Biology view on trait variability
The variance of a trait's allele frequency can follow different trends over time depending on several factors such as whether one or several of the alleles are consistently selected for or the population dynamics. For example Disruptive Selection will tend to increase the allele variance. On the other hand Directional selection, or Stabilizing selection will tend to decrease variance by driving the allele frequency to one side of the distribution (in the first case) or by "cutting down" its sides in the second case. It is true that stabilizing and directional selection processes are more common especially under relatively stable environments. Therefore for the majority of cases, during the first phase of selection for a trait variance will most commonly decrease . This, however, is not a rule. 
There are additional, rare, but from an evolutionary point of view extremely important cases where allele frequency variance can see a sudden "ballooning". Consider for example the case of selection processes after mass extinction events. Then, because of the sudden availability of previously occupied niches, genetic drift due to small population sizes as well as changed conditions the previously stabilized traits will start...well...drifting. The same is true for almost any circumstances that will destabilize equilibrium and lead to speciation.