Threshold III:
Effects of a Changing Environment

The threshold models that we have discussed thus far treated the environment as if it were a constant phenomenon. From a learning perspective, this is justified. But in terms of real life, it may be quite stupid. Environments are constantly changing and a person's liability will vary accordingly. Indeed, all forms of psychopathology show remission--significant periods during which the signs and symptoms of the disorder are absent--so the threshold model should accommodate this phenomenon. Let us begin with some exercises and discuss the threshold model as we proceed.


  1. Enter .50 for the heritability, 1.0 for the threshold, 1.0 for the genotypic value, and .90 for the autocorrelation. (The autocorrelation gives the extent to which the environment of one time period predicts the environment in the next time period. We will discuss it in more detail later). Click the Submit button. This generates a hypothetical person whose genotype predisposes him to a liability of 1.0--just at the threshold--and shows his actual liability for 100 time points. Times during which the person's liability exceeds the threshold are plotted in red and times in which the person is unaffected are plotted in black. Now click Submit several times and examinee the curves. Each click generates a different "person," each with the same genotypic value but with differing environmental courses over the time period. Notice the variability across individuals with the time spend in the affected state. This will give you some appreciation for how the environment can change the amount of time that a person spends in a psychopathological state.
  2. Change the genotypic value from 1.0 to -1.0, keeping all other values the same. This set of parameters generates individuals with genotypic values of one standard deviation below the mean--a fairly protective or buffering genotype. As you keep clicking on Submit, you will notice that most individuals never enter the affected state. Occasionally, however, you encounter an individual who crosses the threshold for several time periods. This illustrates the probabilistic nature of heritability--a genotype can protect on average but does not always guarantee a phenotype.
  3. The degree of protection and risk conferred by a genotype depends on the heritability. To verify this, change the heritability to .60, generate 15 individuals by clicking on Submit 15 times, and count the number of people who show the disorder at any point in the time span. Now change the heritability to .30 and do the same.
  4. In doing exercise 3, you may have noticed that the time courses for people under a heritability of .30 "bounced around" more than those under a heritability of .60. This is indeed another consequence of heritability. When the environment changes, the change in phenotypic values depends on the heritability. Let's examine the extreme case when heritability is 0.0. Change the heritability to 0.0 and the genotypic value to 0.0, keeping everything else the same. Click on Submit several times and notice the degree to which the phenotype changes over time. Now change the heritability to 1.0. No matter how many times you click on the Submit button, you will always have a straight line at 0.0 (the genotypic value). These two extreme cases are of theoretical interest only. Because human behavioral traits have moderate heritabilities, the results of exercises 1, 2, and 3 are more realistic portraits of behavior.
  5. Set the heritability to .5, the genotypic value to 0, keep the threshold at 1.0, but change the value for the autocorrelation to 1.0. This models a theoretically possible but improbable case in which the environment is constant over the time period. Each click on Submit generates a flat straight line although the phenotypic value (i.e., the height of the line) will vary from one click to the next. For each click the computer selects a random environmental value at time 0. With an autocorrelation of 1.0, the value of the next time period will always be the same as the value of the previous time period. Hence, once an environmental value is set, it remains unchanged over time. If a person is unlucky enough to have the disorder at time 0, then the person will be affected during the entire time period.
  6. Keep everything the same, but change the autocorrelation to 0.0. The time plots now have a very jagged look and virtually everyone crosses the threshold at several time points. In this case, the environment is completely random from one time period to the next. Again, this is theoretically possible but improbable. However, exercises 5 and 6 tell us something about the threshold model--not only the threshold model depend upon heritability and environmentability of the liability, it also depends on the extent of change versus constancy in the environment.