When there is a situation when sufficient number of members of one species are reproductively isolated, and if there is an evolutionary pressure for them to start developing new advantageous traits, then a new species will gradually emerge. In this kind of scenario the genetic diversity will be minimized, as the number of individuals is much smaller, and that will result in only changes that will go in only one direction and they will also occur quicker than if there was a greater genetic diversity. This is called the founder effect, and it is easy to see why this term has been chosen, as the limited number of members of a species that have been reproductively isolated are giving the foundation for the development of a new, separate species.
They can know if the trait has been carried on by looking at the bred dogs that have the trait and determining if the trait has been passed down by similar characteristics between the parent with the trait and the puppy that could have the trait.
The purpose of scientific notation is to demonstrate very large or very small numbers, this is what it looks like, 7800000000000 in scientific notation would be 7.8* hope this helps