Stabilizing selection is a type of natural selection that favors the average or intermediate phenotype in a population. This means that individuals with extreme or unusual traits are at a disadvantage and are less likely to survive and reproduce. As a result, the population becomes more stable and homogeneous over time.

There are several properties of stabilizing selection that can help us understand its effects on a population:

a) Operates in a constant environment:
Stabilizing selection is most likely to occur in a constant or stable environment where the selective pressures remain relatively unchanged over time. In such an environment, the average phenotype is well adapted and has a higher fitness compared to individuals with extreme traits. As a result, the population becomes more homogeneous as extreme variations are selected against.

b) Mean value changes:
Contrary to the statement, stabilizing selection does not cause a change in the mean value of a trait. Instead, it maintains the mean value by favoring individuals with traits close to the average. This prevents the mean value from shifting towards the extremes of the trait distribution.

c) Peak gets lower and wider:
Stabilizing selection does not necessarily result in a lower and wider peak. Instead, it tends to narrow the range of variation around the mean value. This means that the frequency of extreme traits decreases, leading to a narrower distribution. However, the peak of the distribution remains relatively unchanged.

d) Favors the complex phenotype:
Stabilizing selection does not specifically favor complex phenotypes. It favors individuals with traits that are close to the average of the population. Complex phenotypes may or may not be close to the average, depending on the specific trait and its distribution in the population.

In summary, stabilizing selection operates in a constant environment and favors individuals with traits close to the average of the population. It does not cause a change in the mean value of a trait or result in a lower and wider peak. Stabilizing selection does not specifically favor complex phenotypes; rather, it favors traits that are close to the average.