What makes it possible for a goat and a sheep to produce in rare cases live offspring?

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Also if you keep trying hard enough would live offspring be possible between humans and warthogs?

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Goats and sheep have relatively recent common ancestors so the DNA is relatively similar and thus then can have viable offspring.

I can’t say where the common ancestor of a warthog and human would be – probably close to the evolution of first mammals. Thus the DNA between Humans and Warthogs has diverged too much for viable offspring.

The goat and sheep split is around four million years ago. The split between humans and our closest relative, the chimpanzee, was 5-6 million years ago.

Sheep have 54 chromosomes goats have 60 which makes it quite hard to get living offspring from them.

Humans have 46 chromosomes and chimpanzees have 48. This make hybridization harder then if they are equal. We do not know if you can have human-chimp hybrids, this is because experiments would not be considered to be ethical research so is not done today. That said there has been met to do that but there is no evidence of any success [https://en.wikipedia.org/wiki/Humanzee](https://en.wikipedia.org/wiki/Humanzee)

Even if the probability of a life offspring is the same for Goat-sheep and Human-Chimpanzee the number of mating between the species will not be the same so it is not surprising there are no examples of human hybrids. Even if the goat-sheep hybrid is less likely so survive we would expect to see more of them.

More common hybrids, in comparison to the number of matings, are ligers https://en.wikipedia.org/wiki/Liger and https://en.wikipedia.org/wiki/Tigon which are tiger lion hybrids. They split apart around 3.9 million years ago. The do have a advantage and that is both still have 38 chromosomes so hybridization is easier.

The number of chromosomes is in no way the only factor for hybridization but if the number change it get harder.

Human and warthogs’ last common ancestor would be a [Boreoeutheria](https://en.wikipedia.org/wiki/Boreoeutheria) the split is around 90 million years ago