The evolutionary species concept is defined as species that has a single lineage of ancestor-dependent population of organisms. Purebreds that are controlled or bred by humans will maintain their unique identity from other animal D breeds and will have their own evolutionary tendencies and historical fate. Purebreds will have a shared future only if they have a shared ancestry.
On the contrary, if there is no control of the breeding activity, then each breed may follow a diverse evolutionary path. If humans continue to breed them in future, then each breed shall have a unique evolutionary path that they will follow and they shall have a unique entity in the evolutionary species concept. If humans stop controlling the breeding activity in these breeds, then each breed will probably not have a distinctive evolutionary future as they might interbreed.
From the evolutionary point of view, purebreds will have different fates depending upon their lineage and their history of being bred under the control of humans. If the breeding is controlled for a longer period, then different species are likely to have different evolutionary future. However, if the breeding is not controlled, then the animals D are likely to have the same evolutionary future.