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Humans use selective breeding to pass desired traits to the next generation of plants or animals.
They selectively breed them. So that the animal has the best characteristics possible. Examples are pigs with more fat or sheep with thicker wool.
Selected breeding. You select the plants that you want and breed them and get rid of the others.
This is called selective breeding or artificial selection, opposed to natural selection.
Biomes
humans select which plant will reproduce with which plant. http://en.wikipedia.org/wiki/Selection_methods_in_plant_breeding_based_on_mode_of_reproduction
artificial selection
Genetic modification is a new technique. The oldest is domestication, where you select and breed the best plants or animals.
elective breeding
DNA analysis is being used to select animals for selective breeding. Studies are underway correlating certain genetic profiles with characteristics such as disease resistance, milk production, growth rates, and feed utilization.
can choose bulls that have been selected for health traits by culling stock that get the disease, and offspring,you end up mob less likely to get desease
I'm unaware of any animals which cannot be selectively bred. If offspring are produced through the mating of male and female of the species, you should be able to select for the most desirable traits in both parents. This assumes, of course, that the breeding stock are already in captivity.