The starter pets have starter traits and the potential to give birth to pets with non-starter traits.
Upon Release there will be a range of non-starter traits for you to breed out from your starter pets.
Additional non-starter traits will be released for breeding at regular intervals, when released all pet's conceived after that point have the potential to give birth to pets with the new non-starter traits.
Each pet has either one or two hidden traits that can be bred out.
Go to the trait page for your pet: