An animal population is the population of a group of animal individuals that belong to the same species and live in the same area at the same time. The interaction between human and other species is in the core when we talk about diversity among native and breeded breeds. In a certain area there may be a stable local population that never has been recogniced as a breed. A population is not usually selected for a certain trait but kept other characteristica such as healthy animals and good mothers. Seiskarinkoira dog is a population. There has been choosen dogs that have the characteristics of dogs used in seal hunting at the Finnish gulf island. There are not descendents of dogs from those islands. They are not officially recognized as a breed.
A native breed is a breed of horse, cattle, sheep, goat, rabbit, horse, pig, poultry (chickens, ducks and geese) dog, cat and bee. To qualify as a native breed, it must have existed in a particular area long enough to have become adapted to the local environment.
A breed is a biological term most often used to describe a group of animals resulting from breeding with certain predefined permanent characteristics (selection criterias). A breed has usually the same unique apparence (outlook). As the definition for a breed is created by humans due to the need of having domestic animals with a certain characteristica for example are black and high producing, then breeds have mostly been bread on a few animals, less that is used in a population.
The difference between a population, native animals and a breed is difficult to notice only by looking on the animal. Populations and native animals are in general diverse but they can also look exactly as uniform as a breed. This if there was left only one small part of the whole wild genetic population. To make this even more complicated, then you may get the same DNA of a native animal as for a breed. For example Estonian black head sheep is a crossbreed between estonian native sheep on mother line and Shropshire sheep on father line. There was in the middle of 2000ies found a native sheep whose DNA grouped into the estonian black head sheep group, but it did look like a native sheep, not as the estonian black head breed. This can be explained with the breeding history of the estonian black head sheep.
Human is the key factor when making research on native breeds and that is why it is always important to make an interview with those who keep the animals. Only then you will get information about the history of the animal and also information about its characteristics. It is not enough to just make a DNA analyses.
All our domestic animals are descendants from wild animals or later native breeds. It mean that you may find an animal looking exactly as a breeded animal among a native population. Usually wild animals behaviour and apparance have been changed when the animals were domesticated. It mean that you may have animals in native populations that you will not find in the wild.