simple example. Set the heritability to .50, the threshold to 1.0, and N (the number of observations) to its maximum value of 5000. Press Submit.

A large number of dots will appear on the screen, and just as in the exercise Heritability I, each dot represents an observation or person. The dots plot the phenotypic value of a person as a function of the genotypic value of the person using the equation

.

Here, P is the phenotypic value, G is the genotypic value, and E is the environmental value for a person. The quantity h is the square root of heritability and e is the square root of environmentability. Because we set heritability to .50, the value of h is the square root of .50 or .7071. Because environmentability is 1.0 - heritability, the value for e also works out to be .7071.

Notice the horizontal red line that crosses the axis where the phenotypic value is 1.0. This line is the threshold. All the dots above this line are affected and all the dots below the line are unaffected.

There are four colors to the dots:

• Blue dots represent all those people who, if they were raised in an average environment, would be affected because of their genotype. (The vertical blue line is used to separate them from the other dots.) We may term these dots as genetically vulnerable individuals, recognizing that the term "vulnerable" is defined arbitrarily. Notice that a number of the blue dots fall below the red line. These are genetically vulnerable individuals who have been buffered or protected by the environment. Their favorable environments have saved them from being affected.
• Green dots represent all those people who, if they had an average genotype, would be affected because of their environment. They are environmentally vulnerable individuals. Again, a number of these dots fall above the red line and are affected and a number of dots fall below the red line and are unaffected. Just as the environment buffered those blue dots below the threshold, the genotype buffers or protects the green dots below the red line.
• Red dots are interesting. They are all those observations who quality to be blue dots and green dots at the same time. You can think of them as people who are double whammied--they are both genetically and environmentally vulnerable to the disorder.
• Black dots are all those observations that do not fill any of the above criteria. Notice that a significant number of black dots fall above the threshold. These people might be called unfortunates. They are neither genetically nor environmentally vulnerable. But they are unfortunate enough to be just high enough on both genetic and environmental liabilities to pass the threshold and become affected.

Exercises:

1. Keep the same values for the heritability, threshold and number of observations. Click on Submit a few times, pausing to observe the scatterplot and examine the dots. Without counting the dots, try to estimate the ratio of genetically vulnerable (blue dots) to environmentally vulnerable (green dots) individual to unfortunates (black dots) who are affected.
2. Keep heritability at .50 and N at 5000 and change the threshold to 1.96. For this threshold value, 2.5% of the population is affected. (For the threshold of 1.0, 16% of the population would be affected.) Again, click on Submit a few times, pausing to examine the ratio of blue, green, and black dots above the threshold. The ratios have changed, haven't they? Indeed, if you keep entering different values for the threshold, you will soon find that the larger the threshold is (i.e., the rarer the disorder is), the more that unfortunates make up the bulk of affected people.
3. The heritability of schizophrenia is on the high side for behavioral traits with some estimates in the area of .70. The lifetime risk for someone developing schizophrenia is a bit under 1%. Enter .70 for the heritability and 2.33 for the threshold (this threshold corresponds to a 1% population prevalence). Again, set N to 5000, click Submit several times, and pay attention to the ratio of the colored dots above the threshold. This should give you some appreciation for the implications of the threshold model for a fairly heritable rare disorder (i.e., rare for psychopathology).
4. If you want to imagine what other disorders may look like according to the threshold model, set the heritability to the moderate range (.30 to .60) and use the threshold values in the table below. Make certain to enter the threshold value and not the prevalence value into the Applet.
 Lifetime prevalence for several forms of psychopathology (from the Epidemiological Catchment Area study). Women Men Prevalence Threshold Prevalence Threshold Depression 10.2 1.27 5.2 1.63 Panic Disorder 2.1 2.03 1.0 2.33 Phobic Disorder 17.4 .94 10.4 1.26 Antisocial Personality 1.0 2.33 4.5 1.70 Alcohol Abuse/Dependence 4.6 1.69 23.8 .71 Drug Abuse/Dependence 4.8 1.66 7.7 1.42