As you likely know, shininess is determined by genetics, and in turn, genetics are governed by the basic principles of biological inheritance and natural selection. That is, if two individuals both have a certain trait, then there is a certain chance that their offspring will also have it. The offspring, in turn, has a chance of passing that trait to their offspring, and so on and so forth.
In an area with a larger pool of eligible mating partners—such as the Johtonian mainland, for example—the frequency of shiny individuals is kept low because, as shininess is a rare trait to begin with, the likelihood of two hoothoot with the shiny trait is lower than the likelihood of two hoothoot without.
However, islands are isolated communities, which means they’re considerably more restrictive when it comes to eligible breeding pools, and thus, it’s far easier for two individuals with the shiny gene to mate. If they pass their genes on to their offspring, that offspring enters the mating pool and, in turn, has a chance of passing their shiny gene on to their offspring, even if their partner is not a carrier. If this is allowed to continue over many, many years, then soon enough, the traits for standard colorization ends up being bred out of the community, leaving only those who carry the gene for shininess.
In short, what you’re observing are the results of many, many years of natural selection at work, anonymous.