Answer:

The change of the light-coloured variety of the peppered moth (Biston betularia) to its darker variety (Biston carbonaria) is primarily due to mutation.

Mutation:
Mutation refers to a change or alteration in the DNA sequence of an organism. It is a random process that introduces new genetic variations into a population. In the case of the peppered moth, a spontaneous mutation occurred in the gene responsible for pigmentation, leading to the development of the darker variety.

Industrial Revolution and Natural Selection:
During the Industrial Revolution in the 19th century, there was a significant increase in pollution due to the burning of coal. This resulted in the darkening of tree trunks and the surrounding environment as a result of soot deposition. The light-coloured variety of the peppered moth, which was well-camouflaged on the light-colored tree trunks, became more visible and vulnerable to predation by birds.

However, a few peppered moths had a naturally occurring genetic variation that caused them to have darker pigmentation. These dark individuals were better camouflaged against the darkened tree trunks and had a survival advantage over the light-coloured moths. As a result, they were more likely to survive, reproduce, and pass on their dark pigmentation genes to the next generation.

Natural Selection and Adaptation:
This process of natural selection led to the gradual increase in the proportion of the darker variety of peppered moths in the population over time. The darker moths had a higher fitness in the polluted environment, as they were less likely to be preyed upon. Consequently, the frequency of the dark allele for pigmentation increased, while the frequency of the light allele decreased.

Over several generations, the majority of the peppered moth population became the darker variety (Biston carbonaria), while the light-coloured variety (Biston betularia) became less common. This change in the moth population's appearance was primarily driven by the mutation that caused the darker pigmentation and the subsequent natural selection favoring the better-camouflaged individuals in the polluted environment.

In conclusion, the change from the light-coloured variety of the peppered moth to its darker variety is due to a mutation that resulted in a genetic variation for pigmentation. The industrial pollution during the Industrial Revolution provided selective pressure in favor of the darker variety, leading to its increase in frequency within the population.