For thousands of years cats did just fine with managing their own breeding! At the beginning of their domestication they were primarily used for hunting and for killing rodents of all sorts. Essentially to keep rats, mice, shrews, voles, etc. from eating the grains that early farmers and settlers had stored away. And they did that well then and still do.
A farmer friend of mine does nothing to care for his barn cats except make sure they have their shots to prevent various diseases like rabies and feline leukemia. They breed prolifically and are managed by local predators, like hawks, owls and coyotes.
Their population keeps his barns totally free from rats and other rodent invasions and their population is relatively stable because he does not interfere with natural predation. But those are “working cats”, he does not view them as pets.
For the purpose of having domesticated cats as pets, people began breeding and selecting particular traits to suit their preferences. As mentioned in an earlier post the precise number of breeds varies with different cat registries and ranges from 40 -70 distinct breeds of cats. Even within those breeds there are variations with the length and color of their fur.
Some Japanese cat breeds can be traced as far back as 1000 years or more, like the Japanese Bobtail. During Medieval Japan, they were very well known. Today it is hard to find them anywhere.
In North America the most common breeds include the Persian cat, long haired cat and the alley cat. Siamese cats are another common cat breed. They are exceptionally curious and can be temperamental. The precious Persian cats are quite popular and they become gentle and loving companions. But be careful, they can be very expensive, too.
Who decides what cat is an alley cat? They are the most common in North America. Even though they are different breeds and there are thousands of them, many people simply call them alley cats. They can become very good pets. Many of these cats are homeless and simply continue to breed independently.
How do you recognize their breed? Look at them. Do not depend on the color, it is not always reliable. Body type and shape combined with their type of fur and eyes are all a part of the cat breed identification process. I always used to identify Siamese cats by their distinctive posture and coloring with black ears and tail. Recently I learned that they are often all black, or nearly so. One black kitten that is part Siamese is exceptionally playful and flexible in our neighborhood.
Millions of people around the world own cats. Consider your lifestyle before you get a pet, particularly a cat. Some will be much better pets if they are living with another cat. If you are away from home often that will be distressing for a cat who prefers less change in its surroundings.